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

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 105 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.