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 long-term 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 two-body part, solvable analytically, and an interaction part that we approximate with a NN. Our neural symplectic *N*-body code integrates a general three-body 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.

# Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational N-body Problem

Publication date:

December, 2021

Journal:

NeurIPS 2021 workshop

Abstract: