MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics
This addresses a key bottleneck in industrial-scale solid mechanics simulations, offering a scalable solution for applications like impact dynamics, though it is an incremental improvement over existing methods.
The paper tackles the problem of inefficient long-range information propagation in mesh-based learned simulations for solid mechanics by introducing MeshGraphNet-Transformer, which combines Transformers with MeshGraphNets to enable scalable and accurate modeling on high-resolution meshes, outperforming state-of-the-art methods with higher accuracy and fewer parameters.
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.