EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909641002188800 |
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| author | Chen, Qianyi Gao, Tianrun Jiang, Chenbo Wu, Tailin |
| author_facet | Chen, Qianyi Gao, Tianrun Jiang, Chenbo Wu, Tailin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator Chen, Qianyi Gao, Tianrun Jiang, Chenbo Wu, Tailin Machine Learning Computational Engineering, Finance, and Science Robotics 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. |
| title | EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator |
| topic | Machine Learning Computational Engineering, Finance, and Science Robotics |
| url | https://arxiv.org/abs/2506.05797 |