Recent advances in describing and driving crystal nucleation using machine learning and artificial intelligence

Q: Why is classical nucleation theory not sufficient for all crystal nucleation events?

Not all nucleation follows a purely classical pathway where the reaction coordinate is only the size of a spherical nucleus. Many systems proceed through non-classical routes such as the Ostwald step mechanism, which involves at least two energy barriers.

Q: How can machine learning help in describing non-classical nucleation?

ML methods can be used to construct more nuanced, potentially non-linear reaction coordinates that depend on many input features, enabling better representation of complex nucleation behaviors than one-dimensional classical approaches.

Q: What roles do ML-based methods play in crystal identification and force fields?

Robust ML-based classification methods improve identification of crystal phases and structures, including imperfect or defective motifs. ML-driven force fields can reach density-functional-theory-level accuracy while enabling simulations at speeds far beyond direct DFT calculations.

Aug 5, 2026

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Rapid advances in computing—especially the widespread use of GPUs—have accelerated machine learning (ML) and artificial intelligence (AI) for data-intensive studies, making crystal nucleation a key beneficiary. This review summarizes ML/AI applications addressing four central challenges: finding improved reaction coordinates for non-classical pathways, building more accurate force fields for multiple polymorphs or phases, developing robust crystal-phase and structure identification, and creating improved coarse-grained models to study nucleation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Introduction

Classical nucleation theory and its limitations

Discovering better reaction coordinates with ML

Crystal structure and phase identification

Machine-learned force fields and efficient simulation

arXiv :2304 . 13815v2 [ cond-mat .stat-mech] 1 May 2023 Recent advances in describing and driving crystal nucleation using machine learning and artiﬁcial intelligence Eric R. Beyerlea,< , Ziyue Zoub and Pratyush Tiwarya,b a Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, United States b Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, United States | ARTICLE INFO | | AB STRACT | | --- | --- | --- | | Keywords:
Nucleation Molecular simulation Machine learning Enhanced sampling
Crystal structure identiﬁcation | | With the advent of faster computer processors and especially graphics processing units (GPUs) over the last few decades, the use of data-intensive machine learning (ML) and artiﬁcial intelligence (AI) has increased greatly, and the study of crystal nucleation has been one of the beneﬁciaries. In this review, we outline how ML and AI have been applied to address four outstanding diﬃculties of crystal nucleation: how to discover better reaction coordinates (RCs) for describing accurately non-classical nucleation situations; the development of more accurate force ﬁelds for describing the nucleation of multiple polymorphs or phases for a single system; more robust identiﬁcation methods for determining crystal phases and structures; and as a method to yield improved course-grained models for studying nucleation. | 1. Introduction For many years, the picture painted by classical nucleation theory (CNT)[1–4] was seen as an accurate method for describing nucleation processes, and, indeed, the robustness of this method can be seen in its continued use for describing both the thermodynamics and kinetics of many nucleation processes.[5–7] However, it has also become clear that not all nucleation events follow a purely classical pathway where the necessary and suﬃcient reaction coordinate (RC) is the size of the spherical crystal nucleus.[3, 8–18] Furthermore, even if N , the size of the nascent crystal nucleus, can be shown to be a suﬃciently good RC, CNT also stipulates that there is a single energy barrier along the RC corresponding to the barrier required to form the surface of the spherical critical nucleus of size N < . However, it is well-known that for many nucleation processes the Ostwald step mechanism,[19] whereby the most kinetically accessible crystalline structure forms ﬁrst, followed by the more thermodynamically stable one, is the preferred nucleation pathway. This mechanism that requires the presence of at least two energetic barriers, one to go from the liquid state to the kinetically stabilized crystal structure and a second to go from the kinetically stabilized crystal structure to the thermodynamically stable crystal structure. With these two points in mind, it is clear, both from a simple thought experiment and from reported results, that, in at least some cases, CNT is not an eﬀective way to describe the nucleation process. Unfortunately, at least some of the appeal of CNT is in its simplicity: it is an analytical, one-dimensional theory with both past and contemporary success. So, to obtain new RCs for the description of nonclassical nucleation events, we must almost certainly use more nuanced, potentially non-linear RCs that are functions of many input features, which are themselves functions of the original coordinate space. One eﬃcient method to construct [ebeyerle@umd.edu](ebeyerle@umd.edu) (E.R. Beyerle) ORCID(s): 0000-0001-5717-3197 (E.R. Beyerle) such non-linear, feature-heavy RCs, at least in theory, is through the use of machine learning techniques, such as deep neural networks (deep NNs) of various ﬂavors.[20–29] These deep NNs are ideal in that they are, under certain conditions, universal function approximators,[30] meaning they should, with proper parameterization, be able to characterize arbitrarily complex RCs for describing almost any nucleation process.[31] However, ﬁnding goo

FAQs

Why is classical nucleation theory not sufficient for all crystal nucleation events?

Not all nucleation follows a purely classical pathway where the reaction coordinate is only the size of a spherical nucleus. Many systems proceed through non-classical routes such as the Ostwald step mechanism, which involves at least two energy barriers.

How can machine learning help in describing non-classical nucleation?

ML methods can be used to construct more nuanced, potentially non-linear reaction coordinates that depend on many input features, enabling better representation of complex nucleation behaviors than one-dimensional classical approaches.

What roles do ML-based methods play in crystal identification and force fields?

Robust ML-based classification methods improve identification of crystal phases and structures, including imperfect or defective motifs. ML-driven force fields can reach density-functional-theory-level accuracy while enabling simulations at speeds far beyond direct DFT calculations.

Aug 5, 2026

Upload by Logic