Robust discovery of governing equations through symmetry

ICLR 2026 Conference Submission24790 Authors

Keywords: Dynamical systems, Equation discovery, Symmetry, Noisy and sparse data

TL;DR: Robust equation discovery via symmetry identification

Abstract: Discovering governing equations of dynamical systems directly from data remains a fundamental challenge, especially under noise and data scarcity. We propose a symmetry-inspired symbolic regression (SI-SR) framework that automatically identifies intrinsic physical invariances and embeds them into a symmetry-constrained variable set, enhancing robustness and promoting sparsity. The framework combines a validation step for symmetry confirmation with symbolic regression for expressive nonlinear modelling. We evaluate SI-SR on canonical partial differential equations (PDEs) and variable-coefficient systems, with systematic comparisons against state-of-the-art baselines. Results show that leveraging symmetry reduces redundancy and enables the recovery of compact, accurate models. This establishes symmetry as a powerful inductive bias for data-driven equation discovery.

Primary Area: learning on time series and dynamical systems

Submission Number: 24790