用符号回归发现常微分方程的对称性，突破传统工具局限。
Discovering Symmetries of ODEs by Symbolic Regression
- 基于搜索的符号回归方法寻找微分方程对称性生成元
- 成功识别出现有计算机代数系统无法找到的对称性
- 适用于难以解析求解的非线性微分方程研究
求解常微分方程（ODEs）对于理解动力系统行为至关重要，但自动化求解仍具挑战性，尤其在非线性系统中。计算机代数系统（CAS）通过利用李点对称性简化方程提供支持，但对称性的发现本身对CAS而言仍是难题。近期符号回归在从数据中恢复符号表达式方面展现出潜力。本文将基于搜索的符号回归方法应用于寻找李点对称性生成元，实现了对现有CAS无法发现的对称性的有效识别。
原文摘要 · Abstract (English)
Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra systems (CASs) provide support for solving ODEs by first simplifying them, in particular through the use of Lie point symmetries. Finding these symmetries is, however, itself a difficult problem for CASs. Recent works in symbolic regression have shown promising results for recovering symbolic expressions from data. Here, we adapt search-based symbolic regression to the task of finding generators of Lie point symmetries. With this approach, we can find symmetries of ODEs that existing CASs cannot find.
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