Rediscovering the Lunar Equation of the Centre with AI Feynman via Embedded Physical Biases

TL;DR

This paper demonstrates how AI Feynman, with embedded physical biases, can automatically rediscover the lunar Equation of the Centre from observational data, highlighting both its potential and current limitations in physics law discovery.

Contribution

The study introduces an automated preprocessing extension to identify the canonical coordinate system, enhancing AI Feynman's ability to rediscover physical laws.

Findings

Successfully recovered the first-order form of the lunar Equation of the Centre

Embedded physical biases improve symbolic regression performance

Manual coordinate selection remains a key limitation

Abstract

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.