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.
@article{arxiv.1909.12790,
title = {Hamiltonian Graph Networks with ODE Integrators},
author = {Alvaro Sanchez-Gonzalez and Victor Bapst and Kyle Cranmer and Peter Battaglia},
journal= {arXiv preprint arXiv:1909.12790},
year = {2019}
}