Describing materials via interpretable machine learning: the example of superconductivity

Modeling materials properties is often challenged by the intricate interplay of multiple underlying physical processes that govern materials behavior. Machine learning (ML) approaches may capture such intricacy more effectively than physics-based models, as they can identify nontrivial correlations based on appropriate data. However, their flexibility often comes at the expense of physical interpretability. Here, we employ the sure-independence screening and sparsifying operator (SISSO) symbolic-regression method to identify an interpretable analytical equation for the superconducting critical temperature (T_c) as an example of a materials property. We start from a dataset of 81 conventional superconductors and a broad pool of 43 candidate physical parameters describing these materials and capturing processes that may govern superconductivity, including those related to electronic structure and lattice dynamics. SISSO selects only a small subset of these variables and combines them into a compact analytical expression. The resulting model correlates T_c with the electron-phonon coupling parameter and the logarithmic average phonon frequency together with the density of the compound and composition-derived quantities based on the electronegativity of the constituent elements. These results demonstrate how SISSO distills a large space of candidate parameters into a model that depends on a few key variables, thereby accelerating the search for improved materials.