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

We develop an extensive dataset of Allen-Cahn simulations of crystal growth in 2D, including kinetic anisotropy to produce hexagonally faceted profiles, and a variable supersaturation parameter to control the growth rates and local faceting. A phase-field numerical approach based on a finite-difference explicit time integration scheme is used to generate such evolution sequences. Two Convolutional Recurrent Neural Network architectures are then exploited to train quantitative surrogate models reproducing such evolution sequences conditioned to the supersaturation value. The first infers the supersaturation parameter implicitly from an input mini-sequence of a few evolution frames while the second takes it as an explicit input along with a single initial frame. The predictive performances of the two models are evaluated by extensive testing on dedicated testsets. In particular, the analysis includes both the testing on a large dataset of the same kind of the training one, and on dedicated datasets with assigned values of the supersaturation parameter. While the architecture using the parameter as explicit input yields the best performance, with quantitative reproduction of the true phase-field solutions, the mini-sequence model produce satisfactory results only by taking comparatively larger dataset sizes. The generalization capabilities of the trained models are finally inspected by considering larger domains, longer evolution times and different initial coverages.