Symmetry-Informed Governing Equation Discovery

Jianke Yang, Wang Rao, Nima Dehmamy, Robin Walters, Rose Yu

Keywords: Equation Discovery, Dynamical Systems, Symmetry, Equivariant Neural Networks, Symbolic Regression, Lie Group, Ordinary Differential Equation, Lie Point Symmetry

TL;DR: A new approach to improve equation discovery of dynamical systems with symmetry priors

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.

Primary Area: Machine learning for physical sciences (for example: climate, physics)

Submission Number: 12120