用AI重发现月球中心方程，靠物理先验提升符号回归效率
Rediscovering the Lunar Equation of the Centre with AI Feynman via Embedded Physical Biases
- 通过数据预处理和搜索空间限制嵌入物理先验
- 从月球星历数据中成功恢复一阶解析解
- 适合对符号回归与天体力学交叉研究者
本研究利用受物理启发的AI Feynman符号回归算法，自动重发现天文学中的基础方程——月球中心方程。通过在数据预处理和搜索空间中引入观测与归纳偏差以反映系统物理特性，该方法成功从月球星历数据中恢复出该方程的一阶解析形式。然而，这一手动流程凸显了其对专家主导坐标系选择的依赖。为此，本文提出一种自动化预处理扩展以识别规范坐标系。结果表明，有针对性地嵌入领域知识可使符号回归重新发现物理规律，但也揭示了在利用定制化偏置时进一步约束符号回归以推导物理方程的挑战。
原文摘要 · Abstract (English)
This work explores using the physics-inspired AI Feynman symbolic regression algorithm to automatically rediscover a fundamental equation in astronomy -- the Equation of the Centre. Through the introduction of observational and inductive biases corresponding to the physical nature of the system through data preprocessing and search space restriction, AI Feynman was successful in recovering the first-order analytical form of this equation from lunar ephemerides data. However, this manual approach highlights a key limitation in its reliance on expert-driven coordinate system selection. We therefore propose an automated preprocessing extension to find the canonical coordinate system. Results demonstrate that targeted domain knowledge embedding enables symbolic regression to rediscover physical laws, but also highlight further challenges in constraining symbolic regression to derive physics equations when leveraging domain knowledge through tailored biases.
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