Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic anisotropy. Two network architectures are developed to take into account the effects of a variable supersaturation value. The first infers it implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes the supersaturation parameter as an explicit input along with a single initial frame and predicts the entire sequence. The two models are systematically tested to establish strengths and weaknesses, comparing the prediction performance for models trained on datasets of different size and, in the first architecture, different lengths of input mini-sequence. The analysis of point-wise and mean absolute errors shows how the explicit parameter conditioning guarantees the best results, reproducing with high-fidelity the ground-truth profiles. Comparable results are achievable by the mini-sequence approach only when using larger training datasets. The trained models show strong conditioning by the supersaturation parameter, consistently reproducing its overall impact on growth rates as well as its local effect on the faceted morphology. Moreover, they are perfectly scalable even on 256 times larger domains and can be successfully extended to more than 10 times longer sequences with limited error accumulation. The analysis highlights the potential and limits of these approaches in view of their general exploitation for crystal growth simulations.

翻译：基于卷积循环神经网络代理模型对晶体生长过程进行模拟，模型通过艾伦-卡恩动力学（含动力学各向异性刻面效应）数值积分计算的时间序列数据集训练。针对变过饱和度值的影响，开发了两种网络架构：第一种通过处理若干演化帧的输入小序列隐式推断过饱和度，并返回一致的连续演化结果；第二种将过饱和度参数作为显式输入，与单个初始帧共同处理并预测完整序列。系统测试了两模型的优劣势，对比了不同规模数据集训练模型的预测性能，以及第一架构中输入小序列长度的影响。逐点误差和平均绝对误差分析表明，显式参数条件化能保证最优结果，高保真再现真实轮廓。仅当使用更大训练数据集时，小序列方法方可达到可比拟效果。训练模型表现出对过饱和度参数的强条件依赖性，能一致再现该参数对生长速率的整体影响及其对刻面形貌的局部效应。此外，模型在256倍更大域上完美可扩展，成功外推至10倍以上长度序列且误差累积有限。该分析揭示了这些方法在晶体生长模拟中通用应用的潜力与局限性。