A small world.
A model that learns it.

Dynamics learning predicts the consequence of an action. Random exploration is useful because we need examples of many movements, not just successful ones. Browse transitions: the same action can have different effects depending on the pointer’s existing speed.

Imitation learning instead predicts the action a demonstrator would choose in a situation. We are not doing that here: there is no expert player to copy and no training objective to pick winning moves. The data teaches how the world responds, not which goal to pursue.

Coverage matters: behavior never seen during collection may be predicted poorly. We vary motor strength and damping to expose the model to more than one exact simulated setup. Saved features are measurements from pixels; raw images are not retained in this dataset.

Training loss measures error on examples used to update the model. Validation loss measures error on episodes it does not train on. If training error falls while validation error rises, the model may be fitting the training examples without improving on new ones. Holding out entire episodes avoids mixing neighboring frames from the same recording into both sets.

The chart combines angle and speed errors after scaling them. The degree metric is easier to interpret: it measures next-angle error against the image-derived measurement. It does not measure success at reaching a target, and it does not include all camera measurement error.

What is learned? Only the dynamics. Color detection and image rendering are still programmed. MIRA learns to generate visual outcomes; this smaller, structured model lets us study the prediction-and-control loop before adding learned vision. Motor strength and damping are hidden inputs, so this model learns a typical response across their training range.

Compare Drive right → coast with Drive right → brake left → hold. Scrub the timeline and watch when the two pointers diverge. The error shown averages their angle differences over the rollout. It is not the validation error from the previous step: predicting many steps without correction is a harder test.

This model is not choosing the actions. You provide them. It predicts consequences, without deciding which consequence is desirable. That decision is the next step.

For this tiny task, the programmed simulator is already cheap and accurate. The learned copy is useful as a learning experiment, not because it is a better replacement. The wider motivation is learning usable dynamics from experience when writing an accurate simulator is difficult. Success here does not prove that broader capability or physical transfer.

No separate policy network is trained here. The action chooser is a programmed planner using learned dynamics. A different design could train a policy to choose actions directly. The model and the mechanism that selects actions are distinct components.

Change motor strength or damping beyond the training ranges to test distribution shift: the controller now faces unfamiliar dynamics. Fresh observations help it recover from prediction errors, but do not guarantee success. Compare with the simple visual controller below; a learned model is not automatically better.

Success is defined narrowly: within about 4.6° of the target for one continuous second at any point in a ten-second trial. A pointer can satisfy that and drift later, which is why final error is also shown. The playback shows a computed simulation run, not a live robot.

Sim-to-real comes next: replace rendered observations with camera measurements and map actions to a servo. Camera geometry, latency, and motor response must match closely enough—or require adaptation. Physical transfer is not implemented or verified by these simulation results.