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Building accurate and predictive models of the underlying mechanisms ofcelestial motion has inspired fundamental developments in theoretical physics.Candidate theories seek to explain observations and predict future positions ofplanets, stars, and other astronomical bodies as faithfully as possible. We usea data-driven learning approach, extending that developed in Lu et al. ($2019$)and extended in Zhong et al. ($2020$), to a derive stable and accurate modelfor the motion of celestial bodies in our Solar System. Our model is based on acollective dynamics framework, and is learned from the NASA Jet PropulsionLab's development ephemerides. By modeling the major astronomical bodies in theSolar System as pairwise interacting agents, our learned model generateextremely accurate dynamics that preserve not only intrinsic geometricproperties of the orbits, but also highly sensitive features of the dynamics,such as perihelion precession rates. Our learned model can provide a unifiedexplanation to the observation data, especially in terms of reproducing theperihelion precession of Mars, Mercury, and the Moon. Moreover, Our modeloutperforms Newton's Law of Universal Gravitation in all cases and performssimilarly to, and exceeds on the Moon, the Einstein-Infeld-Hoffman equationsderived from Einstein's theory of general relativity.

Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides