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

Saumya Shah, Zi-Yu Khoo, Abel Yang, Stéphane Bressan

TL;DR

The study tackles automatic discovery of orbital governing equations by attempting to rediscover the Equation of the Centre for the Moon using the AI Feynman symbolic regression framework. It introduces observational and inductive biases via data preprocessing to steer search toward canonical, physically interpretable forms and evaluates three configurations. Results show that with a trigonometric bias and preprocessing, the first-order term $e\sin M$ of the centre equation can be recovered and yields an eccentricity estimate close to the true value of $e\approx 0.0549$, though higher-order terms remain elusive. The work demonstrates the potential of physics-guided symbolic regression for discovering physical laws while revealing critical limitations in automatic coordinate-frame inference, motivating an automated preprocessing extension that tests multiple reference frames to approach canonical representations.

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.

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

TL;DR

The study tackles automatic discovery of orbital governing equations by attempting to rediscover the Equation of the Centre for the Moon using the AI Feynman symbolic regression framework. It introduces observational and inductive biases via data preprocessing to steer search toward canonical, physically interpretable forms and evaluates three configurations. Results show that with a trigonometric bias and preprocessing, the first-order term of the centre equation can be recovered and yields an eccentricity estimate close to the true value of , though higher-order terms remain elusive. The work demonstrates the potential of physics-guided symbolic regression for discovering physical laws while revealing critical limitations in automatic coordinate-frame inference, motivating an automated preprocessing extension that tests multiple reference frames to approach canonical representations.

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.

Paper Structure

This paper contains 22 sections, 3 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Astronomical Coordinate Systems
  4. Canonical Coordinates
  5. Equation of the Centre
  6. Lunar Perturbations
  7. Causes of Perturbations
  8. Related Work
  9. Classical Symbolic Regression
  10. Physics-Informed Symbolic Regression
  11. SINDy
  12. Graph Neural Networks & PySR
  13. AI Feynman
  14. Methodology
  15. Overview
  16. ...and 7 more sections

Figures (1)

  • Figure 1: Monthly Lunar Declination vs Right Ascension