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Machine Learning (ML) techniques are revolutionizing the way to performefficient materials modeling. Nevertheless, not all the ML approaches allow forthe understanding of microscopic mechanisms at play in different phenomena. Toaddress the latter aspect, we propose a combinatorial machine-learning approachto obtain physical formulas based on simple and easily-accessible ingredients,such as atomic properties. The latter are used to build materials features thatare finally employed, through Linear Regression, to predict the energeticstability of semiconducting binary compounds with respect to zincblende androcksalt crystal structures. The adopted models are trained using dataset builtfrom first-principles calculations. Our results show that alreadyone-dimensional (1D) formulas well describe the energetics; a simplegrid-search optimization of the automatically-obtained 1D-formulas enhances theprediction performances at a very small computational cost. In addition, ourapproach allows to highlight the role of the different atomic propertiesinvolved 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 structurewith respect to the other, suggesting the major relevance of the radiusassociated to the $p$-shell of the cation species.

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