We propose GrainGNN, a surrogate model for polycrystalline grain formation under rapid solidification conditions in metal additive manufacturing. Such grain formation problems are modeled by a multicomponent partial differential equation PDE 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 node) over a high-fidelity phase-field simulation (CUDA on a single NVIDIA A100 GPU) is 300$\times$--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，一个针对金属增材制造快速凝固条件下多晶粒形成的代理模型。此类晶粒形成问题由含移动界面的多组分偏微分方程（PDE）描述。由于PDE初始条件（晶粒种子）的固有随机性，需要系综模拟来预测微观结构统计量，例如晶粒尺寸、纵横比和晶体取向。当前此类系综模拟成本极高，因此代理模型不可或缺。在GrainGNN中，我们使用动态图来表示晶粒粗化过程中的界面移动和拓扑变化。我们采用基于手工特征（hand-crafted features）的微观结构降阶表示；将模式发现与图算法修改相结合，并结合两个神经网络：一个分类器（用于拓扑变化）和一个回归器（用于界面移动）。这两个网络均采用编码器-解码器架构：编码器使用多层Transformer长短期记忆（LSTM）结构；解码器为单层感知机。我们通过将GrainGNN与高保真相场模拟在激光粉末床熔融条件下的分布内和分布外晶粒构型进行对比来评估其性能。结果显示，GrainGNN的点态精度达到80%–90%；基于Kolmogorov-Smirnov检验，相场模拟与GrainGNN模拟所得的标量关注量（QoI）分布几乎一致。在处理100初始晶粒问题时，GrainGNN（在单x86节点上使用PyTorch）相比高保真相场模拟（在单块NVIDIA A100 GPU上使用CUDA）的推理加速比为300倍至2000倍。此外，使用GrainGNN，我们在单CPU核心上仅用220秒即可模拟11600个晶粒的形成过程。