Learning glass transition temperatures via dimensionality reduction with data from computer simulations: Polymers as the pilot case

TL;DR

This study demonstrates that diffusion map analysis of molecular simulation data, combined with Gaussian mixture models, can accurately predict glass transition temperatures in polymers, offering a unified computational framework.

Contribution

It introduces a novel approach using diffusion maps and GMMs to evaluate glass transition temperatures from molecular simulation data, outperforming PCA in accuracy.

Findings

Diffusion maps with GMMs accurately identify $T_g$ from simulation data.

RDF and MSD descriptors with DM closely match experimental $T_g$ values.

PCA was less effective than DM in predicting $T_g$.

Abstract

Machine learning (ML) methods provide advanced means for understanding inherent patterns within large and complex datasets. Here, we employ the principal component analysis (PCA) and the diffusion map (DM) techniques to evaluate the glass transition temperature ($T_\mathrm{g}$) from low-dimensional representations of all-atom molecular dynamic (MD) simulations of polylactide (PLA) and poly(3-hydroxybutyrate) (PHB). Four molecular descriptors were considered: radial distribution functions (RDFs), mean square displacements (MSDs), relative square displacements (RSDs), and dihedral angles (DAs). By applying a Gaussian Mixture Model (GMM) to analyze the PCA and DM projections, and by quantifying their log-likelihoods as a density-based metric, a distinct separation into two populations corresponding to melt and glass states was revealed. This separation enabled the $T_\mathrm{g}$ evaluation from a cooling-induced sharp increase in the overlap between log-likelihood distributions at different temperatures. $T_\mathrm{g}$ values derived from the RDF and MSD descriptors using DM closely matched the standard computer simulation-based dilatometric and dynamic $T_\mathrm{g}$ values for both PLA and PHB models. This was not the case for PCA. The DM-transformed DA and RSD data resulted in $T_\mathrm{g}$ values in agreement with experimental ones. Overall, the fusion of atomistic simulations and diffusion maps complemented with the Gaussian Mixture Models presents a promising framework for computing $T_\mathrm{g}$ and studying the glass transition in a unified way across various molecular descriptors for glass-forming materials.