EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator

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 show that EqCollide achieves accurate, stable, and scalable simulations across diverse object configurations, and our model achieves 24.34% to 35.82% lower rollout MSE even compared with the best-performing baseline model. Furthermore, our model could generalize to more colliding objects and extended temporal horizons, and stay robust to input transformed with group action.