用拓扑与物理规律增强神经网络，更好模拟刚体碰撞与长期动态。
Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamics
- 用高阶拓扑结构替代传统网格，保持物理一致性。
- 长时预测误差显著低于现有图神经网络方法。
- 适合需要精确物理交互的机器人、游戏与仿真领域。
刚体相互作用是众多科学领域的基础，但因其突变的非线性特性和对复杂未知环境因素的高度敏感，仿真难度大。这需要具备自适应能力的学习方法，以捕捉超出显式物理模型的复杂交互。尽管图神经网络能处理简单场景，但在复杂场景和长期预测中表现不佳。本文提出一种新框架，用于建模刚体动力学与学习碰撞交互，解决现有图基方法的关键局限。通过引入高阶拓扑复形扩展传统网格表示，实现物理一致的表征；并设计融合物理定律的消息传递神经架构。实验表明，该方法在长时滚动预测中仍具更高精度，且对未见场景有强泛化能力。本工作特别针对多实体动态交互挑战，适用于广泛的科学与工程应用。
原文摘要 · Abstract (English)
Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for adaptable learning-based methods capable of capturing complex interactions beyond explicit physical models and simulations. While graph neural networks can handle simple scenarios, they struggle with complex scenes and long-term predictions. We introduce a novel framework for modeling rigid body dynamics and learning collision interactions, addressing key limitations of existing graph-based methods. Our approach extends the traditional representation of meshes by incorporating higher-order topology complexes, offering a physically consistent representation. Additionally, we propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model. Our method demonstrates superior accuracy, even during long rollouts, and exhibits strong generalization to unseen scenarios. Importantly, this work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains.
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