Modelling the dielectric constants of crystals using machine learning

The relative permittivity of a crystal is a fundamental property that links microscopic chemical bonding to macroscopic electromagnetic response. Multiple models, including analytical, numerical and statistical descriptions, have been made to understand and predict dielectric behaviour. Analytical models are often limited to a particular type of compounds, whereas machine learning (ML) models often lack interpretability. Here, we combine supervised ML, density functional perturbation theory, and analysis based on game theory to predict and explain the physical trends in optical dielectric constants of crystals. Two ML models, support vector regression and deep neural networks, were trained on a dataset of 1,364 dielectric constants. Shapley additive explanations (SHAP) analysis of the ML models reveals that they recover correlations described by textbook Clausius-Mossotti and Penn models, which gives confidence in their ability to describe physical behavior, while providing superior predictive power.