Three-body problem -- from Newton to supercomputer plus machine learning

TL;DR

This paper introduces a machine learning approach using neural networks to find and predict periodic orbits in the three-body problem with arbitrary masses, leveraging high-performance computing and AI.

Contribution

It presents a novel neural network-based method to numerically discover and predict periodic orbits in the three-body problem across varying masses, expanding the known solution space.

Findings

Neural network model successfully predicts periodic orbits for different masses.

The approach enlarges the domain of known periodic orbits.

AI and high-performance computing are key to solving classical physics problems.

Abstract

The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effective approach and roadmap to numerically gain planar periodic orbits of three-body systems with arbitrary masses by means of machine learning based on an artificial neural network (ANN) model. Given any a known periodic orbit as a starting point, this approach can provide more and more periodic orbits (of the same family name) with variable masses, while the mass domain having periodic orbits becomes larger and larger, and the ANN model becomes wiser and wiser. Finally we have an ANN model trained by means of all obtained periodic orbits of the same family, which provides a convenient way to give accurate enough predictions of periodic orbits with arbitrary masses for physicists and astronomers. It suggests that the high-performance computer and artificial intelligence (including machine learning) should be the key to gain periodic orbits of the famous three-body problem.