Hamiltonian Graph Networks with ODE Integrators

TL;DR

This paper presents a novel graph network approach incorporating Hamiltonian mechanics and differentiable ODE integrators to improve learned physical simulations, achieving better accuracy and generalization.

Contribution

It introduces a Hamiltonian graph network with ODE integrators, enhancing predictive and energy accuracy and zero-shot generalization in learned simulation models.

Findings

Outperforms baselines in predictive accuracy

Achieves better energy conservation

Generalizes to unseen time-step sizes and integrator orders

Abstract

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.