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

2026-01-30

AI Summary

This work addresses the limitation of traditional MeshGraphNet in efficiently propagating long-range information across high-resolution meshes due to its reliance on iterative message passing, which hinders its applicability in industrial-scale solid mechanics simulations. The authors propose a novel architecture that integrates the global modeling capacity of Transformers with the geometric inductive biases of MeshGraphNet, enabling end-to-end learning directly on the original high-resolution mesh while preserving its geometric and topological structure. Central to this approach is a physics-aware attention mechanism that allows the model to capture long-range physical interactions without requiring deep message-passing stacks or mesh coarsening. The method accurately simulates complex phenomena such as self-contact and plasticity in impact dynamics, achieving significantly higher accuracy and computational efficiency with substantially fewer parameters, outperforming existing approaches on established benchmarks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Low Level & Physics-based Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Web data generation and simulation

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.

Problem

• mesh-based simulation
• long-range information propagation
• solid mechanics
• industrial-scale meshes
• message-passing inefficiency

Innovation

• MeshGraphNet-Transformer
• physics-aware attention
• long-range interaction modeling
• mesh-based simulation
• solid mechanics