Governing Equation Discovery with Relaxed Symmetry Constraints

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 with 79.18% and 18.14% lower RMSE than both standard and invariant-based genetic programming, respectively, across all experiments.