Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery
Jing Xiao Xinhai Chen Jiaming Peng Qinglin Wang Menghan Jia Zhiquan Lai Guangping Yu Dongsheng Li Tiejun Li Jie Liu
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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.引用本文复制引用
Jing Xiao,Xinhai Chen,Jiaming Peng,Qinglin Wang,Menghan Jia,Zhiquan Lai,Guangping Yu,Dongsheng Li,Tiejun Li,Jie Liu.Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery[EB/OL].(2026-02-16)[2026-02-19].https://arxiv.org/abs/2602.13021.学科分类
自然科学研究方法
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