{
  "records": [
    {
      "config": {
        "laws": [
          "burgers",
          "oscillatory",
          "saturating"
        ],
        "nx": 64,
        "test_nx": 128,
        "train_steps": 100,
        "test_steps": 400,
        "dt": 0.002,
        "nu": 0.03,
        "n_train": 6,
        "train_amplitude": 0.65,
        "test_amplitude": 1.05,
        "snapshot_stride": 4,
        "target_mode": "finite_difference",
        "max_samples": 30000,
        "spline_domain": 1.35,
        "knots": 25,
        "ridge": 1e-08,
        "innovation_ridge": 0.0001,
        "max_frequency": 6,
        "max_pole_terms": 6,
        "kan_knots": 13,
        "kan_hidden": 8,
        "epochs": 1200,
        "batch": 4096,
        "lr": 0.002,
        "seed": 20260910,
        "out": "operator_compiled_constitutive_kan_fd_seed20260910_outputs",
        "smoke": false
      },
      "results": [
        {
          "law": "burgers",
          "training_samples": 9600,
          "training_u_range": [
            -0.6678117497711028,
            0.6645562387479006
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 5.972756353111737e-08,
                "nrmse_extrap_horizon": 1.727622878324541e-07,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.06509013170173508,
                "nrmse_extrap_horizon": 0.1712802713379125,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.1388174777818677e-07,
                "nrmse_extrap_horizon": 3.8875249417091974e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.062299205295084335,
                "nrmse_extrap_horizon": 0.13320065632870354,
                "mass_drift": 7.892991815694472e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8727543837423387,
              "fit_s": 0.004652042058296502,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 5.848236650159343e-08,
                "nrmse_extrap_horizon": 1.6859750997806297e-07,
                "mass_drift": 2.42861286636753e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 3.5557072659135657e-07,
                "nrmse_extrap_horizon": 1.1992540990783708e-06,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.1536358695461158e-07,
                "nrmse_extrap_horizon": 3.9293686011087245e-07,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 3.9459371076208227e-07,
                "nrmse_extrap_horizon": 1.2753338034081765e-06,
                "mass_drift": 6.678685382510707e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 3.0164941131135786e-06,
              "fit_s": 0.004248208017088473,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 5.659061818125787e-08,
                "nrmse_extrap_horizon": 1.903933427450077e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 5.83323574211215e-07,
                "nrmse_extrap_horizon": 2.413851304057354e-06,
                "mass_drift": 1.5265566588595902e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.108858913152826e-07,
                "nrmse_extrap_horizon": 3.810273143642404e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 5.943252157150879e-07,
                "nrmse_extrap_horizon": 2.3524773883645165e-06,
                "mass_drift": 3.903127820947816e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.0742595828508781e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49998334949961437
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 2,
                  "coefficient": -8.963083930228057e-06
                }
              ],
              "fit_s": 0.00312504090834409,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 5.8526473197533516e-08,
                "nrmse_extrap_horizon": 1.6873947558959075e-07,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 6.152534496274192e-07,
                "nrmse_extrap_horizon": 2.5674823916543056e-06,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.1529339705513222e-07,
                "nrmse_extrap_horizon": 3.927049684951944e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 6.494844104001802e-07,
                "nrmse_extrap_horizon": 2.597407585588024e-06,
                "mass_drift": 7.719519468096792e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.0971157436761541e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49998334949961437
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 2,
                  "coefficient": -8.963083930228057e-06
                }
              ],
              "fit_s": 0.007273999974131584,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 4.5992083957859475e-08,
                "nrmse_extrap_horizon": 1.578184985957593e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 4.376821404953664e-07,
                "nrmse_extrap_horizon": 1.8127294408785005e-06,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.1699526930678345e-07,
                "nrmse_extrap_horizon": 3.993790951781565e-07,
                "mass_drift": 7.632783294297951e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 4.543843095157266e-07,
                "nrmse_extrap_horizon": 1.8013809037577174e-06,
                "mass_drift": 5.117434254131581e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.1724575325751815e-05,
              "fit_s": 0.00034141691867262125,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.04479081920078403,
                "nrmse_extrap_horizon": 0.18128583115264568,
                "mass_drift": 1.36067979106258e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.07038738101018702,
                "nrmse_extrap_horizon": 0.29085848394510594,
                "mass_drift": 4.6925797830832394e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.04689065090136382,
                "nrmse_extrap_horizon": 0.18499229684791632,
                "mass_drift": 3.549363400412453e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0776620502138992,
                "nrmse_extrap_horizon": 0.3119920393046536,
                "mass_drift": 2.3560155866172994e-10,
                "finite": true
              },
              "fit_s": 0.00021308299619704485,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0007375473177115855,
                "nrmse_extrap_horizon": 0.0023273348773538262,
                "mass_drift": 0.00013016270436860128,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.03315100159998527,
                "nrmse_extrap_horizon": 0.1161057853386121,
                "mass_drift": 0.00785415101937055,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0018642820866752567,
                "nrmse_extrap_horizon": 0.0056196439704354175,
                "mass_drift": 0.0008799044834874106,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.03645493492189316,
                "nrmse_extrap_horizon": 0.12007165100293683,
                "mass_drift": 0.005656475029012667,
                "finite": true
              },
              "fit_s": 4.027065249974839,
              "training_loss_trace": [
                1.4929850101470947,
                0.6398193836212158,
                0.14325332641601562,
                0.04172714054584503,
                0.017607254907488823,
                0.008857929147779942,
                0.006940786261111498,
                0.005465606693178415,
                0.003781819250434637,
                0.0023618615232408047,
                0.001947649521753192,
                0.002185978228226304,
                0.001554875634610653,
                0.0013478384353220463,
                0.0013406190555542707,
                0.001081110560335219,
                0.0012958412989974022,
                0.0007208364550024271,
                0.0006937628495506942,
                0.0003841414290945977,
                0.00045166051131673157
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.00039754550776725686,
                "nrmse_extrap_horizon": 0.0020579172868663217,
                "mass_drift": 8.901135913034e-05,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.014879275833083416,
                "nrmse_extrap_horizon": 0.049911408608086315,
                "mass_drift": 0.002150279149869025,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0005410139025141036,
                "nrmse_extrap_horizon": 0.001845015661663302,
                "mass_drift": 0.00021395102495692236,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.018653903878599182,
                "nrmse_extrap_horizon": 0.06485589506041603,
                "mass_drift": 0.0018278365132452234,
                "finite": true
              },
              "fit_s": 0.8165209169965237,
              "training_loss_trace": [
                1.0087796449661255,
                0.5844943523406982,
                0.0842965766787529,
                0.03971811756491661,
                0.02151399664580822,
                0.012972019612789154,
                0.008907469920814037,
                0.006058650091290474,
                0.004231183789670467,
                0.0031700781546533108,
                0.002068404806777835,
                0.001491599134169519,
                0.001106747891753912,
                0.0007282277219928801,
                0.0005907704471610487,
                0.0004181906988378614,
                0.000372606999007985,
                0.0003112278936896473,
                0.0002424474514555186,
                0.00019471505947876722,
                0.00016843702178448439
              ]
            }
          }
        },
        {
          "law": "oscillatory",
          "training_samples": 9600,
          "training_u_range": [
            -0.6677844222949308,
            0.6645233117376854
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 5.4567591273347606e-05,
                "nrmse_extrap_horizon": 0.00014195873959155662,
                "mass_drift": 3.8163916471489756e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.07521503868201501,
                "nrmse_extrap_horizon": 0.17707519281380138,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 4.2833871598146516e-05,
                "nrmse_extrap_horizon": 0.0001345605960094249,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.07079590268636494,
                "nrmse_extrap_horizon": 0.1398628262645373,
                "mass_drift": 3.5561831257524545e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8577300397421459,
              "fit_s": 0.003953916952013969,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 5.639157397622675e-05,
                "nrmse_extrap_horizon": 0.00014815540365332379,
                "mass_drift": 5.898059818321144e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.03722585462053574,
                "nrmse_extrap_horizon": 0.13573288290257707,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 4.370751538916946e-05,
                "nrmse_extrap_horizon": 0.00013669043599653696,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.034782466739638626,
                "nrmse_extrap_horizon": 0.10566261776418255,
                "mass_drift": 5.984795992119984e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.7743760744598417,
              "fit_s": 0.004284583032131195,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 1.6026362861577044e-06,
                "nrmse_extrap_horizon": 6.9876136195026075e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.943076989789475e-06,
                "nrmse_extrap_horizon": 8.47542344852383e-06,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.5507953649223265e-06,
                "nrmse_extrap_horizon": 6.473527930964349e-06,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 2.0938798398469366e-06,
                "nrmse_extrap_horizon": 9.204857497961503e-06,
                "mass_drift": 7.892991815694472e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.730435034018016e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999926225051161
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.07999692102818683
                }
              ],
              "fit_s": 0.0022911669220775366,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 5.417626882749772e-05,
                "nrmse_extrap_horizon": 0.00013833292389808558,
                "mass_drift": 7.632783294297951e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 6.509624714629868e-05,
                "nrmse_extrap_horizon": 0.0001943083612634113,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 4.191290223156012e-05,
                "nrmse_extrap_horizon": 0.00013826186446795806,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 6.710321839478821e-05,
                "nrmse_extrap_horizon": 0.00018724243170948444,
                "mass_drift": 3.382710778154774e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.00024570764990233194,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999926225051161
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.07999692102818683
                }
              ],
              "fit_s": 0.006763874902389944,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 0.00019158876434689938,
                "nrmse_extrap_horizon": 0.0005941121096627417,
                "mass_drift": 5.204170427930421e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.012044979569608857,
                "nrmse_extrap_horizon": 0.04188734291836722,
                "mass_drift": 1.3877787807814457e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0001915799312776889,
                "nrmse_extrap_horizon": 0.0006693210660872127,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010211849151874114,
                "nrmse_extrap_horizon": 0.0334415329530441,
                "mass_drift": 5.421010862427522e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.37890975571168567,
              "fit_s": 0.000343875028192997,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.05271375895532165,
                "nrmse_extrap_horizon": 0.20126939930304155,
                "mass_drift": 1.635464055849134e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.10005923905010491,
                "nrmse_extrap_horizon": 0.3921748400198576,
                "mass_drift": 5.640229241987704e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.038012529782063036,
                "nrmse_extrap_horizon": 0.1492175900464684,
                "mass_drift": 4.266144673636951e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.10883475465010548,
                "nrmse_extrap_horizon": 0.4037911991240305,
                "mass_drift": 2.8318054888856747e-10,
                "finite": true
              },
              "fit_s": 0.00021716603077948093,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0022269922547135616,
                "nrmse_extrap_horizon": 0.005600221879825498,
                "mass_drift": 0.0005783554973216795,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0475738902630891,
                "nrmse_extrap_horizon": 0.1654895999149823,
                "mass_drift": 0.008574173809048541,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0022144447366977725,
                "nrmse_extrap_horizon": 0.006006033333451611,
                "mass_drift": 0.0013182428374802907,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.05295370122248978,
                "nrmse_extrap_horizon": 0.18847452789685246,
                "mass_drift": 0.006711242165988869,
                "finite": true
              },
              "fit_s": 3.71658133296296,
              "training_loss_trace": [
                1.5660487413406372,
                0.5908723473548889,
                0.15478642284870148,
                0.051539719104766846,
                0.019244089722633362,
                0.014200306497514248,
                0.011308721266686916,
                0.012893560342490673,
                0.006112098693847656,
                0.008548530749976635,
                0.00538118788972497,
                0.004371006041765213,
                0.003423424670472741,
                0.0032406277023255825,
                0.002592794131487608,
                0.003605902660638094,
                0.0017013049218803644,
                0.0011486939620226622,
                0.001247112755663693,
                0.0010009859688580036,
                0.0006420693243853748
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.00106517695427006,
                "nrmse_extrap_horizon": 0.0037986426847068403,
                "mass_drift": 5.637778951494629e-05,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.019420754549601005,
