深度符号回归：基于单位约束的物理引导——迈向物理定律的自动发现
Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws
AI总结：
提出$\Phi$-SO物理符号优化框架，利用深度强化学习并嵌入单位约束，自动发现物理定律，在费曼基准上噪声下性能最优，且对10%噪声稳健。
摘要：
符号回归是研究自动化搜索拟合数据的解析表达式算法的学科。尽管深度学习的近期进展重新激发了人们对这类方法的兴趣，但符号回归方法的发展并未聚焦于物理学，而在物理学中，由于数据关联的单位，我们拥有重要的额外约束。在此，我们提出$\Phi$-SO，一个物理符号优化框架，利用深度强化学习技术，通过学习单位约束，从物理数据中恢复解析符号表达式。我们的系统从底层构建，以提出物理单位在构造上一致的解决方案。这不仅有助于消除物理上不可能的解决方案，而且因为量纲分析的“语法”规则极大地限制了方程生成器的自由度，从而大幅提升了性能。该算法可用于拟合无噪声数据，例如在尝试推导物理模型的解析性质时，也可用于获得噪声数据的解析近似。我们在《费曼物理学讲义》及其他物理教科书中的标准方程基准上测试了我们的机制，在存在噪声（超过0.1%）的情况下实现了最先进的性能，并表明即使在存在显著（10%）噪声的情况下，它也是稳健的。我们在一组天体物理学示例中展示了其能力。
英文摘要：
Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic regression methods has not been focused on physics, where we have important additional constraints due to the units associated with our data. Here we present $Φ$-SO, a Physical Symbolic Optimization framework for recovering analytical symbolic expressions from physics data using deep reinforcement learning techniques by learning units constraints. Our system is built, from the ground up, to propose solutions where the physical units are consistent by construction. This is useful not only in eliminating physically impossible solutions, but because the "grammatical" rules of dimensional analysis restrict enormously the freedom of the equation generator, thus vastly improving performance. The algorithm can be used to fit noiseless data, which can be useful for instance when attempting to derive an analytical property of a physical model, and it can also be used to obtain analytical approximations to noisy data. We test our machinery on a standard benchmark of equations from the Feynman Lectures on Physics and other physics textbooks, achieving state-of-the-art performance in the presence of noise (exceeding 0.1%) and show that it is robust even in the presence of substantial (10%) noise. We showcase its abilities on a panel of examples from astrophysics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
