Identifying "materials genes" by symbolic regression: The hierarchical SISSO approach*

A key goal in materials science is the identification of interpretable and basic physical features that correlate with materials properties and functions. These correlations reflect the actuators, i.e. the facilitators or obstructors of the different governing processes, for a given property, and have thus been referred to as "materials genes". Here, we illustrate how to find these "materials genes", even in the limit of small datasets, using symbolic regression [1]. In particular, we discuss a new strategy for discovering more complicated relationships between the features and properties by exploiting the learning of simpler, but related properties: the hierarchical sure-independence screening and sparsifying operator (hiSISSO) approach. We demonstrate this strategy by using models for the lattice constants of ABO₃ perovskites to learn their bulk moduli. We show that the hierarchical approach not only outperforms traditional machine-learning methods when trained on small datasets, but also provides exploitable models, which are suitable for materials optimization and design.
[1] R. Ouyang, et al., Phys. Rev. Mater. 2, 083802 (2018).