                "nrmse_extrap_horizon": 0.09176026174719727,
                "mass_drift": 0.012630892606859428,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0008741092052205831,
                "nrmse_extrap_horizon": 0.0031490479449975193,
                "mass_drift": 0.0002722049690578182,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.026239731875539334,
                "nrmse_extrap_horizon": 0.1298234595504673,
                "mass_drift": 0.015505172674659964,
                "finite": true
              },
              "fit_s": 0.8217926670331508,
              "training_loss_trace": [
                0.9706791639328003,
                0.4423484206199646,
                0.17456260323524475,
                0.08780883252620697,
                0.0618286058306694,
                0.03645433858036995,
                0.02298475056886673,
                0.014764192514121532,
                0.009735523723065853,
                0.007215107791125774,
                0.004011789336800575,
                0.003053603693842888,
                0.0026568821631371975,
                0.0014980771811679006,
                0.0014468999579548836,
                0.000918047793675214,
                0.0009015053510665894,
                0.0007661757990717888,
                0.0006481055170297623,
                0.0006132170092314482,
                0.0004817004082724452
              ]
            }
          }
        },
        {
          "law": "saturating",
          "training_samples": 9600,
          "training_u_range": [
            -0.6678172759449965,
            0.6645497670340634
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 1.6271105081787974e-05,
                "nrmse_extrap_horizon": 4.731753670592529e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.05747792074466306,
                "nrmse_extrap_horizon": 0.1643921302510879,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.3289701117347824e-05,
                "nrmse_extrap_horizon": 4.350765408418392e-05,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.05601648040388631,
                "nrmse_extrap_horizon": 0.12765341881766198,
                "mass_drift": 7.719519468096792e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8199307587231107,
              "fit_s": 0.0039753749733790755,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 1.5509845646694874e-05,
                "nrmse_extrap_horizon": 4.5284260635016555e-05,
                "mass_drift": 7.632783294297951e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.021689320149057358,
                "nrmse_extrap_horizon": 0.07783295413677081,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.3626863220790626e-05,
                "nrmse_extrap_horizon": 4.474731706972968e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.02085487030991281,
                "nrmse_extrap_horizon": 0.06515088928238585,
                "mass_drift": 5.2909066017292616e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.3618071888242113,
              "fit_s": 0.004123708000406623,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 8.49064528695692e-06,
                "nrmse_extrap_horizon": 2.498817012336407e-05,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0009212758125785672,
                "nrmse_extrap_horizon": 0.0030660913191592966,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 7.604714239619972e-06,
                "nrmse_extrap_horizon": 2.4126715183274418e-05,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.000713374403757308,
                "nrmse_extrap_horizon": 0.002060175257463188,
                "mass_drift": 6.808789643208968e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.03887868137789735,
              "active_operator_atoms": [
                {
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -0.21681510054566372
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": 0.013110451980614068
                },
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": -0.12095815884319783
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": -0.01032689027181863
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 2,
                  "coefficient": -0.3449580298386055
                }
              ],
              "fit_s": 0.0026833750307559967,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 1.2603775375814439e-05,
                "nrmse_extrap_horizon": 3.471164407417394e-05,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.000913487372241441,
                "nrmse_extrap_horizon": 0.0030523350544833087,
                "mass_drift": 1.1102230246251565e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.982032274899025e-06,
                "nrmse_extrap_horizon": 3.231949832369537e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0007076559843011103,
                "nrmse_extrap_horizon": 0.002069858598536852,
                "mass_drift": 6.678685382510707e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.038883418711348816,
              "active_operator_atoms": [
                {
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -0.21681510054566372
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": 0.013110451980614068
                },
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": -0.12095815884319783
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": -0.01032689027181863
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 2,
                  "coefficient": -0.3449580298386055
                }
              ],
              "fit_s": 0.007238250109367073,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 0.0006097752385142087,
                "nrmse_extrap_horizon": 0.0021795653333163776,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.01113388777522727,
                "nrmse_extrap_horizon": 0.04113403651272089,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0005016510403075422,
                "nrmse_extrap_horizon": 0.0016084670987736665,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010173995983619748,
                "nrmse_extrap_horizon": 0.034281049211535,
                "mass_drift": 8.239936510889834e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.274804291995246,
              "fit_s": 0.0003476249985396862,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.05483032062930227,
                "nrmse_extrap_horizon": 0.22162732345939026,
                "mass_drift": 1.621440450655376e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0683748525507091,
                "nrmse_extrap_horizon": 0.28857433223308365,
                "mass_drift": 5.591865817611286e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.055076454465352837,
                "nrmse_extrap_horizon": 0.21773432321028557,
                "mass_drift": 4.229563636826139e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.07617958984927771,
                "nrmse_extrap_horizon": 0.31417512038414613,
                "mass_drift": 2.8075233891172724e-10,
                "finite": true
              },
              "fit_s": 0.0002116659888997674,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0009136571919654994,
                "nrmse_extrap_horizon": 0.002480859380074029,
                "mass_drift": 0.00022722069945787376,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.024827577608726975,
                "nrmse_extrap_horizon": 0.08785637240695007,
                "mass_drift": 0.009879197807972792,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0017072597219266732,
                "nrmse_extrap_horizon": 0.006969544662003295,
                "mass_drift": 0.0006318024795841579,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.029183047045696752,
                "nrmse_extrap_horizon": 0.09353495289686993,
                "mass_drift": 0.0076157402631039876,
                "finite": true
              },
              "fit_s": 3.7034569999668747,
              "training_loss_trace": [
                1.4910398721694946,
                0.6233532428741455,
                0.1283997893333435,
                0.037733644247055054,
                0.01901918090879917,
                0.009410478174686432,
                0.008724253624677658,
                0.007259156554937363,
                0.00533103384077549,
                0.0032967051956802607,
                0.002697594463825226,
                0.0030248642433434725,
                0.0021533118560910225,
                0.0018349138554185629,
                0.0014949426986277103,
                0.0012920477893203497,
                0.0015251481672748923,
                0.00090843066573143,
                0.0008182669407688081,
                0.0003996106388512999,
                0.0005234120762906969
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.0005873920154588505,
                "nrmse_extrap_horizon": 0.002416107644047954,
                "mass_drift": 0.00016879297895985163,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.011667856757809158,
                "nrmse_extrap_horizon": 0.040166686998269426,
                "mass_drift": 0.0018078943535220077,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.000855419160125326,
                "nrmse_extrap_horizon": 0.002003318651341993,
                "mass_drift": 0.00019494811612899565,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.01409646045786905,
                "nrmse_extrap_horizon": 0.04596230375065818,
                "mass_drift": 0.0020239869298990234,
                "finite": true
              },
              "fit_s": 0.825807832996361,
              "training_loss_trace": [
                1.0059373378753662,
                0.5824861526489258,
                0.07149392366409302,
                0.03240812569856644,
                0.01569553092122078,
                0.00972325075417757,
                0.0059743840247392654,
                0.004184181801974773,
                0.0029384007211774588,
                0.0023617702536284924,
                0.0016042417846620083,
                0.0011641355231404305,
                0.001023279968649149,
                0.0006852258811704814,
                0.0005723325302824378,
                0.00041580700781196356,
                0.0003317753435112536,
                0.00031997342011891305,
                0.00026301617617718875,
                0.0002042259875452146,
                0.0001815671712392941
              ]
            }
          }
        }
      ]
    },
    {
      "config": {
        "laws": [
          "burgers",
          "oscillatory",
          "saturating"
        ],
        "nx": 64,
        "test_nx": 128,
        "train_steps": 100,
        "test_steps": 400,
        "dt": 0.002,
        "nu": 0.03,
        "n_train": 6,
        "train_amplitude": 0.65,
        "test_amplitude": 1.05,
        "snapshot_stride": 4,
        "target_mode": "finite_difference",
        "max_samples": 30000,
        "spline_domain": 1.35,
        "knots": 25,
        "ridge": 1e-08,
        "innovation_ridge": 0.0001,
        "max_frequency": 6,
        "max_pole_terms": 6,
        "kan_knots": 13,
        "kan_hidden": 8,
        "epochs": 1200,
        "batch": 4096,
        "lr": 0.002,
        "seed": 20260911,
        "out": "operator_compiled_constitutive_kan_fd_seed20260911_outputs",
        "smoke": false
      },
      "results": [
        {
          "law": "burgers",
          "training_samples": 9600,
          "training_u_range": [
            -0.5563677663248865,
            0.6467044420960361
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 0.00020884363614102953,
                "nrmse_extrap_horizon": 0.0003476269885014815,
                "mass_drift": 7.979727989493313e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.08549957666683587,
                "nrmse_extrap_horizon": 0.2454252307307084,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.8419360158707012e-07,
                "nrmse_extrap_horizon": 4.4299888463267544e-07,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.00885391315905711,
                "nrmse_extrap_horizon": 0.018627385915243867,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8766712304041693,
              "fit_s": 0.004608833114616573,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 1.3604489095179363e-07,
                "nrmse_extrap_horizon": 4.983402694334354e-07,
                "mass_drift": 3.122502256758253e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.6258483514236594e-07,
                "nrmse_extrap_horizon": 4.582538102918179e-07,
                "mass_drift": 1.1102230246251565e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.7159131764968e-08,
                "nrmse_extrap_horizon": 3.402776010189106e-07,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 2.4466763635409485e-07,
                "nrmse_extrap_horizon": 9.068626530091584e-07,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 2.219220704622277e-06,
              "fit_s": 0.004137582960538566,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 1.5938702855633091e-07,
                "nrmse_extrap_horizon": 5.642894351658324e-07,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.2283157156830468e-06,
                "nrmse_extrap_horizon": 5.218441394845123e-06,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.648287140544029e-08,
                "nrmse_extrap_horizon": 3.327735103883394e-07,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 4.154029982694749e-07,
                "nrmse_extrap_horizon": 1.4541220058079429e-06,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.1634903998076805e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999945521915032
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": -1.356951459085402e-06
                },
                {
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": 1.0459301643292944e-06
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 6,
                  "coefficient": 2.0822092301303068e-07
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 5,
                  "coefficient": -2.2574411398795967e-07
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": 5.762025578336043e-07
                }
              ],
              "fit_s": 0.003590957960113883,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 1.4327399274693032e-07,
                "nrmse_extrap_horizon": 5.141631663471822e-07,
                "mass_drift": 5.204170427930421e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.2331655482148705e-06,
                "nrmse_extrap_horizon": 5.223136013503206e-06,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.705269194856577e-08,
                "nrmse_extrap_horizon": 3.3998943168072085e-07,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 3.9178101153701173e-07,
                "nrmse_extrap_horizon": 1.3537341717362832e-06,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.1612551251104295e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999945521915032
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": -1.356951459085402e-06
                },
                {
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": 1.0459301643292944e-06
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 6,
                  "coefficient": 2.0822092301303068e-07
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 5,
                  "coefficient": -2.2574411398795967e-07
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": 5.762025578336043e-07
                }
              ],
              "fit_s": 0.007079792092554271,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 1.512927391576404e-07,
                "nrmse_extrap_horizon": 5.378396045437043e-07,
                "mass_drift": 5.204170427930421e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.772666897137166e-06,
                "nrmse_extrap_horizon": 7.141963814196062e-06,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.685113340333663e-08,
                "nrmse_extrap_horizon": 3.379037121301595e-07,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 3.959660505935999e-07,
                "nrmse_extrap_horizon": 1.3771026551128177e-06,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.6525756494631422e-05,
              "fit_s": 0.00032891693990677595,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.05150602427502902,
