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.

Practical Performative Policy Learning with Strategic Agents

This paper studies the performative policy learning problem, where agents adjust their features in response to a released policy to improve their potential outcomes, inducing an endogenous distribution shift. There has been growing interest in training machine learning models in strategic environments, including strategic classification and performative prediction. However, existing approaches often rely on restrictive parametric assumptions: micro-level utility models in strategic classification and macro-level data distribution maps in performative prediction, severely limiting scalability and generalizability. We approach this problem as a complex causal inference task, relaxing parametric assumptions on both micro-level agent behavior and macro-level data distribution. Leveraging bounded rationality, we uncover a practical low-dimensional structure in distribution shifts and construct an effective mediator in the causal path from the deployed model to the shifted data. We then propose a gradient-based policy optimization algorithm with a differentiable classifier as a substitute for the high-dimensional distribution map. Our algorithm efficiently utilizes batch feedback and limited manipulation patterns. Our approach achieves high sample efficiency compared to methods reliant on bandit feedback or zero-order optimization. We also provide theoretical guarantees for algorithmic convergence. Extensive and challenging experiments on high-dimensional settings demonstrate our method's practical efficacy.