Abstract

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time. Ideal mass-spring system Baseline NN Prediction Noisy observations Hamiltonian NN PredictionFigure 1: Learning the Hamiltonian of a mass-spring system. The variables q and p correspond toposition and momentum coordinates. As there is no friction, the baseline’s inner spiral is due tomodel errors. By comparison, the Hamiltonian Neural Network learns to exactly conserve a quantitythat is analogous to total energy.