                "nrmse_extrap_horizon": 0.21778357763136436,
                "mass_drift": 2.564221966705471e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.09024077637783409,
                "nrmse_extrap_horizon": 0.3632924252516602,
                "mass_drift": 4.809161201213552e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.04938904595664032,
                "nrmse_extrap_horizon": 0.19465660578348176,
                "mass_drift": 8.516427632554446e-10,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.07296780694353026,
                "nrmse_extrap_horizon": 0.2856290433306747,
                "mass_drift": 5.798138177914858e-09,
                "finite": true
              },
              "fit_s": 0.00021758303046226501,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.004653403315963638,
                "nrmse_extrap_horizon": 0.037792768868606885,
                "mass_drift": 0.00574300328116871,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.061590451748484515,
                "nrmse_extrap_horizon": 0.23989135797613265,
                "mass_drift": 0.0013313485766805258,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.004320664144182878,
                "nrmse_extrap_horizon": 0.0060420323227200045,
                "mass_drift": 0.0008990997870511677,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0396579986259192,
                "nrmse_extrap_horizon": 0.17365044475344504,
                "mass_drift": 0.00693228730163592,
                "finite": true
              },
              "fit_s": 3.9772211249219254,
              "training_loss_trace": [
                1.417758822441101,
                0.49274566769599915,
                0.11463243514299393,
                0.04024621099233627,
                0.01701808162033558,
                0.008662287145853043,
                0.005315821617841721,
                0.005597271025180817,
                0.004019636195152998,
                0.0024886573664844036,
                0.0025225987192243338,
                0.002401140984147787,
                0.0017348816618323326,
                0.0022972007282078266,
                0.0019726918544620275,
                0.0013381816679611802,
                0.0007224089931696653,
                0.0010420288890600204,
                0.0008742654463276267,
                0.000846131588332355,
                0.0011460017412900925
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.003162599634253252,
                "nrmse_extrap_horizon": 0.02171667218398328,
                "mass_drift": 0.003316755903736184,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.03936207933467452,
                "nrmse_extrap_horizon": 0.16154542120904358,
                "mass_drift": 0.00751862705887707,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0019696581633237334,
                "nrmse_extrap_horizon": 0.003512346144359545,
                "mass_drift": 0.0003908568360103601,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.019192254953560153,
                "nrmse_extrap_horizon": 0.10400064880704102,
                "mass_drift": 0.00626885183382371,
                "finite": true
              },
              "fit_s": 0.8042190000414848,
              "training_loss_trace": [
                1.0155558586120605,
                0.39777201414108276,
                0.05462171137332916,
                0.027850955724716187,
                0.016356339678168297,
                0.010588724166154861,
                0.007795391604304314,
                0.005664471536874771,
                0.004224290605634451,
                0.0028780940920114517,
                0.002071391325443983,
                0.0016444965731352568,
                0.001245938939973712,
                0.0009467585477977991,
                0.0007863723440095782,
                0.0005759669002145529,
                0.0004399971221573651,
                0.00035375740844756365,
                0.0002848808071576059,
                0.0002511963830329478,
                0.00018315864144824445
              ]
            }
          }
        },
        {
          "law": "oscillatory",
          "training_samples": 9600,
          "training_u_range": [
            -0.5563692763790924,
            0.6467345365179911
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 0.0003808433768937722,
                "nrmse_extrap_horizon": 0.0006281515263005024,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.09735255184527121,
                "nrmse_extrap_horizon": 0.27636879936206404,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.550308558067689e-05,
                "nrmse_extrap_horizon": 3.304574615554833e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.011197212597937491,
                "nrmse_extrap_horizon": 0.02830409209898134,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8667139704832245,
              "fit_s": 0.003946749959141016,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 0.0004261676049542634,
                "nrmse_extrap_horizon": 0.0007564077369061105,
                "mass_drift": 7.632783294297951e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.06515872585519566,
                "nrmse_extrap_horizon": 0.2522576347321122,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 2.0219377181079946e-05,
                "nrmse_extrap_horizon": 4.908302037863291e-05,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.009634265890448662,
                "nrmse_extrap_horizon": 0.02355930842931231,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8485863428703327,
              "fit_s": 0.0041921669617295265,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 6.341748889599443e-08,
                "nrmse_extrap_horizon": 2.598956871946556e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.202738128340916e-07,
                "nrmse_extrap_horizon": 6.34678120734044e-07,
                "mass_drift": 7.632783294297951e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 6.599442526513896e-08,
                "nrmse_extrap_horizon": 2.772182221264459e-07,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 8.662406883674417e-08,
                "nrmse_extrap_horizon": 2.959098869224929e-07,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.1184187858574684e-06,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49999943624350635
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.07999992179953458
                }
              ],
              "fit_s": 0.0021964999614283442,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 1.6326433282878837e-06,
                "nrmse_extrap_horizon": 4.3325199149547735e-06,
                "mass_drift": 2.42861286636753e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.5890425562270992e-06,
                "nrmse_extrap_horizon": 4.65052422449056e-06,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.733610316363058e-06,
                "nrmse_extrap_horizon": 4.816061551620164e-06,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 5.560459041404842e-06,
                "nrmse_extrap_horizon": 1.8070574717928285e-05,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 2.536635468596217e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49999943624350635
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.07999992179953458
                }
              ],
              "fit_s": 0.0065576250199228525,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 0.0001590583997823032,
                "nrmse_extrap_horizon": 0.0004030861679922601,
                "mass_drift": 4.5102810375396984e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.029775437166257784,
                "nrmse_extrap_horizon": 0.09678616864487403,
                "mass_drift": 7.632783294297951e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0001576678470954994,
                "nrmse_extrap_horizon": 0.0005292003241220791,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0023859345342504344,
                "nrmse_extrap_horizon": 0.006933426361297207,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.4265831926015661,
              "fit_s": 0.00032887503039091825,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.06811257636495238,
                "nrmse_extrap_horizon": 0.26832211317424787,
                "mass_drift": 3.3244877267746276e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.13161081547851525,
                "nrmse_extrap_horizon": 0.4925824037052897,
                "mass_drift": 6.235028715551039e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.04219768853538258,
                "nrmse_extrap_horizon": 0.16110804898446224,
                "mass_drift": 1.1041463715555366e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.08684794036294145,
                "nrmse_extrap_horizon": 0.30834615242619756,
                "mass_drift": 7.517227423869954e-09,
                "finite": true
              },
              "fit_s": 0.00021395902149379253,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.013875462809246258,
                "nrmse_extrap_horizon": 0.08863163972494953,
                "mass_drift": 0.00699211855146864,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0903484418861749,
                "nrmse_extrap_horizon": 0.3420618738082253,
                "mass_drift": 0.01722551717982658,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.006696202997479917,
                "nrmse_extrap_horizon": 0.0156270651290753,
                "mass_drift": 0.002215495810414407,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.046308153940403815,
                "nrmse_extrap_horizon": 0.162411683873587,
                "mass_drift": 0.0050364732125236095,
                "finite": true
              },
              "fit_s": 3.6655902919592336,
              "training_loss_trace": [
                1.7682682275772095,
                0.5794575810432434,
                0.1029835119843483,
                0.028173871338367462,
                0.01019483432173729,
                0.004118029959499836,
                0.0026847105473279953,
                0.001743245404213667,
                0.0013498972402885556,
                0.0010635165963321924,
                0.001011507585644722,
                0.0007897061877883971,
                0.0006214266177266836,
                0.0004619056999217719,
                0.00043368959450162947,
                0.00040210451697930694,
                0.000292794342385605,
                0.0003191861615050584,
                0.00026436103507876396,
                0.00021559206652455032,
                0.00022565403196495026
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.008046664569548926,
                "nrmse_extrap_horizon": 0.09045780060989063,
                "mass_drift": 0.010709790889513321,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.06333989578745808,
                "nrmse_extrap_horizon": 0.29774823982167264,
                "mass_drift": 0.026796741146788303,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0017395904879784789,
                "nrmse_extrap_horizon": 0.005217203530719586,
                "mass_drift": 0.0006326094958835279,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.03525500992966454,
                "nrmse_extrap_horizon": 0.17166294276232136,
                "mass_drift": 0.02273579382022553,
                "finite": true
              },
              "fit_s": 0.8029959170380607,
              "training_loss_trace": [
                0.9884624481201172,
                0.41051697731018066,
                0.1560860276222229,
                0.05045244097709656,
                0.02811453677713871,
                0.01586298644542694,
                0.009767192415893078,
                0.005565847270190716,
                0.003473936580121517,
                0.0022102450020611286,
                0.0015166545053943992,
                0.0011923983693122864,
                0.0008522533462382853,
                0.0006975754513405263,
                0.0005842509563080966,
                0.0005137022235430777,
                0.000428843020927161,
                0.00036057259421795607,
                0.0003190900606568903,
                0.00029124243883416057,
                0.0002495134249329567
              ]
            }
          }
        },
        {
          "law": "saturating",
          "training_samples": 9600,
          "training_u_range": [
            -0.556367825540837,
            0.6467094153731461
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 0.000168711483789709,
                "nrmse_extrap_horizon": 0.0002858406564417885,
                "mass_drift": 4.5102810375396984e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.07323636595711874,
                "nrmse_extrap_horizon": 0.22819460730577665,
                "mass_drift": 1.0408340855860843e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 7.928154361236471e-06,
                "nrmse_extrap_horizon": 1.8738411468393018e-05,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.007690616415035033,
                "nrmse_extrap_horizon": 0.015955697262874047,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8237618573973007,
              "fit_s": 0.003966792020946741,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 0.0003812407323655929,
                "nrmse_extrap_horizon": 0.0006471227062595217,
                "mass_drift": 3.122502256758253e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.03893977674008305,
                "nrmse_extrap_horizon": 0.14938471117417657,
                "mass_drift": 1.1102230246251565e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.110564870980067e-06,
                "nrmse_extrap_horizon": 2.2118099140730934e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.008246643005377325,
                "nrmse_extrap_horizon": 0.021556396758027948,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.420689516017819,
              "fit_s": 0.004181999946013093,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 3.180824468545846e-06,
                "nrmse_extrap_horizon": 8.330365885653665e-06,
                "mass_drift": 7.979727989493313e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0024896521506968497,
                "nrmse_extrap_horizon": 0.008152607590298693,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 3.460231325814232e-06,
                "nrmse_extrap_horizon": 9.45451090313423e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 9.489401873086311e-05,
                "nrmse_extrap_horizon": 0.00023301715348629564,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.038270420690382834,
              "active_operator_atoms": [
                {
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -0.7476519221928977
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": 0.06327502186469035
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": -0.019592099329619774
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 4,
                  "coefficient": -0.0955218908010541
                }
              ],
              "fit_s": 0.0024415410589426756,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 2.314181454661699e-06,
                "nrmse_extrap_horizon": 6.123659552766726e-06,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.002488511280688424,
                "nrmse_extrap_horizon": 0.008146669852022066,
                "mass_drift": 1.1796119636642288e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.956450380742484e-06,
                "nrmse_extrap_horizon": 4.773751153351375e-06,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 8.945562483601838e-05,
                "nrmse_extrap_horizon": 0.00021606758234351544,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.03826870412240703,
              "active_operator_atoms": [
                {
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -0.7476519221928977
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": 0.06327502186469035
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": -0.019592099329619774
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 4,
                  "coefficient": -0.0955218908010541
                }
              ],
              "fit_s": 0.007061542011797428,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 0.0010208467356087672,
