Governing Equation Discovery with Relaxed Symmetry Constraints

Andrew J Chen, Jianke Yang, Rose Yu

Track: Extended Abstract (non-archival, 4 pages)

Keywords: Equation discovery, symmetry, symbolic regression, partial differential equations, genetic programming, symmetry breaking

TL;DR: A method for incorporating relaxed symmetry in genetic-programming-based differential equation discovery.

Abstract: Existing methods for discovering governing equations from data often struggle with the vast search space of possible equations. Physical inductive biases such as symmetry are shown to reduce complexity and force symmetrical equations. State-of-the-art methods enforce symmetry by using symmetry invariants as relevant terms in symbolic regression. While effective, they assume perfect symmetry and fail to identify systems with symmetry-breaking effects. To solve this problem, we propose Symmetry-Breaking Fine-Tuning (SBFT) for genetic programming-based equation search, which aims to relax the symmetry constraints. Our method first searches with an emphasis toward invariants to recover a symmetric backbone, then fine-tunes those results with equal emphasis on invariants and raw variables to capture symmetry-breaking terms. On benchmark PDEs, SBFT recovers equations achieving median RMSE reduction of 85.56% and 67.83% relative to standard and invariant-based genetic programming, respectively, across all experiments.

Submission Number: 18