Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery

• URL: http://arxiv.org/abs/2601.22328v1
• Date: Thu, 29 Jan 2026 21:15:52 GMT
• Title: Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery
• Authors: Luca Muscarnera, Silas Ruhrberg Estévez, Samuel Holt, Evgeny Saveliev, Mihaela van der Schaar,
• Abstract summary: MAAT (Model Aware Approximation of Trajectories) is a framework for symbolic discovery built on knowledge-informed Kernel State Reconstruction.<n>It substantially reduces state-estimation MSE for trajectories and derivatives used by downstream symbolic regression.
• Score: 46.9843470803458
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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