                "nrmse_extrap_horizon": 0.0029091871486493595,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.036166675450697135,
                "nrmse_extrap_horizon": 0.12125131124362314,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00039686999450914094,
                "nrmse_extrap_horizon": 0.0013294766109841233,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.004367521528223404,
                "nrmse_extrap_horizon": 0.013420923006233541,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.3994758575202709,
              "fit_s": 0.0003250830341130495,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.05995330291003865,
                "nrmse_extrap_horizon": 0.2542341696045045,
                "mass_drift": 3.3757375714205118e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.08298372108134588,
                "nrmse_extrap_horizon": 0.3455885686745214,
                "mass_drift": 6.331147023308503e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.05867475170081607,
                "nrmse_extrap_horizon": 0.23158343162486045,
                "mass_drift": 1.1211678252465163e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.07773440057398943,
                "nrmse_extrap_horizon": 0.30496134369116107,
                "mass_drift": 7.633111948068816e-09,
                "finite": true
              },
              "fit_s": 0.00021445797756314278,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0038768645557552984,
                "nrmse_extrap_horizon": 0.04928160808189733,
                "mass_drift": 0.007135451367583329,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.04569966124784243,
                "nrmse_extrap_horizon": 0.18393687935472966,
                "mass_drift": 0.0016870078144488043,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0050625010747491275,
                "nrmse_extrap_horizon": 0.007197586059992175,
                "mass_drift": 0.0009044146172840772,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.039523114081510956,
                "nrmse_extrap_horizon": 0.16707728536333757,
                "mass_drift": 0.010006311533580364,
                "finite": true
              },
              "fit_s": 3.7681725000729784,
              "training_loss_trace": [
                1.409617304801941,
                0.47517359256744385,
                0.10537760704755783,
                0.03699328750371933,
                0.01802719011902809,
                0.008991463109850883,
                0.005815605167299509,
                0.0064812153577804565,
                0.004367446526885033,
                0.0032133725471794605,
                0.0039013230707496405,
                0.004001148976385593,
                0.00290666869841516,
                0.0030226116068661213,
                0.002203590702265501,
                0.0020104425493627787,
                0.0009455893887206912,
                0.0010210470063611865,
                0.0014657697174698114,
                0.001191477058455348,
                0.0017562657594680786
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.0029388357426165996,
                "nrmse_extrap_horizon": 0.023533074846748638,
                "mass_drift": 0.0037475211657838556,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.029779709989139487,
                "nrmse_extrap_horizon": 0.1218948215004068,
                "mass_drift": 0.0018122815372286633,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.001974017233062173,
                "nrmse_extrap_horizon": 0.0037910850413911865,
                "mass_drift": 0.0005071918610336165,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.016739683439429495,
                "nrmse_extrap_horizon": 0.08878528529851483,
                "mass_drift": 0.005673432243738077,
                "finite": true
              },
              "fit_s": 0.8011094590183347,
              "training_loss_trace": [
                1.0219162702560425,
                0.3971647024154663,
                0.04641004651784897,
                0.021600309759378433,
                0.012817221693694592,
                0.00848311185836792,
                0.005616835784167051,
                0.004362542647868395,
                0.0031989566050469875,
                0.0023359330371022224,
                0.001702172914519906,
                0.001417539780959487,
                0.001001573633402586,
                0.0007570574525743723,
                0.0005447460571303964,
                0.00039175350684672594,
                0.0002707046514842659,
                0.00018008076585829258,
                0.0001553721958771348,
                0.0001405662769684568,
                0.00011427648860262707
              ]
            }
          }
        }
      ]
    },
    {
      "config": {
        "laws": [
          "burgers",
          "oscillatory",
          "saturating"
        ],
        "nx": 64,
        "test_nx": 128,
        "train_steps": 100,
        "test_steps": 400,
        "dt": 0.002,
        "nu": 0.03,
        "n_train": 6,
        "train_amplitude": 0.65,
        "test_amplitude": 1.05,
        "snapshot_stride": 4,
        "target_mode": "finite_difference",
        "max_samples": 30000,
        "spline_domain": 1.35,
        "knots": 25,
        "ridge": 1e-08,
        "innovation_ridge": 0.0001,
        "max_frequency": 6,
        "max_pole_terms": 6,
        "kan_knots": 13,
        "kan_hidden": 8,
        "epochs": 1200,
        "batch": 4096,
        "lr": 0.002,
        "seed": 20260912,
        "out": "operator_compiled_constitutive_kan_fd_seed20260912_outputs",
        "smoke": false
      },
      "results": [
        {
          "law": "burgers",
          "training_samples": 9600,
          "training_u_range": [
            -0.6309811362474458,
            0.5621317722092868
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 2.0571006928101032e-07,
                "nrmse_extrap_horizon": 7.020884595042947e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.07486686106652173,
                "nrmse_extrap_horizon": 0.15982811721547066,
                "mass_drift": 7.979727989493313e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 7.730006227205118e-08,
                "nrmse_extrap_horizon": 2.517596576023184e-07,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.005644783839101082,
                "nrmse_extrap_horizon": 0.009422232402025414,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8735422864055776,
              "fit_s": 0.004749584011733532,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 1.8917647942554995e-07,
                "nrmse_extrap_horizon": 6.82438105325314e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 4.720520652568985e-07,
                "nrmse_extrap_horizon": 1.612927811975041e-06,
                "mass_drift": 1.1622647289044608e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.5191283380087085e-08,
                "nrmse_extrap_horizon": 2.011971216561555e-07,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 3.81879805946753e-07,
                "nrmse_extrap_horizon": 1.4443187641833087e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 2.4127040573621557e-06,
              "fit_s": 0.004094208008609712,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 1.8473043113906117e-07,
                "nrmse_extrap_horizon": 6.777994794656732e-07,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 8.924518748490308e-07,
                "nrmse_extrap_horizon": 3.637999649191968e-06,
                "mass_drift": 3.122502256758253e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.733403223017327e-08,
                "nrmse_extrap_horizon": 2.102184655865814e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 3.6227030084690177e-07,
                "nrmse_extrap_horizon": 1.3633628306799292e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.3003115724830256e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49998957766171337
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 3,
                  "coefficient": -2.71860770620148e-06
                },
                {
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -2.7183936876526014e-07
                }
              ],
              "fit_s": 0.0033113330136984587,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 1.89860307279584e-07,
                "nrmse_extrap_horizon": 6.831134865121559e-07,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 9.13657770723363e-07,
                "nrmse_extrap_horizon": 3.8184426820325195e-06,
                "mass_drift": 1.3010426069826053e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.52753906643121e-08,
                "nrmse_extrap_horizon": 2.015637418746207e-07,
                "mass_drift": 6.245004513516506e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 4.373569669591739e-07,
                "nrmse_extrap_horizon": 1.5975261092767434e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.3111935652540035e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49998957766171337
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 3,
                  "coefficient": -2.71860770620148e-06
                },
                {
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -2.7183936876526014e-07
                }
              ],
              "fit_s": 0.006698957993648946,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 1.9028095939986604e-07,
                "nrmse_extrap_horizon": 6.873759251290681e-07,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.1977786695829457e-06,
                "nrmse_extrap_horizon": 4.709789194668425e-06,
                "mass_drift": 1.1102230246251565e-16,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.2758262550987354e-08,
                "nrmse_extrap_horizon": 1.9161245905850828e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 4.026067182268111e-07,
                "nrmse_extrap_horizon": 1.4786406020050231e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.6764385108279834e-05,
              "fit_s": 0.0003267918946221471,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.04893285877072598,
                "nrmse_extrap_horizon": 0.2025314012459634,
                "mass_drift": 1.335370057586882e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.08676621160901649,
                "nrmse_extrap_horizon": 0.33780553562329907,
                "mass_drift": 2.861817222435392e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.032278753290896134,
                "nrmse_extrap_horizon": 0.13346389847381793,
                "mass_drift": 5.8790904852723536e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.06266510161481562,
                "nrmse_extrap_horizon": 0.2523872622291707,
                "mass_drift": 7.54067037977979e-10,
                "finite": true
              },
              "fit_s": 0.00020412495359778404,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0005009664350087685,
                "nrmse_extrap_horizon": 0.006267636411093039,
                "mass_drift": 0.0009023906165239043,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0611636014320068,
                "nrmse_extrap_horizon": 0.24623563409232052,
                "mass_drift": 0.016716398049621866,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0003800599855292558,
                "nrmse_extrap_horizon": 0.0013909466564672977,
                "mass_drift": 1.7605580963697687e-05,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.016706972183951334,
                "nrmse_extrap_horizon": 0.08676758497943944,
                "mass_drift": 0.0006124892667866873,
                "finite": true
              },
              "fit_s": 3.9799740000162274,
              "training_loss_trace": [
                1.3839529752731323,
                0.47817081212997437,
                0.07703503221273422,
                0.029891738668084145,
                0.011203562840819359,
                0.004161670338362455,
                0.0020150188356637955,
                0.001369020901620388,
                0.0008733878494240344,
                0.000677224830724299,
                0.0005007035797461867,
                0.000435835710959509,
                0.00035709180519916117,
                0.00028583372477442026,
                0.0002495687222108245,
                0.00019952989532612264,
                0.00018788359011523426,
                0.0001685636379988864,
                0.00014016611385159194,
                0.00011909329623449594,
                0.00010900878987740725
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.0005831454598312314,
                "nrmse_extrap_horizon": 0.0036134060743601825,
                "mass_drift": 0.0006087774090362125,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.03330175481791114,
                "nrmse_extrap_horizon": 0.1636882735118837,
                "mass_drift": 0.016277881672855685,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00037693522473981867,
                "nrmse_extrap_horizon": 0.001336318950459101,
                "mass_drift": 0.000298170812760859,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.007661074395471274,
                "nrmse_extrap_horizon": 0.04446746941101955,
                "mass_drift": 0.0017423858715773927,
                "finite": true
              },
              "fit_s": 0.8010966669535264,
              "training_loss_trace": [
                1.0068249702453613,
                0.38155025243759155,
                0.03756243363022804,
                0.02242186665534973,
                0.013310282491147518,
                0.008871455676853657,
                0.0061073824763298035,
                0.004028689116239548,
                0.0029413148295134306,
                0.0020378287881612778,
                0.0014748454559594393,
                0.0010289562633261085,
                0.0006609417032450438,
                0.00045966808102093637,
                0.00041049561696127057,
                0.0003713636542670429,
                0.0002893133496399969,
                0.0002599621075205505,
                0.00022799427097197622,
                0.00023537912056781352,
                0.0002159194991691038
              ]
            }
          }
        },
        {
          "law": "oscillatory",
          "training_samples": 9600,
          "training_u_range": [
            -0.6309395550771059,
            0.5621367974340143
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 1.0297537537649226e-05,
                "nrmse_extrap_horizon": 2.8170631695220024e-05,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.08572449593816309,
                "nrmse_extrap_horizon": 0.1870416006266388,
                "mass_drift": 3.2959746043559335e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.5313263685659876e-05,
                "nrmse_extrap_horizon": 3.453469333448219e-05,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.00651825971812579,
                "nrmse_extrap_horizon": 0.011297521981710183,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8574811577631763,
              "fit_s": 0.003913166932761669,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 8.08686777748736e-05,
                "nrmse_extrap_horizon": 0.00011613711508156105,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.052108363236028604,
                "nrmse_extrap_horizon": 0.1423345345806753,
                "mass_drift": 3.2959746043559335e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.7942769692937446e-05,
                "nrmse_extrap_horizon": 4.720431758031e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.004221347075154772,
                "nrmse_extrap_horizon": 0.009946001546137354,
                "mass_drift": 9.020562075079397e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8879843434189851,
              "fit_s": 0.004038499901071191,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 1.0345109111968354e-07,
                "nrmse_extrap_horizon": 4.724870899434195e-07,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 2.0116195036467242e-07,
                "nrmse_extrap_horizon": 9.287207539999268e-07,
                "mass_drift": 4.5102810375396984e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 7.263595193327863e-08,
                "nrmse_extrap_horizon": 3.102006159631177e-07,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 1.3295908915746342e-07,
