Title: Sample Efficient Forced Dynamics Recovery
Primary area: learning on time series and dynamical systems
Keywords: equation discovery, liquid time constant networks, SINDY

Abstract: Recovering governing equations of dynamical systems from limited samples is critical for deploying autonomous systems under real-world resource constraints. Classical sparse regression methods (e.g., SINDy-MPC) and physics-informed neural networks achieve good fits when oversampled, but their accuracy degrades sharply when data is available only at the Nyquist rate. We provide an information-theoretic analysis showing that reconstruction error fundamentally decomposes into a data-fit component (linear in sampling frequency) and a model-estimation component (nonlinear in frequency), bounded by the Cramér–Rao lower bound. This motivates MRIDHA, a model recovery framework that constrains the equation search space to physically consistent structures by embedding continuous-time latent variable nodes that enforce stability and time-constant properties. Across nine simulated and three real-world benchmarks—including automated insulin delivery, EEG reconstruction, and a 16D quadcopter—MRIDHA significantly outperforms SINDy-MPC and PINN-SR at Nyquist-rate sampling, demonstrating improved sample efficiency, robustness to input uncertainty, and scalability. Our results establish both new theoretical limits and a practical method for sample-efficient recovery of forced dynamics.

TL;DR: We introduce MRIDHA, a constrained model recovery framework that enforces physical consistency and achieves state-of-the-art reconstruction of forced dynamics at Nyquist-rate sampling across six simulation and three real-world benchmarks.