用图神经网络加速多晶塑性应力预测，150倍提速且精度超99%。
Stress Predictions in Polycrystal Plasticity using Graph Neural Networks with Subgraph Training
- 构建基于节点应变和边距的图神经网络，通过子图训练学习应力映射。
- 训练与测试的R²均超0.99，预测速度比FEM快150倍以上。
- 模型泛化能力强，可准确预测未见模拟中的冯·米塞斯应力。
多晶塑性数值模拟计算成本高。本文采用图神经网络（GNN）从有限元法（FEM）模拟中预测复杂几何下多晶塑性的应力。提出一种新型消息传递GNN，编码节点应变和有限元网格单元间的边距，聚合生成嵌入，并将解码嵌入与节点应变结合以预测节点上的应力张量。在由FEM网格图生成的子图上训练：网格单元转为节点，相邻单元间建立边。应用于具有复杂几何的周期性多晶，基于晶体塑性理论学习应变-应力映射。训练与测试集的R²均大于0.99，相比FEM在应力预测上提速超150倍。对未见模拟的验证显示整体R²达0.992，模型无过拟合，误差分布稳定。该工作展望了利用图数据替代晶体塑性模拟的可能。
原文摘要 · Abstract (English)
Numerical modeling of polycrystal plasticity is computationally intensive. We employ Graph Neural Networks (GNN) to predict stresses on complex geometries for polycrystal plasticity from Finite Element Method (FEM) simulations. We present a novel message-passing GNN that encodes nodal strain and edge distances between FEM mesh cells, and aggregates to obtain embeddings and combines the decoded embeddings with the nodal strains to predict stress tensors on graph nodes. The GNN is trained on subgraphs generated from FEM mesh graphs, in which the mesh cells are converted to nodes and edges are created between adjacent cells. We apply the trained GNN to periodic polycrystals with complex geometries and learn the strain-stress maps based on crystal plasticity theory. The GNN is accurately trained on FEM graphs, in which the $R^2$ for both training and testing sets are larger than 0.99. The proposed GNN approach speeds up more than 150 times compared with FEM on stress predictions. We also apply the trained GNN to unseen simulations for validations and the GNN generalizes well with an overall $R^2$ of 0.992. The GNN accurately predicts the von Mises stress on polycrystals. The proposed model does not overfit and generalizes well beyond the training data, as the error distributions demonstrate. This work outlooks surrogating crystal plasticity simulations using graph data.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。