The great learning ability of deep learning facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour both in academia and industry. 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 behavior and the physical systems’ evolution patterns. Existing learning based methods fail to fully account for the complexities, making them unable to yield satisfactory simulations. To better comprehend the complex physical laws, we propose a novel model – Graph Networks with Spatial–Temporal neural Ordinary Differential 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 can 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 GNSTODE yields better simulations than state-of-the-art methods, showing that GNSTODE can serve as an effective tool for particle simulation in real-world applications. Our code is made available at .

中文翻译：

---

用图神经常方程进行复杂动态物理系统模拟

深度学习强大的学习能力有助于我们理解真实的物理世界，使学习模拟复杂的粒子系统成为学术界和工业界的一项有前途的努力。然而，物理世界的复杂规律对基于学习的模拟提出了重大挑战，例如相互作用的粒子之间不同的空间依赖关系以及不同时间戳中粒子系统状态之间不同的时间依赖关系，它们主导着粒子的相互作用行为和物理系统' 的进化模式。现有的基于学习的方法无法充分考虑复杂性，从而无法产生令人满意的模拟。为了更好地理解复杂的物理定律，我们提出了一种新颖的模型——具有时空神经常微分方程的图网络（GNSTODE）——它使用统一的端到端框架来表征粒子系统中不同的空间和时间依赖性。通过对真实世界粒子间相互作用观测进行训练，GNSTODE 可以高精度模拟任何可能的粒子系统。我们根据经验评估了 GNSTODE 在两个现实世界粒子系统（重力和库仑）上的模拟性能，具有不同程度的空间和时间依赖性。结果表明，GNSTODE 的模拟效果比最先进的方法更好，这表明 GNSTODE 可以作为现实应用中粒子模拟的有效工具。我们的代码可在 处获取。