Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery

2026-01-29

AI Summary

Recovering interpretable governing equations of dynamical systems from noisy, partially observed data remains highly challenging, as existing approaches often fail due to black-box modeling or sensitivity to noise. This work proposes the MAAT framework, which uniquely integrates structural and semantic priors—such as non-negativity and conservation laws—directly into the state reconstruction objective within a reproducing kernel Hilbert space. This yields smooth, physically consistent state trajectories along with their analytical derivatives, providing high-quality inputs for symbolic regression. By bridging fragmented observations to interpretable dynamical models in an end-to-end manner, MAAT substantially reduces mean squared errors in both states and their derivatives across twelve scientific benchmarks under diverse noise conditions, outperforming strong baseline methods.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Feature Construction/Reformulation
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• dynamical system discovery
• governing equations
• noisy observations
• partial observations
• interpretable modeling

Innovation

• Kernel State Reconstruction
• Symbolic Regression
• Knowledge-Informed Priors
• Dynamical System Discovery
• Reproducing Kernel Hilbert Space