RATIO: A Relation-Aware Token Interaction Operator for Deformable Solid Dynamics

Deep learning has enabled efficient simulation of deformable solids, yet accurately modeling contact dynamics requires capturing both localized physical interactions and long-range deformation responses. Graph-based methods rely on multi-hop message passing to capture long-range dependencies, incurring substantial computational overhead, whereas methods that compress physical states into a small set of latent tokens may lose the fine-grained information needed to resolve local interactions. Incorporating local physical structure directly into compact global representations provides a natural route toward combining localized interaction modeling with global information exchange. For deformable dynamics, however, this requires capturing and distinguishing heterogeneous intra-body and contact relations. Graph-based simulators naturally represent such relations through connectivity and relation-specific edge attributes, motivating a relation-aware formulation for global modeling. In this paper, we propose RATIO, a Relation-Aware Token Interaction Operator that jointly models nodal states, intra-body mesh relations, and inter-body contact relations through token interactions. RATIO aggregates nodal states and the two types of edge features into separate groups of tokens, applies attention across these groups, and maps the resulting information back to update node and edge states. This design allows intra-body and contact relations to directly participate in global evolution. RATIO can further be coupled with local graph modules for enhanced local interaction modeling. Experiments on deformable solid dynamics with contact demonstrate state-of-the-art accuracy.