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Learning Hybrid Dynamics Models with Simulator-Informed Latent States
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Proposes a hybrid dynamics model that informs the latent states of a learned GRU-residual model via a trainable KKL observer driven by a black-box simulator's outputs, plus a GRU residuum for non-observable parts.
Problem
Learned recurrent dynamics models are not physically meaningful and accumulate errors over long horizons, while black-box numerical simulators are inaccurate due to modeling simplifications and expose only output trajectories, not latent states.
Approach
Split latent states into simulator-observable (OVS) states, propagated implicitly by a learned KKL observer that receives simulator outputs as input, and non-OVS states driven by a GRU residuum; the simulator thus continuously corrects the observable latent states, and the residuum can be damped over time.
Key results
- KKL-RNN achieves RMSE 0.16 on damped oscillations vs 1.02 for GRU and 0.27 for Hybrid GRU.
- On the double-torsion pendulum, KKL-RNN reaches RMSE 0.24 vs 0.51 for Hybrid GRU and 1.39 for GRU.
- On the Van-der-Pol pure learning task, KKL-RNN reaches RMSE 0.02 vs 0.09 for Hybrid GRU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a simulator-informed KKL observer with an exponentially damped GRU residuum instead of a Hybrid GRU | Hybrid KKL-RNN · System i) Damped oscillations | RMSE: 0.27 (0.08) -> 0.16 (0.03) | Helped |
| Use a simulator-informed KKL observer instead of a Hybrid GRU | Hybrid KKL-RNN · System ii) Double-torsion pendulum | RMSE: 0.51 (0.04) -> 0.24 (0.02) | Helped |
| Use a simulator-informed KKL observer instead of a Hybrid GRU | Hybrid KKL-RNN · System iii) Drill-string system | RMSE: 0.26 (0.01) -> 0.23 (0.01) | Helped |
| Use a simulator-informed KKL observer instead of a Hybrid GRU | KKL-RNN with a learned simulator substitute · System iv) Van-der-Pol oscillator (pure learning-based) | RMSE: 0.09 (0.065) -> 0.02 (0.001) | Helped |
| Replace the KKL observer with GRU architectures for the partially OVS system (ablation) | Hybrid KKL-RNN · Partially OVS systems | accuracy | Hurt |
Surprising findings
- Standard residual model shows unphysical behavior on the damped oscillation system, and the GRU baseline can underestimate or ignore the simulator input.
Limitations
- Only a single trajectory is observed per experiment and evaluations use four relatively small systems.
- Latent states have no direct physical interpretation.
- Results for Hybrid GRU are comparable on the drill-string system, so advantage is not uniform.
Experimental setup
Datasets: simulated damped oscillations double-torsion pendulum measurements and simulation drill-string measurements and simulator simulated Van-der-Pol oscillator
Benchmarks: damped oscillations double-torsion pendulum drill-string system Van-der-Pol oscillator
Metrics: RMSE
Baselines: GRU Hybrid GRU Residual model Filter Sim
Builds on: KKL observer GRU residual modeling
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