Parsimonious neural networks learn classical mechanics and can teach it

We combine neural networks with genetic algorithms to find parsimonious models that describe the time evolution of a point particle subjected to an external potential. The genetic algorithm is designed to find the simplest, most interpretable network compatible with the training data. The parsimonious neural network (PNN) can numerically integrate classical equations of motion with negligible energy drifts and good time reversibility, significantly outperforming a generic feed-forward neural network. Our PNN is immediately interpretable as the position Verlet algorithm, a non-trivial integrator whose justification originates from Trotter's theorem.