EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator

2025-06-06

AI Summary

Deformable object collision simulation must jointly model solid mechanics and multi-body interactions; however, existing data-driven approaches suffer from three key limitations: lack of equivariance, inadequate collision modeling, and poor scalability. This paper introduces the first end-to-end equivariant neural field simulator, which rigorously enforces physical symmetries—including rotation and translation—via strict equivariant modeling. We propose a collision-aware message-passing mechanism and control-point-conditioned neural fields to enable continuous spatiotemporal modeling and infinite-resolution output. The framework integrates an equivariant encoder, graph neural ODEs, and explicit collision constraints. Evaluated on diverse deformable collision tasks, our method reduces rollout MSE by 24.34%–35.82% over prior work. It further demonstrates significantly improved generalization and stability across unseen object counts, long-horizon trajectories, and group-action transformations.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision
• Intelligent Robots: Embodied AI

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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 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.

Problem

• Simulating deformable object collisions with physical symmetries
• Handling multi-body interactions and collisions effectively
• Achieving scalable and resolution-independent motion predictions

Innovation

• Equivariant encoder for latent control points
• Collision-aware GNN-based Neural ODE
• Neural field for continuous motion prediction