Symmetry-Informed Governing Equation Discovery

TL;DR

This paper introduces a symmetry-informed approach to governing equation discovery that leverages physical invariances to enhance accuracy, simplicity, and robustness of learned models across dynamical systems.

Contribution

It develops a method to incorporate symmetry constraints into equation discovery algorithms, improving their performance and interpretability.

Findings

Enhanced robustness against noise in equation discovery.

Higher probability of correctly recovering governing equations.

Applicable to diverse dynamical systems.

Abstract

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may search an unnecessarily large space and discover less accurate or overly complex equations. In this paper, we propose to leverage symmetry in automated equation discovery to compress the equation search space and improve the accuracy and simplicity of the learned equations. Specifically, we derive equivariance constraints from the time-independent symmetries of ODEs. Depending on the types of symmetries, we develop a pipeline for incorporating symmetry constraints into various equation discovery algorithms, including sparse regression and genetic programming. In experiments across diverse dynamical systems, our approach demonstrates better robustness against noise and recovers governing equations with significantly higher probability than baselines without symmetry. Our codebase is available at https://github.com/Rose-STL-Lab/symmetry-ode-discovery.