                "nrmse_extrap_horizon": 6.070880651077068e-07,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 1.8755010086358688e-06,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49999904264876416
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.07999990639558653
                }
              ],
              "fit_s": 0.0022192090982571244,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 1.8402976637038338e-06,
                "nrmse_extrap_horizon": 4.66262744856887e-06,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.5068342151287785e-05,
                "nrmse_extrap_horizon": 4.2721297370105346e-05,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.6902593876257012e-06,
                "nrmse_extrap_horizon": 4.4016811663646725e-06,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 1.1034710444754012e-05,
                "nrmse_extrap_horizon": 3.628665657548217e-05,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 5.294834318207864e-05,
              "active_operator_atoms": [
                {
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49999904264876416
                },
                {
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.07999990639558653
                }
              ],
              "fit_s": 0.0066125839948654175,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 0.0002523984023610007,
                "nrmse_extrap_horizon": 0.0005306944095402954,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.01731558444577317,
                "nrmse_extrap_horizon": 0.06476962069221905,
                "mass_drift": 4.5102810375396984e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.946843507454553e-05,
                "nrmse_extrap_horizon": 0.0003574388510808425,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0020187849752342003,
                "nrmse_extrap_horizon": 0.005934730260117636,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.44665853466325456,
              "fit_s": 0.0003439580323174596,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.07159737962936806,
                "nrmse_extrap_horizon": 0.27879490969368476,
                "mass_drift": 1.99036036263589e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.1282882414280072,
                "nrmse_extrap_horizon": 0.45382976851333606,
                "mass_drift": 4.265519638890769e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.038574913153867185,
                "nrmse_extrap_horizon": 0.1567635037354011,
                "mass_drift": 8.762745640211733e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0850597273106358,
                "nrmse_extrap_horizon": 0.30774818654837355,
                "mass_drift": 1.1239320654721219e-09,
                "finite": true
              },
              "fit_s": 0.00021104200277477503,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0009027433097490697,
                "nrmse_extrap_horizon": 0.053626251201938584,
                "mass_drift": 0.00713031051179043,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0935482541881758,
                "nrmse_extrap_horizon": 0.3299771074715571,
                "mass_drift": 0.011256716262350223,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00051584964063602,
                "nrmse_extrap_horizon": 0.0021106008568808933,
                "mass_drift": 0.0001142635941468878,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0283291095003108,
                "nrmse_extrap_horizon": 0.15117599519259062,
                "mass_drift": 0.008719647724200641,
                "finite": true
              },
              "fit_s": 3.6278480830369517,
              "training_loss_trace": [
                1.28803288936615,
                0.41182732582092285,
                0.08045395463705063,
                0.031184038147330284,
                0.011204232461750507,
                0.004938781261444092,
                0.002608557930216193,
                0.0017336710589006543,
                0.0011753661092370749,
                0.000861000211443752,
                0.0008240569732151926,
                0.0006774049834348261,
                0.0004234103253111243,
                0.0003903229080606252,
                0.00029611398349516094,
                0.000251191173447296,
                0.00022195131168700755,
                0.00020034913904964924,
                0.00020526512525975704,
                0.00014184349856805056,
                0.00014069306780584157
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.001397016573945385,
                "nrmse_extrap_horizon": 0.03956535442348456,
                "mass_drift": 0.005355953737424042,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0632829942802647,
                "nrmse_extrap_horizon": 0.3301218190791899,
                "mass_drift": 0.04164504314672375,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0007834858358414426,
                "nrmse_extrap_horizon": 0.002322477933026714,
                "mass_drift": 0.00045508270940385065,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.016130501086771675,
                "nrmse_extrap_horizon": 0.11809263823194686,
                "mass_drift": 0.020785702207859358,
                "finite": true
              },
              "fit_s": 0.8049377920106053,
              "training_loss_trace": [
                1.0381343364715576,
                0.4991444945335388,
                0.15659773349761963,
                0.07245238125324249,
                0.03808162733912468,
                0.02136049047112465,
                0.012530338019132614,
                0.006821063347160816,
                0.004530486650764942,
                0.0034813513047993183,
                0.002104331273585558,
                0.0016727345064282417,
                0.0012876682449132204,
                0.000906194094568491,
                0.0009207788971252739,
                0.0008538088877685368,
                0.0005397888598963618,
                0.00044517748756334186,
                0.0003717091167345643,
                0.0003719091764651239,
                0.0003113960847258568
              ]
            }
          }
        },
        {
          "law": "saturating",
          "training_samples": 9600,
          "training_u_range": [
            -0.6309866295473631,
            0.5621316577837042
          ],
          "models": {
            "oc_ckan": {
              "params": 25,
              "id": {
                "nrmse_fit_horizon": 6.014931251585479e-06,
                "nrmse_extrap_horizon": 1.4004361781644088e-05,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.06665913867385742,
                "nrmse_extrap_horizon": 0.15160422140880367,
                "mass_drift": 6.245004513516506e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.702459488424862e-06,
                "nrmse_extrap_horizon": 1.035347084822331e-05,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.005061702014736525,
                "nrmse_extrap_horizon": 0.008379829872290025,
                "mass_drift": 3.122502256758253e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.8203351451921445,
              "fit_s": 0.003935917047783732,
              "training_loss_trace": []
            },
            "anchored_oc_ckan": {
              "params": 28,
              "id": {
                "nrmse_fit_horizon": 5.5007130437169235e-05,
                "nrmse_extrap_horizon": 7.33445035206556e-05,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.024116410730075644,
                "nrmse_extrap_horizon": 0.0771694620858159,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 7.161620626522901e-06,
                "nrmse_extrap_horizon": 1.8205301129940298e-05,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.002513979269630128,
                "nrmse_extrap_horizon": 0.006322871299440934,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.40473458724055145,
              "fit_s": 0.004032457945868373,
              "training_loss_trace": []
            },
            "pole_atlas": {
              "params": 15,
              "id": {
                "nrmse_fit_horizon": 3.987753820910472e-06,
                "nrmse_extrap_horizon": 7.262536352438698e-06,
                "mass_drift": 5.551115123125783e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.001798468180687905,
                "nrmse_extrap_horizon": 0.005198945087941907,
                "mass_drift": 4.336808689942018e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 2.019469104215644e-06,
                "nrmse_extrap_horizon": 5.939728245303327e-06,
                "mass_drift": 8.326672684688674e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.00011497090851438414,
                "nrmse_extrap_horizon": 0.00027690402414114315,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.05393307887032758,
              "active_operator_atoms": [
                {
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -0.5306974034765053
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": 0.04061816473448975
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": -0.016846946053616113
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 4,
                  "coefficient": -0.023105043250166404
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 3,
                  "coefficient": -0.10090533774184265
                }
              ],
              "fit_s": 0.002619040897116065,
              "training_loss_trace": []
            },
            "pole_oc_ckan": {
              "params": 40,
              "id": {
                "nrmse_fit_horizon": 8.963123791587681e-07,
                "nrmse_extrap_horizon": 2.1813987063778675e-06,
                "mass_drift": 6.938893903907228e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0018184804624034338,
                "nrmse_extrap_horizon": 0.005187352271967678,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 7.733455406309228e-07,
                "nrmse_extrap_horizon": 2.183387725556083e-06,
                "mass_drift": 2.0816681711721685e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 8.005941883401918e-05,
                "nrmse_extrap_horizon": 0.00016345616855559746,
                "mass_drift": 3.469446951953614e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.05392325009325158,
              "active_operator_atoms": [
                {
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -0.5306974034765053
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 5,
                  "coefficient": 0.04061816473448975
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 6,
                  "coefficient": -0.016846946053616113
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 4,
                  "coefficient": -0.023105043250166404
                },
                {
                  "kind": "cos",
                  "order_or_frequency": 3,
                  "coefficient": -0.10090533774184265
                }
              ],
              "fit_s": 0.0071823750622570515,
              "training_loss_trace": []
            },
            "sindy_poly5": {
              "params": 5,
              "id": {
                "nrmse_fit_horizon": 0.0005326032266352035,
                "nrmse_extrap_horizon": 0.001456645156891413,
                "mass_drift": 2.7755575615628914e-17,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.011582358233774228,
                "nrmse_extrap_horizon": 0.03840415998588077,
                "mass_drift": 4.85722573273506e-17,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0002891369191464615,
                "nrmse_extrap_horizon": 0.0010649967246034767,
                "mass_drift": 4.163336342344337e-17,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.002460685822265316,
                "nrmse_extrap_horizon": 0.0077702585315572,
                "mass_drift": 6.245004513516506e-17,
                "finite": true
              },
              "flux_nrmse_amplitude_range": 0.36449608178517856,
              "fit_s": 0.00032970798201859,
              "training_loss_trace": []
            },
            "linear": {
              "params": 3,
              "id": {
                "nrmse_fit_horizon": 0.055986542331070775,
                "nrmse_extrap_horizon": 0.23341043727250502,
                "mass_drift": 1.8193884454564824e-09,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.08365664587428864,
                "nrmse_extrap_horizon": 0.33321432762293013,
                "mass_drift": 3.899111672422961e-09,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0396256745462316,
                "nrmse_extrap_horizon": 0.163792001827527,
                "mass_drift": 8.010026163185469e-09,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0683206390322103,
                "nrmse_extrap_horizon": 0.2762406206952935,
                "mass_drift": 1.0273862594001315e-09,
                "finite": true
              },
              "fit_s": 0.00020658306311815977,
              "training_loss_trace": []
            },
            "direct_ckan": {
              "params": 345,
              "id": {
                "nrmse_fit_horizon": 0.0004974886183177084,
                "nrmse_extrap_horizon": 0.003886760348136616,
                "mass_drift": 0.0007034172697288898,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.05325471133167742,
                "nrmse_extrap_horizon": 0.21635747228983532,
                "mass_drift": 0.018082845184469055,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0003819308767874231,
                "nrmse_extrap_horizon": 0.0013432756421401378,
                "mass_drift": 0.0002495839096476049,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.015451634135242438,
                "nrmse_extrap_horizon": 0.08551427264147687,
                "mass_drift": 0.002240212417242274,
                "finite": true
              },
              "fit_s": 3.7209309169556946,
              "training_loss_trace": [
                1.389241337776184,
                0.467952698469162,
                0.07141987234354019,
                0.024872463196516037,
                0.008789962157607079,
                0.0034985756501555443,
                0.0016183014959096909,
                0.001120204571634531,
                0.0006850400241091847,
                0.0005334134912118316,
                0.00040026556234806776,
                0.0003542159975040704,
                0.0002926688175648451,
                0.0002487705205567181,
                0.00022424606140702963,
                0.00018751596508082002,
                0.0001830466353567317,
                0.00016172692994587123,
                0.0001375877036480233,
                0.00011545461893547326,
                0.00010490386193851009
              ]
            },
            "mlp": {
              "params": 337,
              "id": {
                "nrmse_fit_horizon": 0.0005471068982512798,
                "nrmse_extrap_horizon": 0.0029259629092786006,
                "mass_drift": 0.000545428103687351,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.022971531147763593,
                "nrmse_extrap_horizon": 0.11651181485202529,
                "mass_drift": 0.011139767672952737,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0005732055814987516,
                "nrmse_extrap_horizon": 0.002254782968281491,
                "mass_drift": 0.00032137103990166616,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.006240964329822647,
                "nrmse_extrap_horizon": 0.03884652077596781,
                "mass_drift": 0.002913462996623581,
                "finite": true
              },
              "fit_s": 0.8137124999193475,
              "training_loss_trace": [
                1.0057604312896729,
                0.3868461847305298,
                0.028867525979876518,
                0.016018420457839966,
                0.00984905380755663,
                0.006462103687226772,
                0.0046454002149403095,
                0.003226245753467083,
                0.0025304406881332397,
                0.0019645546562969685,
                0.0015650455607101321,
                0.001298403018154204,
                0.0009154912550002337,
                0.0006825278396718204,
                0.0005752298166044056,
                0.00047376740258187056,
                0.00037276523653417826,
