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arXiv · 2506.05797

EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator

Qianyi Chen·Tianrun Gao·Chenbo Jiang·Tailin Wu
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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

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Qianyi Chen, Tianrun Gao, Chenbo Jiang, Tailin Wu. 2026-06-16. EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator. https://arxiv.org/abs/2506.05797

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