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

2026-04-23

AI Summary

This study addresses the challenge of efficiently simulating crystal growth kinetics under varying supersaturation conditions by developing a convolutional recurrent neural network surrogate model trained on high-resolution spatiotemporal data generated from the Allen–Cahn equation. The authors systematically compare explicit conditioning—where the model takes an initial frame and supersaturation parameters as input—with implicit conditioning, which relies solely on short input sequences. Their findings indicate that explicit modeling achieves superior performance with limited training data, whereas implicit approaches require large datasets to excel. Both strategies demonstrate excellent scalability, accurately predicting dynamics over domains 256 times larger and sequences 10 times longer than those in the training set, with controlled error accumulation. Notably, the explicit model faithfully reproduces realistic crystal morphologies and growth rates, offering a novel paradigm for surrogate modeling of complex phase-field processes.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

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.

Problem

• crystal growth
• supersaturation
• neural surrogates
• conditioning
• dynamics

Innovation

• neural surrogate
• crystal growth dynamics
• variable supersaturation
• explicit conditioning
• implicit conditioning