# Efficient Probabilistic Modeling of Crystallization at Mesoscopic Scale

arXiv: https://arxiv.org/abs/2405.16608 · HTML: https://mlsanity.com/paper/2405.16608/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 26 May 2024.

## Builds on (most cited first, 13 of 13)

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- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [A Denoising Diffusion Model for Fluid Field Prediction](https://mlsanity.com/paper/2301.11661/) (2023)
- [Plasma Surrogate Modelling using Fourier Neural Operators](https://mlsanity.com/paper/2311.05967/) (2023)
- [Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates](https://mlsanity.com/paper/2305.18944/) (2023)
- [Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics](https://mlsanity.com/paper/2305.14286/) (2023)

## Abstract (arXiv)

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.