Rediscovering orbital mechanics with machine learning

• Published in: Machine learning: science and technology Vol. 4; no. 4; pp. 45002 - 45014
• Main Authors: Lemos, Pablo, Jeffrey, Niall, Cranmer, Miles, Ho, Shirley, Battaglia, Peter
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.12.2023; IOP Publishing Ltd
• Subjects: AI scientist; Astrophysics; Computer Science; General Relativity and Quantum Cosmology; graph neural network; Graph neural networks; Gravitation; inductive biases; Instrumentation and Detectors; Machine learning; Neural networks; Orbital mechanics; Physical properties; Physics; scientific discovery; Solar system; symbolic regression; scientific discovery; inductive biases; graph neural network; symbolic regression; AI scientist
• ISSN: 2632-2153; 2632-2153
• DOI: 10.1088/2632-2153/acfa63

We present an approach for using machine learning to automatically discover the governing equations and unknown properties (in this case, masses) of real physical systems from observations. We train a ‘graph neural network’ to simulate the dynamics of our Solar System’s Sun, planets, and large moons from 30 years of trajectory data. We then use symbolic regression to correctly infer an analytical expression for the force law implicitly learned by the neural network, which our results showed is equivalent to Newton’s law of gravitation. The key assumptions our method makes are translational and rotational equivariance, and Newton’s second and third laws of motion. It did not, however, require any assumptions about the masses of planets and moons or physical constants, but nonetheless, they, too, were accurately inferred with our method. Naturally, the classical law of gravitation has been known since Isaac Newton, but our results demonstrate that our method can discover unknown laws and hidden properties from observed data.