Solving the Three-Body Problem Using Numerical Simulations and Neural Networks

The general solution of the three-body problem under gravitational force remains unsolved due to its chaotic nature (highly sensitive to initial conditions, a small change in one state can result in a significant difference in a later state). This paper will review some of the current mathematical simulations of the three-body problem, such as Brutus, clean numerical simulation, and the Hermite integration scheme, as well as the proposed neural networks, including deep neural network, Hamiltonian neural network and reservoir computing methods that can be trained using trajectories generated by numerical integrators to simulate the three-body problem in less time.