Interpretability of linear regression models of glassy dynamics

Abstract

Data-driven models can accurately describe and predict the dynamical properties of glass-forming liquids from structural data. Accurate predictions, however, do not guarantee an understanding of the underlying physical phenomena and the key factors that control them. In this paper, we illustrate the merits and limitations of linear regression models of glassy dynamics built on high-dimensional structural descriptors. By analyzing data for a two-dimensional glass model, we show that several descriptors commonly used in glass-transition studies display multicollinearity, which hinders the interpretability of linear models. Ridge regression suppresses some of the shortcomings of multicollinearity, but its solutions are not concise enough to be physically interpretable. Only by using dimensional reduction techniques we do eventually obtain linear models that strike a balance between prediction accuracy and interpretability. Our analysis points to a key role of local packing and composition fluctuations in the glass model under study.