Research & AlgorithmsDANIEL SCHMITTER · RESEARCH & ENGINEERING

Physical systems · Research & Algorithms

How small can a learned drone model become?

A tiny dynamics program can be dramatically cheaper than a neural ensemble without being more accurate. That tradeoff is worth measuring honestly.

Daniel Schmitter · Research story · Revised draft

Read the paper ↗Paper PDF
EXPLORE THE IDEA

A smaller onboard model

Program size and prediction quality are different axes.

AI-generated editorial physical contextEditorial illustration
RETAINED PROGRAMSmall is a resource result24,288bytes · compact program≈24.79 MBsource + adapted neural programsNeural ensemble wins predictive accuracy
50%
AI-generated editorial nano-drone. Sizes are archived retained-program counts: 24,288 bytes compact versus approximately 24.79 MB for source-plus-adapted neural programs. They are not total process memory. The adapted ensemble was more accurate. The reveal is not a flight replay.

Follow the information

From input to outcome

The compact program receives a requested horizon and predicts displacement directly. It does not repeatedly roll its own predicted state through a long learned trajectory. Teacher acquisition and adaptation costs are separate from retained runtime arrays.

Scroll the diagram horizontally to follow the route. Keyboard: focus the diagram, then use the arrow keys.

Rotor commands → Actuator-memory bank → Physical feature vector → Direct horizon readout → Predicted displacement. The compact program receives a requested horizon and predicts displacement directly. It does not repeatedly roll its own predicted state through a long learned trajectory. Teacher acquisition and adaptation costs are separate from retained runtime arrays.
Information-flow map. Base compact architecture; the later hybrid adds different translation/angular components. Original vector schematic based on the method and evidence discussed in this article; signal shapes and icons are illustrative, not additional measurements. Open full-size diagram ↗

Read the main route from left to right; labelled side branches show additional inputs, checks or feedback. The sections below explain the operations and their experimental limits.

The goal is a useful onboard component

A small aircraft has little room for computation, but modeling its dynamics can require memory of past motor commands and several physical outputs. Our program uses exact sampled actuator-memory recurrences, rotor mixtures, and direct horizon-dependent readouts. It predicts displacement; it does not autonomously fly the drone.

zt+1=e−Δt/τzt+(1−e−Δt/τ)ut\begin{gathered}z_{t+1}=e^{-\Delta t/\tau}z_t+(1-e^{-\Delta t/\tau})u_t\end{gathered}
A held command updates an actuator-memory coordinate exactly for its assumed first-order dynamics. Unknown physical behavior still has to be identified.

Separate the tiny program from the entire learner

The compact drone model predicts displacement over a requested horizon from causal traces and physical features. It does not recursively feed its predicted future state back through fifty steps of the same learned network. That direct interface is part of its computational advantage and part of its limitation.

The strong comparison adapts a released neural ensemble on a related sparse endpoint task. The operator program is far smaller and cheaper to fit, but its four groups of physical errors are all worse. A later hybrid uses teacher execution statistics and different translation/angular components; its improved accuracy comes with additional inherited learning and prior exposure.

Compress the state, then fit the response
Compress the state, then fit the response. Original scientific diagram; the stated component and information flow, not an additional experiment. Open full-size figure ↗

A strong comparator changed the headline

An early comparison looked favorable against published numbers under different observation protocols. The later study reproduced a released ASIA neural ensemble and adapted both approaches using corresponding sparse Melon-flight tasks. On the same 130 run-three starts, the adapted neural model wins position, velocity, orientation, and angular-velocity accuracy. That is the relevant accuracy conclusion.

The resource difference is still substantial

The compact program retains 24,288 bytes versus about 24.79 MB for the source-plus-adapted neural programs—roughly 1,020 times less. Measured compilation takes 1.538 seconds versus 101.33 seconds of target optimization. Label counts are close but unequal: 3,250 versus 3,380. These are program and fitting measurements, not total runtime RSS, battery consumption, or weak-device timing.

Combining mechanisms helped, with a remaining gap

A later post-exposure program uses a recurrent model for translation and direct heads for angular outputs. It consolidates pseudo-experience from more than one teacher execution through additive Grams. Its mean physical error ratio to the adapted ensemble becomes 1.1218, while retained size remains about 314 times smaller. The teacher disappears at runtime but its acquisition cost is not free.

Find the application on the error–resource frontier

For an onboard use case, the question is whether this error–resource tradeoff meets a real tolerance: perhaps a monitoring estimate, a planning approximation, or a fallback model. The archive has not tested that decision. The scientific result is a measured frontier and an explanation of what the small program contains—not a demonstration that a tiny network can replace the drone controller.

The meaningful frontier

A deployment may accept a small accuracy cost to obtain a much smaller model; another may not. Neither answer can be chosen from a compression ratio alone. The next application would need to show that the compact model meets the controller’s actual tolerance on the intended hardware. The current paper establishes a predictive accuracy–resource tradeoff, not a flight-control breakthrough.

Evidence & further reading

The links below distinguish the project record from foundational literature. This revised story does not add a new application-validation experiment.

  1. Consolidated research results, including constitutive edges and continual memory. Daniel Schmitter (2026). Local archive snapshot.
  2. Consolidated limitations and research boundaries. Daniel Schmitter (2026). Local archive snapshot.
  3. Experiment-family evidence map. Spline research archive (2026). Local archive snapshot.

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