Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery

TL;DR

This paper introduces PG-SR, a prior-guided symbolic regression framework that incorporates domain priors and a novel evaluation mechanism to discover scientifically consistent equations, improving interpretability and reliability.

Contribution

We propose PG-SR, a three-stage symbolic regression method that explicitly encodes domain priors and uses a prior annealing evaluation to ensure scientific consistency.

Findings

PG-SR outperforms state-of-the-art methods across multiple domains.

PG-SR maintains robustness to noisy data and limited data scenarios.

Theoretically, PG-SR reduces hypothesis space complexity, providing generalization guarantees.

Abstract

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.