# MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics

arXiv: https://arxiv.org/abs/2601.23177 · HTML: https://mlsanity.com/paper/2601.23177/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries](https://mlsanity.com/paper/2502.02414/) (2025)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Structure-preserving neural networks](https://mlsanity.com/paper/2004.04653/) (2020)
- [AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformers](https://mlsanity.com/paper/2502.09692/) (2025)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [Reversible and irreversible bracket-based dynamics for deep graph neural networks](https://mlsanity.com/paper/2305.15616/) (2023)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks](https://mlsanity.com/paper/2308.01602/) (2023)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics](https://mlsanity.com/paper/2506.06045/) (2025)
- [Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics](https://mlsanity.com/paper/2409.11899/) (2024)
- [On the feasibility of foundational models for the simulation of physical phenomena](https://mlsanity.com/paper/2410.14645/) (2024)
- [Automated model discovery of finite strain elastoplasticity from uniaxial experiments](https://mlsanity.com/paper/2408.14615/) (2024)
- [EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions](https://mlsanity.com/paper/2410.03779/) (2024)
- [On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition](https://mlsanity.com/paper/2507.08861/) (2025)
- [M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations](https://mlsanity.com/paper/2509.10659/) (2025)
- [Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Framework](https://mlsanity.com/paper/2512.15767/) (2025)

## Built on by (most cited first, 10 of 10)

- [Crash Assessment via Mesh-Based Graph Neural Networks and Physics-Aware Attention](https://mlsanity.com/paper/2605.11784/) (2026)
- [SurgFormer: Scalable Learning of Organ Deformation with Resection Support and Real-Time Inference](https://mlsanity.com/paper/2603.06543/) (2026)
- [Enabling Structure-Only Initialization and Out-of-Distribution Generalization in GNN-based Molecular Dynamics Simulators](https://mlsanity.com/paper/2605.09495/) (2026)
- [A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming](https://mlsanity.com/paper/2605.22845/) (2026)
- [LEIA: Learned Environment for Interactive Architected Materials](https://mlsanity.com/paper/2605.28368/) (2026)
- [Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids](https://mlsanity.com/paper/2606.23251/) (2026)
- [Appearance-Preserving Refinement of Generated 3D Assets for Monochromatic Fabrication](https://mlsanity.com/paper/2606.26850/) (2026)
- [HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networks](https://mlsanity.com/paper/2608.13827/) (2026)
- [MeshPriorDiT: Hierarchical Modeling for Action-Conditioned Cloth Dynamics](https://mlsanity.com/paper/2608.26766/) (2026)
- [Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion](https://mlsanity.com/paper/2610.18871/) (2026)

## Abstract (arXiv)

We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets, while preserving a mesh-based graph representation. MGN-T overcomes a key limitation of standard MGN, the inefficient long-range information propagation caused by iterative message passing on large, high-resolution meshes. A physics-attention Transformer serves as a global processor, updating all nodal states simultaneously while explicitly retaining node and edge attributes. By directly capturing long-range physical interactions, MGN-T eliminates the need for deep message-passing stacks or hierarchical, coarsened meshes, enabling efficient learning on high-resolution meshes with varying geometries, topologies, and boundary conditions at an industrial scale. We demonstrate that MGN-T successfully handles industrial-scale meshes for impact dynamics, a setting in which standard MGN fails due message-passing under-reaching. The method accurately models self-contact, plasticity, and multivariate outputs, including internal, phenomenological plastic variables. Moreover, MGN-T outperforms state-of-the-art approaches on classical benchmarks, achieving higher accuracy while maintaining practical efficiency, using only a fraction of the parameters required by competing baselines.