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EqCollide introduces a novel neural simulator that combines equivariant encoding with collision-aware message passing to accurately model deformable object dynamics. By leveraging Neural Ordinary Differential Equations and graph networks, the system achieves significant reductions in prediction error while maintaining robustness across diverse physical symmetries. This advancement addresses critical gaps in data-driven solid mechanics simulations, offering scalable solutions for robotics and computational engineering applications.
EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator
arXiv:2506.05797v3 Announce Type: replace Abstract: 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
Abstract: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: this https URL
SIGKDD 2026 Oral AI4S Track. 20 pages, 16 figures
Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Robotics (cs.RO)
arXiv:2506.05797 [cs.LG]
(or arXiv:2506.05797v3 [cs.LG] for this version)
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