  We introduce an approach for imposing physically informed inductive biases in
learned simulation models. We combine graph networks with a differentiable
ordinary differential equation integrator as a mechanism for predicting future
states, and a Hamiltonian as an internal representation. We find that our
approach outperforms baselines without these biases in terms of predictive
accuracy, energy accuracy, and zero-shot generalization to time-step sizes and
integrator orders not experienced during training. This advances the
state-of-the-art of learned simulation, and in principle is applicable beyond
physical domains.
