首个可处理变形体碰撞的等变神经场模拟器，兼顾物理对称性与稳定性。
EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator
- 用等变编码器将几何和速度映射为控制点，保持物理对称性。
- 碰撞感知消息传递使模拟在2D/3D场景中误差降低24.34%~57.62%。
- 支持多物体、长时序泛化，适合需高保真物理模拟的研究者。
模拟变形体碰撞是基础但极具挑战的任务，源于固体力学与多体相互作用建模的复杂性。现有数据驱动方法常缺乏对物理对称性的等变性、碰撞处理不足且扩展性差。本文提出EqCollide，首个端到端的变形体及其碰撞等变神经场模拟器。通过等变编码器将物体几何与速度映射为隐式控制点；后续基于图神经网络的神经常微分方程通过碰撞感知消息传递建模控制点间交互；利用条件于控制点特征的神经场查询重构速度场，实现连续且分辨率无关的运动预测。2D与3D实验表明，EqCollide在多种物体配置下实现准确、稳定且可扩展的模拟，滚动预测均方误差相较最优基线模型降低24.34%至57.62%。此外，模型能泛化至更多碰撞物体与更长时序，并对群作用变换保持鲁棒性。代码已开源：https://github.com/AI4Science-WestlakeU/EqCollide
原文摘要 · Abstract (English)
Simulating collisions of deformable objects is a fundamental yet challenging task due to the complexity of modeling solid mechanics and multi-body interactions. Existing data-driven methods often suffer from lack of equivariance to physical symmetries, inadequate handling of collisions, and limited scalability. Here we introduce EqCollide, the first end-to-end equivariant neural fields simulator for deformable objects and their collisions. We propose an equivariant encoder to map object geometry and velocity into latent control points. A subsequent equivariant Graph Neural Network-based Neural Ordinary Differential Equation models the interactions among control points via collision-aware message passing. To reconstruct velocity fields, we query a neural field conditioned on control point features, enabling continuous and resolution-independent motion predictions. Experimental results on 2D and 3D scenarios show that EqCollide achieves accurate, stable, and scalable simulations across diverse object configurations. It achieves $24.34\%$ to $57.62\%$ lower rollout MSE, even compared with the best-performing baseline model. Furthermore, EqCollide could generalize to more colliding objects and extended temporal horizons, and stay robust to input transformed with group action. Code is available at: https://github.com/AI4Science-WestlakeU/EqCollide
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