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

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.