                0.00030249106930568814,
                0.00023687815701123327,
                0.00022077170433476567,
                0.00018168039969168603
              ]
            }
          }
        }
      ]
    },
    {
      "config": {
        "noise": [
          0.0,
          0.001,
          0.005,
          0.01,
          0.02
        ],
        "nx": 64,
        "test_nx": 128,
        "train_steps": 160,
        "test_steps": 400,
        "dt": 0.002,
        "nu": 0.03,
        "n_train": 8,
        "train_amplitude": 0.65,
        "test_amplitude": 0.95,
        "point_stride": 4,
        "window": 24,
        "window_stride": 8,
        "max_mode": 8,
        "max_frequency": 6,
        "max_terms": 8,
        "ridge": 1e-07,
        "seed": 20260910,
        "out": "operator_compiled_noisy_weakform_seed20260910_outputs",
        "smoke": false
      },
      "results": [
        {
          "noise": 0.0,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 5.917826637190594e-05,
                "nrmse_extrap_horizon": 0.00015133202897870752,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0003505598391043076,
                "nrmse_extrap_horizon": 0.0009300859780530755,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.9088502480035046e-05,
                "nrmse_extrap_horizon": 0.00012111071570952907,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0006729952426015391,
                "nrmse_extrap_horizon": 0.0018848649867496362,
                "finite": true
              },
              "flux_nrmse": 0.008204499347934291,
              "reaction_nrmse": 0.005514487999478786,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49994907500333624
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05516204726646278
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.00671177403795396
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.19182235946664733
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.23663671949142118
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 6,
                  "coefficient": -0.0025461133968464012
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 5,
                  "coefficient": 0.006853854137854422
                },
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": 0.005356854984460914
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 5.403081301583075e-07,
                "nrmse_extrap_horizon": 1.4397872114419782e-06,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.704968050642528e-05,
                "nrmse_extrap_horizon": 4.903332393055451e-05,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.226272059635876e-07,
                "nrmse_extrap_horizon": 1.4265290830151208e-06,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 3.240996557398079e-05,
                "nrmse_extrap_horizon": 9.253341088095562e-05,
                "finite": true
              },
              "flux_nrmse": 5.935893424401264e-06,
              "reaction_nrmse": 0.004048384450789665,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999961735442828
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05999992302580172
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.04533068314637485
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.15480878922339794
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": -0.006875465852203499
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.08682140409492284
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 1,
                  "coefficient": 0.0931376142257292
                },
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 4,
                  "coefficient": -6.065384006311155e-07
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00023441022156253435,
                "nrmse_extrap_horizon": 0.000558247724883109,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.005099442958582769,
                "nrmse_extrap_horizon": 0.013342645774944996,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.000261551956544253,
                "nrmse_extrap_horizon": 0.0005766002591885761,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010334068258980852,
                "nrmse_extrap_horizon": 0.028600495334322962,
                "finite": true
              },
              "flux_nrmse": 0.14971161507253866,
              "reaction_nrmse": 0.011360878341987847
            }
          }
        },
        {
          "noise": 0.001,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0012985793858886813,
                "nrmse_extrap_horizon": 0.0038060661245083046,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.001785700457104686,
                "nrmse_extrap_horizon": 0.005261101908043463,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0013538270192363765,
                "nrmse_extrap_horizon": 0.003961065023972553,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.001920359137587855,
                "nrmse_extrap_horizon": 0.0055780172060563476,
                "finite": true
              },
              "flux_nrmse": 0.011985749252101236,
              "reaction_nrmse": 0.06048954105124381,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.5061246269682602
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.059717240481368825
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12682034685510252
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.07216629415430344
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0001004925988607257,
                "nrmse_extrap_horizon": 0.0002899614010335906,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0006137554022883029,
                "nrmse_extrap_horizon": 0.001787484326229607,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.335668317464894e-05,
                "nrmse_extrap_horizon": 0.00026809024926250285,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0010022160202295786,
                "nrmse_extrap_horizon": 0.0029556090528035732,
                "finite": true
              },
              "flux_nrmse": 4.6722003352292704e-05,
              "reaction_nrmse": 0.09362094058099803,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999804537347535
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.060007258348803875
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12579782249905702
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.048844998753667955
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00024077876604697098,
                "nrmse_extrap_horizon": 0.0005733916079022074,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.005085917245389462,
                "nrmse_extrap_horizon": 0.013301533436537965,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00026417772685915526,
                "nrmse_extrap_horizon": 0.0005814785197649668,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010311103099188545,
                "nrmse_extrap_horizon": 0.02854804378105064,
                "finite": true
              },
              "flux_nrmse": 0.14928150704053472,
              "reaction_nrmse": 0.00548016385010991
            }
          }
        },
        {
          "noise": 0.005,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.005022969023848044,
                "nrmse_extrap_horizon": 0.01566418823937697,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.012415653678466575,
                "nrmse_extrap_horizon": 0.037613102397390574,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.005415144125946644,
                "nrmse_extrap_horizon": 0.01621567971681381,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.015050733763215158,
                "nrmse_extrap_horizon": 0.046059539204672366,
                "finite": true
              },
              "flux_nrmse": 0.024735713110105723,
              "reaction_nrmse": 0.9010188022605212,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4878493140564377
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.058086654138779316
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 1,
                  "coefficient": 0.23183347413836403
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 8.66182476583068e-05,
                "nrmse_extrap_horizon": 0.0002619617638125258,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0009230201242704353,
                "nrmse_extrap_horizon": 0.002699476399215948,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00010202314313642635,
                "nrmse_extrap_horizon": 0.0003222840452320664,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0014020141312425544,
                "nrmse_extrap_horizon": 0.00424250704203905,
                "finite": true
              },
              "flux_nrmse": 0.00028702961347908216,
              "reaction_nrmse": 0.11929058268098833,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49993925490356644
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05992981042998558
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.1252444309252141
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.044012688080140576
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00025162682187177075,
                "nrmse_extrap_horizon": 0.0006240738906653482,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0054704269807516765,
                "nrmse_extrap_horizon": 0.014350532626824142,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0003018335857802033,
                "nrmse_extrap_horizon": 0.0009160135867630616,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010979045582690203,
                "nrmse_extrap_horizon": 0.03014067067174844,
                "finite": true
              },
              "flux_nrmse": 0.1549270274830278,
              "reaction_nrmse": 0.07471950277531701
            }
          }
        },
        {
          "noise": 0.01,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.011281637774252423,
                "nrmse_extrap_horizon": 0.03133589784953791,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.011054141209360477,
                "nrmse_extrap_horizon": 0.038444802710976854,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.012909167748266684,
                "nrmse_extrap_horizon": 0.04807953900627435,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.013753084678628546,
                "nrmse_extrap_horizon": 0.06084815082330969,
                "finite": true
              },
              "flux_nrmse": 0.10252741851300988,
              "reaction_nrmse": 0.25965676833228085,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4502584262898408
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.06894128959048168
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": 0.10068531725436831
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.00019068747656759212,
                "nrmse_extrap_horizon": 0.0005641806640413877,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0010347238204734947,
                "nrmse_extrap_horizon": 0.0029594396736460074,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00022374415529214539,
                "nrmse_extrap_horizon": 0.0005917898640341139,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0015333869502435684,
                "nrmse_extrap_horizon": 0.004445533863452493,
                "finite": true
              },
              "flux_nrmse": 0.001549054527184065,
              "reaction_nrmse": 0.12677698137994498,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4992836087555198
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.059820068430266715
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.1251167926311376
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.042647565155760264
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.000367003539693021,
                "nrmse_extrap_horizon": 0.0009842716425472898,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.005538887143008963,
                "nrmse_extrap_horizon": 0.014642049864464447,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00037165989101288407,
                "nrmse_extrap_horizon": 0.0011259402795041496,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010996864570026278,
                "nrmse_extrap_horizon": 0.030462003197787985,
                "finite": true
              },
              "flux_nrmse": 0.15028764801550717,
              "reaction_nrmse": 0.03797115892582749
            }
          }
        },
        {
          "noise": 0.02,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.012267663489793693,
                "nrmse_extrap_horizon": 0.03575693486943984,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.013955099478798682,
                "nrmse_extrap_horizon": 0.043004750855626314,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.012739102054789897,
                "nrmse_extrap_horizon": 0.04088249547700688,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.01620007063417234,
                "nrmse_extrap_horizon": 0.052713921463285095,
                "finite": true
              },
              "flux_nrmse": 0.10904428170625823,
              "reaction_nrmse": 0.542027366915572,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.44476889474993886
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.06463650403978517
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.14349101561460137
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0011165792453140461,
                "nrmse_extrap_horizon": 0.003443280606515263,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.003909480211663288,
                "nrmse_extrap_horizon": 0.011695233206084439,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0012750967746366678,
                "nrmse_extrap_horizon": 0.003933737791202463,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.005195265815868509,
                "nrmse_extrap_horizon": 0.016461807981613286,
                "finite": true
              },
              "flux_nrmse": 0.0007840496345508358,
              "reaction_nrmse": 0.3590469887782205,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4997751098816568
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05982550087818019
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.1202363629053271
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.0007924511980124133,
                "nrmse_extrap_horizon": 0.002320882902876022,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.005619061944403836,
                "nrmse_extrap_horizon": 0.015122753166714723,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.000497431386801651,
                "nrmse_extrap_horizon": 0.0013256608904779546,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.010990733299229002,
                "nrmse_extrap_horizon": 0.03073928474190737,
                "finite": true
              },
              "flux_nrmse": 0.14007647144902982,
              "reaction_nrmse": 0.10558942888328052
            }
          }
        }
      ]
    },
    {
      "config": {
        "noise": [
          0.0,
          0.001,
          0.005,
          0.01,
          0.02
        ],
        "nx": 64,
        "test_nx": 128,
        "train_steps": 160,
        "test_steps": 400,
        "dt": 0.002,
        "nu": 0.03,
        "n_train": 8,
        "train_amplitude": 0.65,
        "test_amplitude": 0.95,
        "point_stride": 4,
        "window": 24,
        "window_stride": 8,
        "max_mode": 8,
        "max_frequency": 6,
        "max_terms": 8,
        "ridge": 1e-07,
        "seed": 20260911,
        "out": "operator_compiled_noisy_weakform_seed20260911_outputs",
        "smoke": false
      },
      "results": [
        {
          "noise": 0.0,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 2.3358846284704087e-06,
                "nrmse_extrap_horizon": 6.53252945678277e-06,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 4.2326267804726665e-06,
                "nrmse_extrap_horizon": 1.32688261092485e-05,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 2.3944383761407953e-06,
                "nrmse_extrap_horizon": 6.878828047811273e-06,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 4.385624401293878e-05,
                "nrmse_extrap_horizon": 0.00011990793421612413,
                "finite": true
              },
              "flux_nrmse": 6.1383030237036496e-06,
              "reaction_nrmse": 0.002903002636092362,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49999748314644377
