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 \name, 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 \name 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, \name 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：对可变形物体的碰撞进行模拟是一项基础但具有挑战性的任务，原因在于固体力学建模和多体交互的复杂性。现有数据驱动方法通常缺乏对物理对称性的等变性、对碰撞处理的不足以及可扩展性有限。本文提出\name，这是首个面向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，将物体几何形状和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，我们查询由控制点特征条件化的神经场，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，\name在不同物体配置下实现了准确、稳定且可扩展的模拟。与表现最佳的基线模型相比，其滚动均方误差降低了24.34%至57.62%。此外，\name能够泛化至更多碰撞物体和更长的时间范围，并对群作用变换的输入保持鲁棒性。代码地址：https://github.com/AI4Science-WestlakeU/EqCollide