Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery

TL;DR

This paper introduces MAAT, a knowledge-informed kernel framework that improves state reconstruction from noisy, partial data, enabling more accurate discovery of governing equations in scientific systems.

Contribution

MAAT uniquely integrates structural and semantic priors into kernel-based state reconstruction, enhancing interpretability and robustness in dynamical system discovery.

Findings

Significantly reduces state-estimation MSE across benchmarks

Provides smooth, physically consistent state estimates with derivatives

Outperforms strong baselines in noisy regimes

Abstract

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.