Neural surrogates for crystal growth dynamics with variable supersaturation: explicit vs implicit conditioning

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 supersaturation implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes supersaturation 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 sizes 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, faithfully reproducing 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. Significant discrepancies emerge only for the mini-sequence model at the lowest supersaturations or under extrapolation. Moreover, both models 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. Most notably, even if trained on uniform and constant supersaturation values, they are found to consistently handle also spatially variable fields and, for the explicit parameter architecture, time-dependent supersaturation values. This opens the way for their general exploitation for crystal growth simulations, eventually including coupled dynamics of temperature or concentration fields responsible for the local supersaturation.