# Learning Deformable Body Interactions With Adaptive Spatial Tokenization

arXiv: https://arxiv.org/abs/2507.13707 · HTML: https://mlsanity.com/paper/2507.13707/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [MAGE: MAsked Generative Encoder to Unify Representation Learning and Image Synthesis](https://mlsanity.com/paper/2211.09117/) (2022)
- [TripoSG: High-Fidelity 3D Shape Synthesis using Large-Scale Rectified Flow Models](https://mlsanity.com/paper/2502.06608/) (2025)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [OctFormer: Octree-based Transformers for 3D Point Clouds](https://mlsanity.com/paper/2305.03045/) (2023)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [Sparse 3D convolutional neural networks](https://mlsanity.com/paper/1505.02890/) (2015)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer](https://mlsanity.com/paper/2312.12467/) (2023)
- [Random Weight Factorization Improves the Training of Continuous Neural Representations](https://mlsanity.com/paper/2210.01274/) (2022)
- [Learning rigid-body simulators over implicit shapes for large-scale scenes and vision](https://mlsanity.com/paper/2405.14045/) (2024)
- [GNN-based physics solver for time-independent PDEs](https://mlsanity.com/paper/2303.15681/) (2023)
- [AnchorFormer: Differentiable Anchor Attention for Efficient Vision Transformer](https://mlsanity.com/paper/2505.16463/) (2025)

## Abstract (arXiv)

Simulating interactions between deformable bodies is vital in fields like material science, mechanical design, and robotics. While learning-based methods with Graph Neural Networks (GNNs) are effective at solving complex physical systems, they encounter scalability issues when modeling deformable body interactions. To model interactions between objects, pairwise global edges have to be created dynamically, which is computationally intensive and impractical for large-scale meshes. To overcome these challenges, drawing on insights from geometric representations, we propose an Adaptive Spatial Tokenization (AST) method for efficient representation of physical states. By dividing the simulation space into a grid of cells and mapping unstructured meshes onto 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, serving as tokens for the entire physical state. Self-attention modules are employed to predict the next state over these tokens in 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 deformable body interactions. Notably, it remains effective on large-scale simulations with meshes exceeding 100,000 nodes, where existing methods are hindered by computational limitations. Additionally, we contribute a novel large-scale dataset encompassing a wide range of deformable body interactions to support future research in this area.