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

TL;DR

MeshGraphNet-Transformer (MGN-T) addresses the under-reaching bottleneck of traditional MeshGraphNets by introducing a physics-attention Transformer that updates all nodal states globally, while preserving a mesh-based representation. The architecture blends local MPNN blocks (pre-processor and refinement) with a global, token-based Transformer that models long-range interactions via eidetic state tokens, enabling accurate simulations on high-resolution industrial meshes with varying geometries and boundary conditions. Empirical results on pi-beam impact dynamics and deforming-plate benchmarks show that MGN-T outperforms standard MGN and remains competitive with state-of-the-art, using far fewer parameters and without hierarchical coarsening. The approach demonstrates scalable, end-to-end trainable surrogates for complex solid-mechanics phenomena, including self-contact and plasticity, with practical computational efficiency on modern GPUs.

Abstract

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.

Figures (7)

• Figure 1: Illustration of the MGN-T architecture. Processor: Pre-processor MPNN (local update), Transformer processor with physics-attention (global update) and Refinement processor MPNN (local update).
• Figure 2: Pi-Beam example. (a) Visualization of the multi-component structure, where each colour represents a different component with different thickness. (b) Visualization of the FEM mesh with rectangular shell elements.
• Figure 3: Error evolution rollout comparison between FEM ground truth and MGN-T predictions for the pi-beam benchmark. Line represents the mean and shade the standard error accross trajectories. Top: RMSE. Bottom: Relative RMSE.
• Figure 4: Prediction MGN-T Pi-Beam dataset: MGN-T prediction on the for a dynamic impact against an obstacle. a) Temporal evolution of hardening variable $\alpha$. b) Temporal evolution of velocity magnitude $\|\boldsymbol{v}\|$ for consecutive temporal predictions, from beginning of trajectory.
• Figure 5: Physical consistency Pi-Beam predictions. Top: Accumulated plastic hardening. Bottom: Kinetic Energy magnitude. Each column is one different test trajectory, for ground truth, MGN-T and MGN.