Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via machine learning implementation

Aug 2, 2026

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A computational framework is presented that implements principal component analysis (PCA) combined with K-means and Gaussian mixture (GM) clustering to identify both structural and dynamical heterogeneities in supercooled liquids. The method uses weighted coordination numbers (WCNs) computed from particle positions to construct a low-dimensional feature representation of structural space, enabling K-means to classify particles into meso-states via PCA. It then maps meso-state identities to configurational real space to form nano-domains while addressing misclassified interfacial particles using an iterative co-learning strategy with GM probabilistic clustering until convergence. The resulting meso-state and domain classifications remain stable over long times and are used to quantify dynamical heterogeneities, indicating that liquid–liquid phase separation after quenching drives the observed heterogeneity.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Abstract

Introduction

Glass formation and supercooling

Heterogeneous dynamics and cage effect

Key unresolved questions

Journal of Physics: Condensed Matter PAPER • OPEN ACCESS Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of machine learning To cite this article: Viet Nguyen and Xueyu Song 2023 J. Phys. : Condens. Matter 35 465401 View the article online for updates and enhancements. You may also like -Structural origin of dynamic heterogeneity in three-dimensional colloidal glass formers and its link to crystal nucleation Takeshi Kawasaki and Hajime Tanaka -Heterogeneous dynamics in liquids: fluctuations in space and time Ranko Richert -Disorder enhanced dynamical heterogeneity in strain glass alloys Xuefei Tao and Hongxiang Zong This content was downloaded from IP address [173.20.96.19](173.20.96.19) on 05/05/2025 at 18:27 J. Phys.: Condens. Matter 35 (2023) 465401 (17pp) [https://doi.org/10.1088/1361-648X/acecef](https://doi.org/10.1088/1361-648X/acecef) Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of machine learning Viet Nguyen􀁂 and Xueyu Song∗ 􀁂 Ames Laboratory and Department of Chemistry, Iowa State University, Ames, IA, United States of America E-mail: [xsong@iastate.edu](xsong@iastate.edu) Received 7 April 2023, revised 26 June 2023 Accepted for publication 2 August 2023 Published 23 August 2023 Abstract A computational approach by an implementation of the principle component analysis (PCA) with K-means and Gaussian mixture (GM) clustering methods from machine learning algorithms to identify structural and dynamical heterogeneities of supercooled liquids is developed. In this method, a collection of the average weighted coordination numbers (WCNs) of particles calculated from particles’ positions are used as an order parameter to build a low-dimensional representation of feature (structural) space for K-means clustering to sort the particles in the system into few meso-states using PCA. Nano-domains or aggregated clusters are also formed in configurational (real) space from a direct mapping using associated meso-states’ particle identities with some misclassified interfacial particles. These classification uncertainties can be improved by a co-learning strategy which utilizes the probabilistic GM clustering and the information transfer between the structural space and configurational space iteratively until convergence. A final classification of meso-states in structural space and domains in configurational space are stable over long times and measured to have dynamical heterogeneities. Armed with such a classification protocol, various studies over the thermodynamic and dynamical properties of these domains indicate that the observed heterogeneity is the result of liquid–liquid phase separation after quenching to a supercooled state. Keywords: supercooled liquids, liquid–liquid phase transition, machine learning (Some figures may appear in colour only in the online journal) ∗ Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1361-648X/23/465401+17$33 .00 Printed in the UK 1 © 2023 The Author(s) . Published by IOP Publishing Ltd 1. Introduction Glass plays a central role in nature and our daily lives. It is essential in food processing, preservation of wildlife animals under extreme cold [1] . Ordinary window glass, mostly made of sand (SiO2 ), lime (CaCO3 ) and soda (Na2 CO3 ) is a best known manufactured amorphous solid product [2] . Optical wave guides use pure amorphous silica while silicon in photovoltaic cell is amorphous. In principle, glassy state is attained by supercooling a liquid below its melting temperature fast enough to avoid crystallization. Under such rapid cooling, the supercooled liquid at

FAQs

What machine-learning method is used to characterize heterogeneity in supercooled liquids?

The approach combines PCA with K-means clustering and Gaussian mixture (GM) clustering, using structural features derived from weighted coordination numbers.

How are structural meso-states related to configurational domains?

Meso-state assignments in structural space are mapped to particle identities to directly form nano-domains in real configurational space, accounting for misclassified interfacial particles.

How does the framework improve classification reliability and what indicates heterogeneity?

A co-learning strategy iteratively transfers information between structural space and configurational space using probabilistic GM clustering until convergence; stable classifications over long times then enable measurement of dynamical heterogeneities, attributed to liquid–liquid phase separation after quenching.

Aug 2, 2026

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