PNEO: Pairwise Neural Energy Operators for Scalable Collision Dynamics of 3D Deformable Objects

Accurate prediction of 3D deformable-object collision dynamics is important for robotic interaction, world model, and a broad range of engineering simulation problems. Numerical methods are accurate but become increasingly inefficient as the number of interacting objects grows. Learning-based simulators predict faster, but typically require training on large multi-object scenes to scale up, limiting generalisation to unseen object counts. We introduce the Pairwise Neural Energy Operator (PNEO), which learns collision dynamics from two-object interactions and composes the same learned interaction law across multi-object interactions. PNEO models the conservative energy exchange and dissipation of each contacting object pair using scalar potential and Rayleigh dissipation terms, which are summed over the contact graph to recover multi-object dynamics. This pair-local formulation makes the learned interaction law independent of scene cardinality. Experiments show that a single PNEO trained only on two-object collisions transfers zero-shot across object count (up to 50), point-cloud resolution, and mechanical properties without retraining or fine-tuning. PNEO outperforms baselines across the main multi-object evaluation settings while maintaining stable trajectory, contact, and deformation accuracy as scene size increases.