We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Currently such ensemble simulations are prohibitively expensive and surrogates are necessary. In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron. We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80\%--90\% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150$\times$--2000$\times$ for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

翻译：我们提出GrainGNN，一种针对金属增材制造快速凝固条件下多晶粒结构演化的代理模型。高保真度凝固微观结构模拟通常采用包含移动界面的多组分偏微分方程（PDE）进行。PDE初始条件（晶粒种子）的固有随机性要求通过系综模拟来预测微观结构统计量（如晶粒尺寸、长径比及晶体取向）。当前此类系综模拟计算成本过高，亟需开发代理模型。在GrainGNN中，我们采用动态图表示界面运动及晶粒粗化导致的拓扑变化。通过手工设计特征构建微观结构的降维表示；将模式识别与图修改算法结合两种神经网络——分类器（处理拓扑变化）与回归器（处理界面运动）。两种网络均采用编码器-解码器架构：编码器为多层Transformer长短期记忆架构，解码器为单层感知机。我们通过将GrainGNN与高保真度相场模拟对比，评估其在激光粉末床熔融条件下对分布内与分布外晶粒构型的凝固过程预测性能。GrainGNN的逐点精度可达80%-90%；经Kolmogorov-Smirnov检验，相场模拟与GrainGNN模拟输出的标量关注量（QoI）分布近乎一致。针对100初始晶粒问题，GrainGNN（基于PyTorch在单x86 CPU上）较之高保真度相场模拟（基于CUDA在单NVIDIA A100 GPU上）的推理加速比达150倍至2000倍。此外，利用GrainGNN，我们可在单CPU内核上220秒内完成11,600个晶粒形成过程的建模。