用机器学习从数据中自动发现物理方程，提升建模效率。
Discovering equations from data: symbolic regression in dynamical systems
- 采用符号回归方法自动寻找数据背后的数学方程。
- PySR在9个系统中表现最优，部分结果与真实方程几乎一致。
- 适合从事物理、生态或流行病建模的研究者使用。
从数据中发现方程是物理学及其他研究领域（如数学生态学和流行病学）的核心任务。近年来，称为符号回归的机器学习方法为自动化这一过程提供了新途径。本研究综述了当前符号回归领域的文献，并比较了五种前沿方法在九类动态过程（包括混沌动力学和流行病模型）中恢复控制方程的效率。基准测试表明，PySR方法在方程推断方面最为有效，部分推导结果与原始解析形式几乎无法区分。这些结果凸显了符号回归作为推断和建模现实现象的稳健工具的巨大潜力。
原文摘要 · Abstract (English)
The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a way to automate this task. This study presents an overview of the current literature on symbolic regression, while also comparing the efficiency of five state-of-the-art methods in recovering the governing equations from nine processes, including chaotic dynamics and epidemic models. Benchmark results demonstrate the PySR method as the most suitable for inferring equations, with some estimates being indistinguishable from the original analytical forms. These results highlight the potential of symbolic regression as a robust tool for inferring and modeling real-world phenomena.
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