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.

翻译：本文提出MeshGraphNet-Transformer（MGN-T）——一种新颖的架构，它融合了Transformer的全局建模能力与MeshGraphNet的几何归纳偏置，同时保留了基于网格的图表示。MGN-T克服了标准MGN的一个关键局限：在大型高分辨率网格上迭代消息传递导致的低效长程信息传播。我们采用物理注意力Transformer作为全局处理器，同步更新所有节点状态，并显式保留节点与边属性。通过直接捕捉长程物理相互作用，MGN-T无需深层消息传递堆栈或分层粗化网格，即可在工业尺度上高效学习具有不同几何、拓扑和边界条件的高分辨率网格。我们证明，MGN-T能成功处理冲击动力学中的工业级网格——该场景下标准MGN会因消息传递范围不足而失效。该方法精确建模了自接触、塑性及多变量输出（包括内部唯象塑性变量）。此外，MGN-T在经典基准测试中优于现有先进方法，仅需竞争基线所需参数的一小部分，在保持实用效率的同时实现了更高精度。