Towards machine learning for microscopic mechanisms: a formula search for crystal structure stability based on atomic properties

TL;DR

This paper introduces a combinatorial machine-learning method to derive simple physical formulas from atomic properties that predict the stability of crystal structures in semiconducting compounds, enhancing interpretability and efficiency.

Contribution

It presents a novel approach to extract physically interpretable formulas using linear regression and grid search, linking atomic properties to crystal stability with minimal computational cost.

Findings

1D formulas effectively predict energetic stability.

Spatial atomic properties, especially p-shell radii, influence crystal structure preference.

Automatically derived formulas highlight key atomic features driving stability.

Abstract

Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address the latter aspect, we propose a combinatorial machine-learning approach to obtain physical formulas based on simple and easily-accessible ingredients, such as atomic properties. The latter are used to build materials features that are finally employed, through Linear Regression, to predict the energetic stability of semiconducting binary compounds with respect to zincblende and rocksalt crystal structures. The adopted models are trained using dataset built from first-principles calculations. Our results show that already one-dimensional (1D) formulas well describe the energetics; a simple grid-search optimization of the automatically-obtained 1D-formulas enhances the prediction performances at a very small computational cost. In addition, our approach allows to highlight the role of the different atomic properties involved in the formulas. The computed formulas clearly indicate that "spatial" atomic properties (i.e. radii indicating maximum probability densities for $s,p,d$ electronic shells) drive the stabilization of one crystal structure with respect to the other, suggesting the major relevance of the radius associated to the $p$-shell of the cation species.