用有限元信息增强图神经网络，高效求解非线性弹性塑性问题。
FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity
- 将FEM计算嵌入超图神经网络的消息传递层，实现物理一致性建模。
- 无需标签数据，3D循环加载测试中精度和效率显著优于现有PINN方法。
- 适合需要高精度与计算效率的非线性固体力学仿真研究者。
图神经网络（GNN）天然适配稀疏算子和非结构化离散化，是计算力学中物理信息机器学习的有前途范式。受离散物理损失和分层深度学习神经网络（HiDeNN）结构启发，本文在节点和高斯点上直接嵌入有限元（FEM）计算，提出数值一致的FEM-Informed超图神经网络（FHGNN）。与传统物理信息神经网络（PINNs）类似，训练完全由物理驱动，无需标注数据：输入为包含网格连接性的节点-单元超图。基于实验结果和条件数分析，采用高效的变分损失。在包含各向同性/运动硬化循环加载的3D基准测试中，该方法相比近期先进PINN变体展现出显著提升的精度与效率。通过利用GPU并行张量运算和离散表示，其可有效扩展至大规模弹塑性问题，在相当精度下比多核FEM实现更快或具竞争力。本工作为非线性固体力学中可扩展、嵌入物理的学习奠定了基础。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and Hierarchical Deep Learning Neural Network (HiDeNN) constructions, we embed finite-element (FEM) computations at nodes and Gauss points directly into message-passing layers and propose a numerically consistent FEM-Informed Hypergraph Neural Networks (FHGNN). Similar to conventional physics-informed neural networks (PINNs), training is purely physics-driven and requires no labeled data: the input is a node element hypergraph whose edges encode mesh connectivity. Guided by empirical results and condition-number analysis, we adopt an efficient variational loss. Validated on 3D benchmarks, including cyclic loading with isotropic/kinematic hardening, the proposed method delivers substantially improved accuracy and efficiency over recent, competitive PINN variants. By leveraging GPU-parallel tensor operations and the discrete representation, it scales effectively to large elastoplastic problems and can be competitive with, or faster than, multi-core FEM implementations at comparable accuracy. This work establishes a foundation for scalable, physics-embedded learning in nonlinear solid mechanics.
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