Rediscovering the Lunar Equation of the Centre with AI Feynman via Embedded Physical Biases
This work addresses the problem of automating the discovery of physical laws in astronomy, but it is incremental as it builds on existing symbolic regression methods with manual biases.
The study used the AI Feynman symbolic regression algorithm with embedded physical biases to automatically rediscover the first-order analytical form of the Equation of the Centre from lunar ephemerides data, successfully recovering this fundamental astronomy equation.
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.