# Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer

arXiv: https://arxiv.org/abs/2312.12467 · HTML: https://mlsanity.com/paper/2312.12467/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 53 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 30 of 32)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (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)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [HOOD: Hierarchical Graphs for Generalized Modelling of Clothing Dynamics](https://mlsanity.com/paper/2212.07242/) (2022)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [SE3-Nets: Learning Rigid Body Motion using Deep Neural Networks](https://mlsanity.com/paper/1606.02378/) (2016)
- [Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks](https://mlsanity.com/paper/2310.09528/) (2023)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [Constraint-based graph network simulator](https://mlsanity.com/paper/2112.09161/) (2021)
- [Reducing Collision Checking for Sampling-Based Motion Planning Using Graph Neural Networks](https://mlsanity.com/paper/2210.08864/) (2022)

## Built on by (most cited first, 18 of 18)

- [Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics](https://mlsanity.com/paper/2506.06045/) (2025)
- [PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks](https://mlsanity.com/paper/2504.04052/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions](https://mlsanity.com/paper/2410.03779/) (2024)
- [Learning Advanced Self-Attention for Linear Transformers in the Singular Value Domain](https://mlsanity.com/paper/2505.08516/) (2025)
- [MaNGO - Adaptable Graph Network Simulators via Meta-Learning](https://mlsanity.com/paper/2510.05874/) (2025)
- [RigidFormer: Learning Rigid Dynamics using Transformers](https://mlsanity.com/paper/2605.09196/) (2026)
- [M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations](https://mlsanity.com/paper/2509.10659/) (2025)
- [PhysiFormer: Learning to Simulate Mechanics in World Space](https://mlsanity.com/paper/2606.27364/) (2026)
- [Thickness-aware E(3)-Equivariant 3D Mesh Neural Networks](https://mlsanity.com/paper/2505.21572/) (2025)
- [Context-aware Learned Mesh-based Simulation via Trajectory-Level Meta-Learning](https://mlsanity.com/paper/2511.05234/) (2025)
- [Learning Deformable Body Interactions With Adaptive Spatial Tokenization](https://mlsanity.com/paper/2507.13707/) (2025)
- [CloDS: Visual-Only Unsupervised Cloth Dynamics Learning in Unknown Conditions](https://mlsanity.com/paper/2602.01844/) (2026)
- [MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation](https://mlsanity.com/paper/2604.04474/) (2026)
- [Mesh Based Simulations with Spatial and Temporal awareness](https://mlsanity.com/paper/2605.01542/) (2026)
- [Point Cloud Sequence Encoding for Material-conditioned Graph Network Simulators](https://mlsanity.com/paper/2605.20978/) (2026)
- [Physics-Informed Coarsening for Multigrid Graph Neural Surrogates](https://mlsanity.com/paper/2605.31013/) (2026)
- [ScaGNN: a Graph Neural Network for Multiple Scattering Simulations](https://mlsanity.com/paper/2609.37509/) (2026)

## Abstract (arXiv)

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.