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The great learning ability of deep learning models facilitates us tocomprehend the real physical world, making learning to simulate complicatedparticle systems a promising endeavour. However, the complex laws of thephysical world pose significant challenges to the learning based simulations,such as the varying spatial dependencies between interacting particles andvarying temporal dependencies between particle system states in different timestamps, which dominate particles' interacting behaviour and the physicalsystems' evolution patterns. Existing learning based simulation methods fail tofully account for the complexities, making them unable to yield satisfactorysimulations. To better comprehend the complex physical laws, this paperproposes a novel learning based simulation model- Graph Networks withSpatial-Temporal neural Ordinary Equations (GNSTODE)- that characterizes thevarying spatial and temporal dependencies in particle systems using a unitedend-to-end framework. Through training with real-world particle-particleinteraction observations, GNSTODE is able to simulate any possible particlesystems with high precisions. We empirically evaluate GNSTODE's simulationperformance on two real-world particle systems, Gravity and Coulomb, withvarying levels of spatial and temporal dependencies. The results show that theproposed GNSTODE yields significantly better simulations than state-of-the-artlearning based simulation methods, which proves that GNSTODE can serve as aneffective solution to particle simulations in real-world application.

Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs