做多尺度仿真和材料力学计算的团队，终于有了一个能同时处理时间依赖和空间应力场的高效替代方案——比有限元快 1000 倍，还能跨网格直接迁移，建议做结构分析的开发者点开看看。
该研究提出了一种结合长短期记忆网络（LSTM）和物理信息图神经网络（GNN）的框架，用于重建非线性、历史依赖载荷下异质微结构的局部应力场。LSTM 编码宏观应力-应变序列，捕捉路径依赖的本构响应；GNN 则重建每个时间步的空间应力场。通过引入带线性热启动的相对权重策略，平衡数据驱动重建损失和离散散度平衡惩罚，解决了弹塑性区域固定权重无法收敛的问题。模型在 10,000 条非比例加载路径上训练，比有限元仿真快三个数量级，且能泛化到两倍训练长度的加载序列，累积误差仅 1.9%。由于图依赖网格连通性而非具体单元类型，训练好的代理模型可直接应用于不同单元类型和粗细网格，无需重新训练。
Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks
Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.