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，即在大规模高分辨率网格上迭代消息传递所导致的低效长程信息传播。一个物理注意力 Transformer 作为全局处理器，同时更新所有节点状态，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 消除了对深层消息传递堆栈或分层粗化网格的需求，从而能够在工业尺度上，对不同几何、拓扑及边界条件的高分辨率网格进行高效学习。我们证明，MGN-T 成功处理了工业尺度的冲击动力学网格，而在此场景下，标准 MGN 因消息传递范围不足而失效。该方法能精确建模自接触、塑性及多变量输出，包括内部现象学塑性变量。此外，MGN-T 在经典基准测试中优于现有先进方法，以仅需竞争基线一小部分的参数量，实现了更高的精度并保持了实际效率。