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This paper trains Convolutional Recurrent Neural Networks to act as surrogate models for simulating crystal growth dynamics governed by the Allen-Cahn equation with kinetic anisotropy. They compare two architectures: one implicitly infers supersaturation from a short input sequence, while the other explicitly conditions on the supersaturation parameter. Results show that explicit conditioning yields higher fidelity predictions, especially with smaller training datasets, and both models demonstrate strong conditioning on the supersaturation parameter, accurately capturing its impact on growth rates and morphology.
Explicitly conditioning neural surrogates on supersaturation dramatically improves their accuracy in simulating crystal growth dynamics compared to implicit inference, especially with limited data.
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.
