Symmetry inspired learning of governing equations from noisy data

Discovering governing equations from data that characterize the behavior of dynamical systems is a fundamental task in physics and engineering. A central challenge in practical scenarios is eliminating redundant terms, particularly when data are noisy and limited. This study introduces a symmetry-inspired symbolic regression (SI-SR) framework to address this issue. By automatically identifying the intrinsic physical invariances, the method recursively constructs symmetry-constrained function libraries, thereby enhancing robustness to noise and naturally promoting sparsity. The framework integrates neural networks for accurate derivative estimation with symbolic regression for expressive nonlinear modeling. We validate SI-SR on canonical partial differential governing equations of fluid dynamics. The results demonstrate that incorporating symmetry constraints enables the discovery of compact and accurate models, even under substantial noise and data scarcity.