Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs

TL;DR

This paper introduces GNSTODE, a novel graph neural ODE framework that effectively models complex physical laws with varying spatial and temporal dependencies, significantly improving simulation accuracy of particle systems.

Contribution

The paper proposes GNSTODE, a new end-to-end graph neural ODE model that captures complex spatial-temporal dependencies for particle system simulation.

Findings

GNSTODE outperforms existing methods on Gravity and Coulomb systems.

It achieves higher simulation accuracy with varying dependencies.

The model demonstrates robustness across different physical scenarios.

Abstract

The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose significant challenges to the learning based simulations, such as the varying spatial dependencies between interacting particles and varying temporal dependencies between particle system states in different time stamps, which dominate particles' interacting behaviour and the physical systems' evolution patterns. Existing learning based simulation methods fail to fully account for the complexities, making them unable to yield satisfactory simulations. To better comprehend the complex physical laws, this paper proposes a novel learning based simulation model- Graph Networks with Spatial-Temporal neural Ordinary Equations (GNSTODE)- that characterizes the varying spatial and temporal dependencies in particle systems using a united end-to-end framework. Through training with real-world particle-particle interaction observations, GNSTODE is able to simulate any possible particle systems with high precisions. We empirically evaluate GNSTODE's simulation performance on two real-world particle systems, Gravity and Coulomb, with varying levels of spatial and temporal dependencies. The results show that the proposed GNSTODE yields significantly better simulations than state-of-the-art learning based simulation methods, which proves that GNSTODE can serve as an effective solution to particle simulations in real-world application.