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.

翻译：深度学习模型强大的学习能力有助于我们理解真实物理世界，使学习模拟复杂粒子系统成为一项有前景的研究。然而，物理世界的复杂规律给基于学习的模拟带来了重大挑战，例如相互作用粒子间变化的空间依赖关系，以及不同时间戳下粒子系统状态间变化的时间依赖关系，这些因素主导了粒子的相互作用行为及物理系统的演化模式。现有基于学习的模拟方法未能充分应对这些复杂性，导致无法产生令人满意的模拟结果。为更好地理解复杂物理规律，本文提出一种新颖的基于学习的模拟模型——时空神经常微分方程图网络（Graph Networks with Spatial-Temporal neural Ordinary Equations, GNSTODE），该模型通过统一的端到端框架刻画粒子系统中变化的空间与时间依赖关系。通过利用真实世界中粒子与粒子间的相互作用观测数据进行训练，GNSTODE能够以高精度模拟任意可能的粒子系统。我们在两个具有不同时空依赖程度的真实粒子系统（重力系统与库仑系统）上实证评估了GNSTODE的模拟性能。结果表明，所提出的GNSTODE比当前最先进的基于学习的模拟方法取得了显著更优的模拟效果，证明GNSTODE可成为实际应用中粒子模拟的有效解决方案。