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

翻译：可变形物体的碰撞模拟是一项基础但具挑战性的任务，原因在于固体力学建模与多体交互的复杂性。现有数据驱动方法常缺乏对物理对称性的等变性、碰撞处理不充分以及可扩展性有限。本文提出EqCollide，这是首个用于可变形物体及其碰撞的端到端等变神经场模拟器。我们设计了一个等变编码器，将物体几何与速度映射到潜在控制点。随后，基于等变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的交互。为重建速度场，我们查询以控制点特征为条件的神经场，从而实现连续且分辨率无关的运动预测。在二维和三维场景上的实验表明，EqCollide在多样化的物体配置下实现了准确、稳定且可扩展的模拟。即使与性能最佳的基线模型相比，其卷积分均方误差也降低了24.34%至57.62%。此外，EqCollide可推广至更多碰撞物体与更长时间范围，并对经过群作用变换的输入保持鲁棒性。代码发布于：https://github.com/AI4Science-WestlakeU/EqCollide