Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery
This addresses the challenge of interpretable dynamical system discovery for scientific applications, though it is incremental as it builds on existing symbolic regression methods.
The paper tackles the problem of recovering governing equations from noisy, partial observations by introducing MAAT, a framework that incorporates structural priors into kernel state reconstruction, which reduced state-estimation MSE across twelve benchmarks.
Recovering governing equations from data is central to scientific discovery, yet existing methods often break down under noisy, partial observations, or rely on black-box latent dynamics that obscure mechanism. We introduce MAAT (Model Aware Approximation of Trajectories), a framework for symbolic discovery built on knowledge-informed Kernel State Reconstruction. MAAT formulates state reconstruction in a reproducing kernel Hilbert space and directly incorporates structural and semantic priors such as non-negativity, conservation laws, and domain-specific observation models into the reconstruction objective, while accommodating heterogeneous sampling and measurement granularity. This yields smooth, physically consistent state estimates with analytic time derivatives, providing a principled interface between fragmented sensor data and symbolic regression. Across twelve diverse scientific benchmarks and multiple noise regimes, MAAT substantially reduces state-estimation MSE for trajectories and derivatives used by downstream symbolic regression relative to strong baselines.