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05999900978132903
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.0036259415163403066
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.1955984751025701
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.2427841312699713
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 5.733473834040529e-07,
                "nrmse_extrap_horizon": 1.5898574613599176e-06,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.3061166330244278e-06,
                "nrmse_extrap_horizon": 4.063965001025435e-06,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.125498684512453e-07,
                "nrmse_extrap_horizon": 1.5054813295449198e-06,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 4.900789515443536e-05,
                "nrmse_extrap_horizon": 0.00013043997898779119,
                "finite": true
              },
              "flux_nrmse": 1.1148477309381483e-05,
              "reaction_nrmse": 0.0038966093856299174,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999888294864334
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05999988119923435
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.04530736149828961
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.15491799444670806
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": -0.006901429399587611
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.0868510780569898
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 1,
                  "coefficient": 0.09323109560401942
                },
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 3,
                  "coefficient": -3.002130008992923e-06
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.0002389347715394116,
                "nrmse_extrap_horizon": 0.0005745737979978322,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0006080363100561977,
                "nrmse_extrap_horizon": 0.0015938227633240905,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00022172088928503066,
                "nrmse_extrap_horizon": 0.0004693096025557338,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.015825676356627065,
                "nrmse_extrap_horizon": 0.037516935345440726,
                "finite": true
              },
              "flux_nrmse": 0.14822532366778332,
              "reaction_nrmse": 0.007999008376889409
            }
          }
        },
        {
          "noise": 0.001,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0011351301380104065,
                "nrmse_extrap_horizon": 0.003509524782279507,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0019661403801873047,
                "nrmse_extrap_horizon": 0.005774019532039639,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0010715221674451783,
                "nrmse_extrap_horizon": 0.0032688278355965717,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.006321391453860764,
                "nrmse_extrap_horizon": 0.018205247560560325,
                "finite": true
              },
              "flux_nrmse": 0.003951142976930983,
              "reaction_nrmse": 0.358704194841073,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49816241828969265
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.06044754772266706
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12018469341407316
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 6.601387746130198e-05,
                "nrmse_extrap_horizon": 0.00018493449141903599,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00017584247324195615,
                "nrmse_extrap_horizon": 0.0005556752843751426,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 6.387027767148915e-05,
                "nrmse_extrap_horizon": 0.00018057295108707904,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0016422056553320188,
                "nrmse_extrap_horizon": 0.004562228622767658,
                "finite": true
              },
              "flux_nrmse": 1.895844728862169e-05,
              "reaction_nrmse": 0.10653908916401635,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4999970435998426
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.059995151494866054
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.1254523254370158
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.046340206406173194
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.0002498847024560679,
                "nrmse_extrap_horizon": 0.0006065239647469353,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0005815983818557042,
                "nrmse_extrap_horizon": 0.0015076312096199088,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00023218193518439038,
                "nrmse_extrap_horizon": 0.000496078042532287,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.015631765953069303,
                "nrmse_extrap_horizon": 0.037096941450240506,
                "finite": true
              },
              "flux_nrmse": 0.14701523867669392,
              "reaction_nrmse": 0.006221562259064586
            }
          }
        },
        {
          "noise": 0.005,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.004649379159035079,
                "nrmse_extrap_horizon": 0.012697923186739953,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00909483609972609,
                "nrmse_extrap_horizon": 0.02439622748067422,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.004184240610564892,
                "nrmse_extrap_horizon": 0.011077580146965221,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.029838896817977724,
                "nrmse_extrap_horizon": 0.07788261684849566,
                "finite": true
              },
              "flux_nrmse": 0.22687327467876517,
              "reaction_nrmse": 0.37141726015627224,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 2,
                  "coefficient": -0.2805224613249141
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05907117509174014
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.1220620581882865
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.00010959218146353732,
                "nrmse_extrap_horizon": 0.0003264032588002428,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00033715502523630074,
                "nrmse_extrap_horizon": 0.0010987003676040917,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 9.872711961941064e-05,
                "nrmse_extrap_horizon": 0.00029580867177823194,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0020481748397804685,
                "nrmse_extrap_horizon": 0.005766556530638491,
                "finite": true
              },
              "flux_nrmse": 0.0008403239148835321,
              "reaction_nrmse": 0.12816413213676078,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.5004308786413836
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.060006666703920415
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12502858568799904
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.04233135162124965
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.000282995837897466,
                "nrmse_extrap_horizon": 0.0007156334271274372,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0006455059267480421,
                "nrmse_extrap_horizon": 0.001745916138338422,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00026914779681613636,
                "nrmse_extrap_horizon": 0.0006047162205187048,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.015331340194522671,
                "nrmse_extrap_horizon": 0.035947072657034305,
                "finite": true
              },
              "flux_nrmse": 0.14127563117539774,
              "reaction_nrmse": 0.052127096030055824
            }
          }
        },
        {
          "noise": 0.01,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.014773239734650511,
                "nrmse_extrap_horizon": 0.0450387736079953,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.013029455896220217,
                "nrmse_extrap_horizon": 0.039573958742260086,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.015219256099637367,
                "nrmse_extrap_horizon": 0.04598298023461564,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.012646842018025121,
                "nrmse_extrap_horizon": 0.03738714796805,
                "finite": true
              },
              "flux_nrmse": 0.06571939207442865,
              "reaction_nrmse": 0.34179617825627645,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -1.0217212966729499
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05934165064450331
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.07520699810160991
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.00023180929250236093,
                "nrmse_extrap_horizon": 0.0007025335941661741,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00047699096553399076,
                "nrmse_extrap_horizon": 0.0014014928545844903,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00021022122352758513,
                "nrmse_extrap_horizon": 0.0006735981195477474,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0022081275606831,
                "nrmse_extrap_horizon": 0.006190681257411242,
                "finite": true
              },
              "flux_nrmse": 0.0007520593418776613,
              "reaction_nrmse": 0.13645655315070787,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4998180885152329
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.0601780357372315
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12544275985931377
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.04138405760213182
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.0004987020730912908,
                "nrmse_extrap_horizon": 0.0014769285031259495,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0011090062121136117,
                "nrmse_extrap_horizon": 0.003194071356185666,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0004195013264323075,
                "nrmse_extrap_horizon": 0.00124470943293542,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.018969979051971425,
                "nrmse_extrap_horizon": 0.04690752775908329,
                "finite": true
              },
              "flux_nrmse": 0.16372815526992054,
              "reaction_nrmse": 0.08532676068123543
            }
          }
        },
        {
          "noise": 0.02,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.036280237701412484,
                "nrmse_extrap_horizon": 0.10633323655486213,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.03662520425629463,
                "nrmse_extrap_horizon": 0.14635289157571552,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0374518431901691,
                "nrmse_extrap_horizon": 0.12667474167375153,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.028920051675226596,
                "nrmse_extrap_horizon": 0.08642415236049922,
                "finite": true
              },
              "flux_nrmse": 0.30471726940945165,
              "reaction_nrmse": 0.2674365401705129,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.5168487809346507
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": 0.11181188713382291
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": 0.1202930337235925
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0010488663206850764,
                "nrmse_extrap_horizon": 0.0032027225112926543,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0020623379328146953,
                "nrmse_extrap_horizon": 0.006581489775135089,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0009716175740869962,
                "nrmse_extrap_horizon": 0.0029841254369282638,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0064235628210923676,
                "nrmse_extrap_horizon": 0.018802726845920218,
                "finite": true
              },
              "flux_nrmse": 0.0037440310975910586,
              "reaction_nrmse": 0.3618676159570631,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.5018926609254077
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.060170818243634606
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12065918219823943
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.0006177491530757048,
                "nrmse_extrap_horizon": 0.001893275065360028,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0016865229982347607,
                "nrmse_extrap_horizon": 0.005064437761651686,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0005400148579811755,
                "nrmse_extrap_horizon": 0.0016539910081514522,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.02252671844592676,
                "nrmse_extrap_horizon": 0.05853762568906336,
                "finite": true
              },
              "flux_nrmse": 0.18352847211042095,
              "reaction_nrmse": 0.19949981574002115
            }
          }
        }
      ]
    },
    {
      "config": {
        "noise": [
          0.0,
          0.001,
          0.005,
          0.01,
          0.02
        ],
        "nx": 64,
        "test_nx": 128,
        "train_steps": 160,
        "test_steps": 400,
        "dt": 0.002,
        "nu": 0.03,
        "n_train": 8,
        "train_amplitude": 0.65,
        "test_amplitude": 0.95,
        "point_stride": 4,
        "window": 24,
        "window_stride": 8,
        "max_mode": 8,
        "max_frequency": 6,
        "max_terms": 8,
        "ridge": 1e-07,
        "seed": 20260912,
        "out": "operator_compiled_noisy_weakform_seed20260912_outputs",
        "smoke": false
      },
      "results": [
        {
          "noise": 0.0,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 8.60116228820108e-06,
                "nrmse_extrap_horizon": 2.5733045515588574e-05,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 1.873801682645331e-05,
                "nrmse_extrap_horizon": 5.418617650234501e-05,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 1.2484610690760535e-05,
                "nrmse_extrap_horizon": 3.679652315065053e-05,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 1.7674163754424954e-05,
                "nrmse_extrap_horizon": 5.7027049967553025e-05,
                "finite": true
              },
              "flux_nrmse": 5.822276515138403e-05,
              "reaction_nrmse": 0.010952857667115191,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49997725781376223
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.05998986839552499
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.012624316610038577
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.1845067199129428
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.22485054834738566
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 3.839302301585506e-07,
                "nrmse_extrap_horizon": 1.1777767268669175e-06,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 2.478536755698461e-06,
                "nrmse_extrap_horizon": 7.34181632780882e-06,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 2.4658208090573784e-07,
                "nrmse_extrap_horizon": 6.422705929000605e-07,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 2.134841923727232e-06,
                "nrmse_extrap_horizon": 6.5130633602919735e-06,
                "finite": true
              },
              "flux_nrmse": 1.1985301917312719e-05,
              "reaction_nrmse": 0.004551627976940109,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49999218701261755
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.059999903953820974
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.04455867920845365
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.154974122429207
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": -0.006671849242860416
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.08768146988229356
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 1,
                  "coefficient": 0.09321486319297567
                },
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 4,
                  "coefficient": -1.2991792134155735e-06
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00013408247310963442,
                "nrmse_extrap_horizon": 0.00034817669980167734,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0007977247185017238,
                "nrmse_extrap_horizon": 0.0021346388422572916,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00015590349663350436,
