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

TL;DR

MeshGraphNet-Transformer (MGN-T) introduces a scalable, mesh-based simulation architecture that combines Transformers with MeshGraphNets, enabling efficient modeling of complex solid mechanics phenomena at industrial scales.

Contribution

The paper presents MGN-T, a novel architecture that integrates Transformers with mesh-based graphs to improve long-range interaction modeling in high-resolution solid mechanics simulations.

Findings

Successfully handles industrial-scale meshes for impact dynamics.

Accurately models self-contact, plasticity, and multivariate outputs.

Outperforms state-of-the-art methods in accuracy and efficiency.

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.