Efficient Probabilistic Modeling of Crystallization at Mesoscopic Scale

TL;DR

This work introduces the Crystal Growth Neural Emulator (CGNE), a probabilistic, autoregressive emulator for mesoscopic crystallization that significantly accelerates simulations while preserving realistic morphologies. Built on a CVAE-based framework with conditional priors and a fully convolutional decoder, CGNE addresses training challenges such as latent variable neglect and identity collapse through samplewise decoder dropout and temporal downsampling. It demonstrates superior overlap with ground-truth LCA morphologies and higher ELBO than a recent baseline (PNS), along with an approximate 11-fold speedup in inference. The approach enables scalable exploration of crystallization dynamics and offers a pathway to apply probabilistic neural simulation to diverse crystallization processes beyond snow crystals.

Abstract

Crystallization processes at the mesoscopic scale, where faceted, dendritic growth, and multigrain formation can be observed, are of particular interest within materials science and metallurgy. These processes are highly nonlinear, stochastic, and sensitive to small perturbations of system parameters and initial conditions. Methods for the simulation of these processes have been developed using discrete numerical models, but these are computationally expensive. This work aims to scale crystal growth simulation with a machine learning emulator. Specifically, autoregressive latent variable models are well suited for modeling the joint distribution over system parameters and the crystallization trajectories. However, successfully training such models is challenging due to the stochasticity and sensitivity of the system. Existing approaches consequently fail to produce diverse and faithful crystallization trajectories. In this paper, we introduce the Crystal Growth Neural Emulator (CGNE), a probabilistic model for efficient crystal growth emulation at the mesoscopic scale that overcomes these challenges. We validate CGNE results using the morphological properties of the crystals produced by numerical simulation. CGNE delivers a factor of 11 improvement in inference time and performance gains compared with recent state-of-the-art probabilistic models for dynamical systems.

Figures (9)

• Figure 1: Original crystal representation on a hexagonal grid.
• Figure 2: Transformed crystal representation on a square grid.
• Figure 3: Crystal growth simulation by numerical LCA model.
• Figure 4: Crystal growth simulation by CGNE.
• Figure 6: CGNE model overview.