用数据自动发现物理规律,让模型既准又可解释。
Introduction to Symbolic Regression in the Physical Sciences
- 通过搜索数学表达式空间,从数据中挖掘可读方程
- 能构建高效代理模型,替代昂贵的物理仿真
- 适合需要可解释性的物理建模与科学发现场景
符号回归(SR)作为一种从数据中发现可解释数学关系的强大方法,在科学发现和高效经验建模方面展现出新路径。本文介绍面向物理科学的符号回归特刊,源于2025年4月皇家学会研讨会。收录工作涵盖自动方程发现、涌现现象建模及计算成本高的模拟的紧凑代理模型构建。综述部分阐述了SR的理论基础,对比传统回归方法,梳理其在物理科学中的主要应用:有效理论推导、经验函数形式建立与代理模型构造。总结了搜索空间设计、算子选择、复杂度控制、特征筛选以及与现代AI融合等方法论考量。指出当前挑战包括可扩展性、抗噪性、过拟合与计算复杂度。强调新兴方向,特别是对称性约束、渐近行为等理论信息的融入。总体而言,本特刊展示了符号回归的快速发展及其在物理科学中的日益重要性。
原文摘要 · Abstract (English)
Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the Special Issue on Symbolic Regression for the Physical Sciences, motivated by the Royal Society discussion meeting held in April 2025. The contributions collected here span applications from automated equation discovery and emergent-phenomena modelling to the construction of compact emulators for computationally expensive simulations. The introductory review outlines the conceptual foundations of SR, contrasts it with conventional regression approaches, and surveys its main use cases in the physical sciences, including the derivation of effective theories, empirical functional forms and surrogate models. We summarise methodological considerations such as search-space design, operator selection, complexity control, feature selection, and integration with modern AI approaches. We also highlight ongoing challenges, including scalability, robustness to noise, overfitting and computational complexity. Finally we emphasise emerging directions, particularly the incorporation of symmetry constraints, asymptotic behaviour and other theoretical information. Taken together, the papers in this Special Issue illustrate the accelerating progress of SR and its growing relevance across the physical sciences.
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