                "nrmse_extrap_horizon": 0.00032817158771301127,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0006808997106745973,
                "nrmse_extrap_horizon": 0.0019296747255904338,
                "finite": true
              },
              "flux_nrmse": 0.1773144915498188,
              "reaction_nrmse": 0.02079773930465652
            }
          }
        },
        {
          "noise": 0.001,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0010877824371914244,
                "nrmse_extrap_horizon": 0.0033529775705284206,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0021723631049287576,
                "nrmse_extrap_horizon": 0.006531283505067647,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0016636362591800646,
                "nrmse_extrap_horizon": 0.005196931377881989,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0021687741656027473,
                "nrmse_extrap_horizon": 0.005584984687660462,
                "finite": true
              },
              "flux_nrmse": 0.00719568592009058,
              "reaction_nrmse": 0.36537803747422337,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49763514123267594
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.061483165642601034
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12117982106044975
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 5.6766207965006244e-05,
                "nrmse_extrap_horizon": 0.0001655846055292331,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00015466030510006803,
                "nrmse_extrap_horizon": 0.000475050435173127,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 5.914214161845494e-05,
                "nrmse_extrap_horizon": 0.00016700439442941746,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.00014036020724746403,
                "nrmse_extrap_horizon": 0.000477084559688666,
                "finite": true
              },
              "flux_nrmse": 0.00010832520214059257,
              "reaction_nrmse": 0.10606344507345913,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.5000119189009611
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.059971597092101515
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.1255502071275943
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.04651374636243603
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.0001378684220794022,
                "nrmse_extrap_horizon": 0.0003629821402948881,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0008090106956924927,
                "nrmse_extrap_horizon": 0.002168466901251425,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00015801113693044756,
                "nrmse_extrap_horizon": 0.0003361452807886165,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.000694351936453976,
                "nrmse_extrap_horizon": 0.0019477080129189236,
                "finite": true
              },
              "flux_nrmse": 0.17884930014373296,
              "reaction_nrmse": 0.05574781830709109
            }
          }
        },
        {
          "noise": 0.005,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.003744170685043566,
                "nrmse_extrap_horizon": 0.011841861458716565,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.007502846643411286,
                "nrmse_extrap_horizon": 0.0239075007561503,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.005201569174437519,
                "nrmse_extrap_horizon": 0.015433033380711357,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.007828399158855352,
                "nrmse_extrap_horizon": 0.022320284725084735,
                "finite": true
              },
              "flux_nrmse": 0.050499181945792025,
              "reaction_nrmse": 0.9021211651441667,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -1.0437949343545072
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.06411743701315349
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 1,
                  "coefficient": 0.23201187925020225
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 9.418301562061114e-05,
                "nrmse_extrap_horizon": 0.00028382080243245724,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00020086493049993728,
                "nrmse_extrap_horizon": 0.0005630644020843266,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00011034543921540005,
                "nrmse_extrap_horizon": 0.00033650331263155946,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0002062317695049866,
                "nrmse_extrap_horizon": 0.0005297929825081749,
                "finite": true
              },
              "flux_nrmse": 0.0014427698053944978,
              "reaction_nrmse": 0.10595763377446774,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49925989796961345
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.059998460844147374
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12554162646987035
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": -0.04652322135716337
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00015797562750277742,
                "nrmse_extrap_horizon": 0.0004225756936190484,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0009523442024533342,
                "nrmse_extrap_horizon": 0.002723898344772669,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00021003836619248599,
                "nrmse_extrap_horizon": 0.0005192095220332017,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0008296617017524315,
                "nrmse_extrap_horizon": 0.0026115353972874593,
                "finite": true
              },
              "flux_nrmse": 0.1820365417217716,
              "reaction_nrmse": 0.05065643745933919
            }
          }
        },
        {
          "noise": 0.01,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.005460782964272085,
                "nrmse_extrap_horizon": 0.016099151736124816,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.010697765205089669,
                "nrmse_extrap_horizon": 0.031989537554633116,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.006324580670125356,
                "nrmse_extrap_horizon": 0.0185620370989641,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.011425294553876007,
                "nrmse_extrap_horizon": 0.03323245260992988,
                "finite": true
              },
              "flux_nrmse": 0.2564816079975666,
              "reaction_nrmse": 0.8696568198753589,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 2,
                  "coefficient": -0.2683243409487909
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.060078323868554426
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 1,
                  "coefficient": 0.19377991440046544
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0001611418459895899,
                "nrmse_extrap_horizon": 0.00048282348125888524,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00028135178052067354,
                "nrmse_extrap_horizon": 0.0008508399161712803,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00017144004190532188,
                "nrmse_extrap_horizon": 0.000549338269082153,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.00025452322917663637,
                "nrmse_extrap_horizon": 0.0007148729388785211,
                "finite": true
              },
              "flux_nrmse": 0.00039115913108116597,
              "reaction_nrmse": 0.20152658293669892,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.49998934335342526
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.060104857783627244
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.08801684187949234
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": 0.025477910607271302
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00034061774062998484,
                "nrmse_extrap_horizon": 0.0009638185325383425,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0008049645676700969,
                "nrmse_extrap_horizon": 0.002204330512409548,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0004440947017660905,
                "nrmse_extrap_horizon": 0.0013133270647051024,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0007883360276577823,
                "nrmse_extrap_horizon": 0.0021295644138354594,
                "finite": true
              },
              "flux_nrmse": 0.14489989499590814,
              "reaction_nrmse": 0.2200666364657907
            }
          }
        },
        {
          "noise": 0.02,
          "weak_rows": 2448,
          "models": {
            "pointwise_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.0226042779149432,
                "nrmse_extrap_horizon": 0.0740203312886859,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0588637523053355,
                "nrmse_extrap_horizon": 0.2763782785148143,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.0262956991754146,
                "nrmse_extrap_horizon": 0.07989136502476014,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.06021518943704649,
                "nrmse_extrap_horizon": 0.2506663445859131,
                "finite": true
              },
              "flux_nrmse": 0.24463516830758228,
              "reaction_nrmse": 7.068920903653162,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "cos",
                  "order_or_frequency": 1,
                  "coefficient": -1.021941561746114
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 3,
                  "coefficient": 0.09003794558528704
                },
                {
                  "edge": "reaction",
                  "kind": "poly",
                  "order_or_frequency": 3,
                  "coefficient": 1.2007554435218868
                }
              ]
            },
            "spacetime_weak_pole": {
              "params": 30,
              "id": {
                "nrmse_fit_horizon": 0.000588113556630719,
                "nrmse_extrap_horizon": 0.0017558111941841112,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.0017686372687236638,
                "nrmse_extrap_horizon": 0.005487269308904535,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.000629002482441078,
                "nrmse_extrap_horizon": 0.0017296754655075346,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0017678184020733195,
                "nrmse_extrap_horizon": 0.005648322325546962,
                "finite": true
              },
              "flux_nrmse": 0.000825032311886907,
              "reaction_nrmse": 0.3631805126463027,
              "active_operator_atoms": [
                {
                  "edge": "flux",
                  "kind": "poly",
                  "order_or_frequency": 2,
                  "coefficient": 0.4995786766079158
                },
                {
                  "edge": "flux",
                  "kind": "sin",
                  "order_or_frequency": 4,
                  "coefficient": 0.06002095898291779
                },
                {
                  "edge": "reaction",
                  "kind": "sin",
                  "order_or_frequency": 2,
                  "coefficient": 0.12085460744728345
                }
              ]
            },
            "spacetime_weak_poly5": {
              "params": 10,
              "id": {
                "nrmse_fit_horizon": 0.00038219774321834383,
                "nrmse_extrap_horizon": 0.0011008378034530716,
                "finite": true
              },
              "amplitude_ood": {
                "nrmse_fit_horizon": 0.00168489807885774,
                "nrmse_extrap_horizon": 0.005207305190986574,
                "finite": true
              },
              "resolution_ood": {
                "nrmse_fit_horizon": 0.00037891686321164244,
                "nrmse_extrap_horizon": 0.0010926395050223283,
                "finite": true
              },
              "joint_ood": {
                "nrmse_fit_horizon": 0.0016011086643542328,
                "nrmse_extrap_horizon": 0.005325113559370276,
                "finite": true
              },
              "flux_nrmse": 0.1967289001707914,
              "reaction_nrmse": 0.6832589820774813
            }
          }
        }
      ]
    }
  ],
  "sources": {
    "operator_compiled_constitutive_kan_fd_seed20260910_outputs/metrics.json": "81e4fbb30b8fec59a49eb8be32561fa531f3847161c889960f660948a535d70e",
    "operator_compiled_constitutive_kan_fd_seed20260911_outputs/metrics.json": "93efb76a09726e8e35ecdcbda8e7885977bae305f2acc76485caffb55259062e",
    "operator_compiled_constitutive_kan_fd_seed20260912_outputs/metrics.json": "86782e44b5b998ebfd16587ffad0cd929d5b18c28839892cd5e92181330debc1",
    "operator_compiled_noisy_weakform_seed20260910_outputs/metrics.json": "f222e446f37aad483e4a23566dcfbb9646b5a8d3a4c3bb1cb9254c4d71ade14b",
    "operator_compiled_noisy_weakform_seed20260911_outputs/metrics.json": "ad2f38084c63a40486b69f8bd026a2a0380cd9894d97574f9164861bc8d29b14",
    "operator_compiled_noisy_weakform_seed20260912_outputs/metrics.json": "cb34b81a4f805e77c3e2c509a373b8899fca6375dd15ebd583daa31c464703f9"
  },
  "new_training": false,
  "summary": {
    "oscillatory": {
      "oc_ckan": {
        "median": 0.1870416006266388,
        "all": [
          0.17707519281380138,
          0.27636879936206404,
          0.1870416006266388
        ]
      },
      "anchored_oc_ckan": {
        "median": 0.1423345345806753,
        "all": [
          0.13573288290257707,
          0.2522576347321122,
          0.1423345345806753
        ]
      },
      "pole_atlas": {
        "median": 9.287207539999268e-07,
        "all": [
          8.47542344852383e-06,
          6.34678120734044e-07,
          9.287207539999268e-07
        ]
      },
      "pole_oc_ckan": {
        "median": 4.2721297370105346e-05,
        "all": [
          0.0001943083612634113,
          4.65052422449056e-06,
          4.2721297370105346e-05
        ]
      },
      "sindy_poly5": {
        "median": 0.06476962069221905,
        "all": [
          0.04188734291836722,
          0.09678616864487403,
          0.06476962069221905
        ]
      },
      "linear": {
        "median": 0.45382976851333606,
        "all": [
          0.3921748400198576,
          0.4925824037052897,
          0.45382976851333606
        ]
      },
      "direct_ckan": {
        "median": 0.3299771074715571,
        "all": [
          0.1654895999149823,
          0.3420618738082253,
          0.3299771074715571
        ]
      },
      "mlp": {
        "median": 0.29774823982167264,
        "all": [
          0.09176026174719727,
          0.29774823982167264,
          0.3301218190791899
        ]
      }
    },
    "saturating": {
      "oc_ckan": {
        "median": 0.1643921302510879,
        "all": [
          0.1643921302510879,
          0.22819460730577665,
          0.15160422140880367
        ]
      },
      "anchored_oc_ckan": {
        "median": 0.07783295413677081,
        "all": [
          0.07783295413677081,
          0.14938471117417657,
          0.0771694620858159
        ]
      },
      "pole_atlas": {
        "median": 0.005198945087941907,
        "all": [
          0.0030660913191592966,
          0.008152607590298693,
          0.005198945087941907
        ]
      },
      "pole_oc_ckan": {
        "median": 0.005187352271967678,
        "all": [
          0.0030523350544833087,
          0.008146669852022066,
          0.005187352271967678
        ]
      },
      "sindy_poly5": {
        "median": 0.04113403651272089,
        "all": [
          0.04113403651272089,
          0.12125131124362314,
          0.03840415998588077
        ]
      },
      "linear": {
        "median": 0.33321432762293013,
        "all": [
          0.28857433223308365,
          0.3455885686745214,
          0.33321432762293013
        ]
      },
      "direct_ckan": {
        "median": 0.18393687935472966,
        "all": [
          0.08785637240695007,
          0.18393687935472966,
          0.21635747228983532
        ]
      },
      "mlp": {
        "median": 0.11651181485202529,
        "all": [
          0.040166686998269426,
          0.1218948215004068,
          0.11651181485202529
        ]
      }
    }
  },
  "weak_summary": {
    "0.01": {
      "pointwise_pole": 0.038444802710976854,
      "spacetime_weak_pole": 0.0014014928545844903,
      "spacetime_weak_poly5": 0.003194071356185666
    },
    "0.02": {
      "pointwise_pole": 0.14635289157571552,
      "spacetime_weak_pole": 0.006581489775135089,
      "spacetime_weak_poly5": 0.005207305190986574
    }
  }
}