Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery
This addresses the issue of scientific inconsistency in equation discovery for researchers in fields like physics and engineering, representing a novel method rather than an incremental improvement.
The paper tackles the problem of symbolic regression producing equations that fit data but violate scientific principles, proposing PG-SR, a prior-guided framework that introduces constraint programs and a PACE mechanism to steer discovery toward consistency, and it outperforms state-of-the-art baselines across domains with robustness to noise and data scarcity.
Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap: producing equations that fit observations well but remain inconsistent with fundamental scientific principles. A key reason is that these approaches are dominated by empirical risk minimization, lacking explicit constraints to ensure scientific consistency. To bridge this gap, we propose PG-SR, a prior-guided SR framework built upon a three-stage pipeline consisting of warm-up, evolution, and refinement. Throughout the pipeline, PG-SR introduces a prior constraint checker that explicitly encodes domain priors as executable constraint programs, and employs a Prior Annealing Constrained Evaluation (PACE) mechanism during the evolution stage to progressively steer discovery toward scientifically consistent regions. Theoretically, we prove that PG-SR reduces the Rademacher complexity of the hypothesis space, yielding tighter generalization bounds and establishing a guarantee against pseudo-equations. Experimentally, PG-SR outperforms state-of-the-art baselines across diverse domains, maintaining robustness to varying prior quality, noisy data, and data scarcity.