Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational $N$body Problem
Abstract
The gravitational $N$body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general analytical solution for $N>2$. Can an $N$body problem be solved accurately by a neural network (NN)? Can a NN observe longterm conservation of energy and orbital angular momentum? Inspired by Wistom & Holman (1991)'s symplectic map, we present a neural $N$body integrator for splitting the Hamiltonian into a twobody part, solvable analytically, and an interaction part that we approximate with a NN. Our neural symplectic $N$body code integrates a general threebody system for $10^{5}$ steps without diverting from the ground truth dynamics obtained from a traditional $N$body integrator. Moreover, it exhibits good inductive bias by successfully predicting the evolution of $N$body systems that are no part of the training set.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.15631
 arXiv:
 arXiv:2111.15631
 Bibcode:
 2021arXiv211115631C
 Keywords:

 Physics  Computational Physics;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Computer Science  Machine Learning
 EPrint:
 7 pages, 2 figures, accepted for publication at the NeurIPS 2021 workshop "Machine Learning and the Physical Sciences"