用图神经网络预测任意孔洞结构的应力分布，无需重新训练即可泛化。
Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries
- 基于节点类型、相对距离和全局载荷构建网格图模型，实现平移旋转不变性
- 在未见几何与载荷下最高达0.97的R²，远超传统模型的0.01–0.86
- 适合需要快速评估多种结构设计的工程场景，尤其适用于复杂几何
有限元分析（FEA）对结构设计至关重要，但计算成本高昂，尤其在多轮设计迭代或不同载荷情景下。机器学习代理模型提供了可行替代方案，但多数方法难以跨不同几何泛化。本文提出一种网格图网络（MGN），用于预测二维结构件中任意孔洞几何下的冯·米塞斯应力场。不同于使用绝对节点坐标的传统方法，该模型利用节点类型（如固定边界、自由表面、孔边）、相对边特征（邻点间距离）和全局特征（施加载荷）。该架构天然具备平移与旋转不变性，可在不重新训练的情况下泛化至未见几何。模型在11种板结构、20种载荷条件下训练，评估于7种未见几何和3种未见载荷。最理想情况下，模型在未见几何与载荷下达到R² ≥ 0.97，而传统模型（随机森林、梯度提升、K近邻）仅在0.01–0.86之间。即使在较差情形下，该模型仍优于传统方法。本工作将Pfaff等人（arXiv:2010.03409）的网格仿真框架扩展至结构力学领域，证明图神经网络可作为跨几何变化的高效有限元分析代理模型。
原文摘要 · Abstract (English)
Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation: generalizing across varying geometries. This work presents a mesh graph network (MGN) for predicting von Mises stress fields in 2D structural components with arbitrary hole geometries. Unlike traditional machine learning approaches that use absolute node coordinates as features, the proposed model builds on existing MGN frameworks that encode node types (e.g., fixed boundary, free surface, hole edge), relative edge features (distance between neighbors), and global features (applied load). This architecture is inherently translation- and rotation-invariant, enabling generalization to unseen geometries without retraining. The MGN was trained on 11 plate geometries under 20 load conditions and evaluated on 7 unseen geometries and 3 unseen loads. In the most favorable case, the model achieves $R^2 \geq 0.97$ on an unseen geometry and unseen load, compared to $R^2 \approx 0.01$--$0.86$ for conventional models (Random Forest, Gradient Boosting , K-Nearest Neighbors) trained on identical data. However, even in less favorable cases, the MGN model still outperforms conventional models. This work extends the mesh-based simulation framework of Pfaff et al. (arXiv:2010.03409) to structural mechanics, demonstrating that graph neural networks can serve as efficient surrogates for finite element analysis across varying geometries.
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