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

arXiv: https://arxiv.org/abs/2108.11894 · HTML: https://mlsanity.com/paper/2108.11894/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems](https://mlsanity.com/paper/2010.03729/) (2020)
- [Data-driven Discovery of Emergent Behaviors in Collective Dynamics](https://mlsanity.com/paper/1912.11123/) (2019)
- [Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe](https://mlsanity.com/paper/1910.10147/) (2019)
- [Learning Interaction Kernels for Agent Systems on Riemannian Manifolds](https://mlsanity.com/paper/2102.00327/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Collective Behaviors from Observation](https://mlsanity.com/paper/2311.00875/) (2023)

## Abstract (arXiv)

Building accurate and predictive models of the underlying mechanisms of celestial motion has inspired fundamental developments in theoretical physics. Candidate theories seek to explain observations and predict future positions of planets, stars, and other astronomical bodies as faithfully as possible. We use a 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 model for the motion of celestial bodies in our Solar System. Our model is based on a collective dynamics framework, and is learned from the NASA Jet Propulsion Lab's development ephemerides. By modeling the major astronomical bodies in the Solar System as pairwise interacting agents, our learned model generate extremely accurate dynamics that preserve not only intrinsic geometric properties of the orbits, but also highly sensitive features of the dynamics, such as perihelion precession rates. Our learned model can provide a unified explanation to the observation data, especially in terms of reproducing the perihelion precession of Mars, Mercury, and the Moon. Moreover, Our model outperforms Newton's Law of Universal Gravitation in all cases and performs similarly to, and exceeds on the Moon, the Einstein-Infeld-Hoffman equations derived from Einstein's theory of general relativity.