This paper was accepted at the AI for Science workshop at NeurIPS 2025.
Simulating interactions between deformable objects is essential in fields such as materials science, mechanical design, and robotics. Learning-based methods using graph neural networks (GNNs) are effective in solving complex physical systems, but face scalability issues when modeling the interactions of deformable objects. Modeling interactions between objects requires dynamic creation of pairwise global edges, which is computationally intensive and impractical for large meshes. To overcome these challenges, we propose an adaptive spatial tokenization (AST) method to efficiently represent physical states by leveraging insights from geometric representations. By dividing the simulation space into a grid of cells and mapping an unstructured mesh to this structured grid, our approach naturally groups adjacent mesh nodes. We then apply a cross-attention module to map the sparse cells into a compact fixed-length embedding that serves as a token for the entire physical state. The self-attention module is used to predict the next state of these tokens in the latent space. This framework leverages the efficiency of tokenization and the expressive power of attention mechanisms to achieve accurate and scalable simulation results. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art approaches in modeling interactions of deformable objects. In particular, it remains effective even in large-scale simulations involving meshes exceeding 100,000 nodes, where computational limitations preclude existing methods. Additionally, we provide a new large-scale dataset covering a wide range of deformable object interactions to support future research in this area.
