Spectral operator representations

Machine learning in atomistic materials science has grown to become a powerful tool, with most approaches focusing on atomic arrangements, typically decomposed into local atomic environments. This approach, while well-suited for machine-learned potentials, is conceptually at odds with learning complex intrinsic properties, which are often driven by spectral properties (e.g., band gaps or mobilities) that cannot be readily atomically partitioned. For such applications, methods which represent the electronic rather than the atomic structure are promising. We discuss a general framework for these spectral operator representations (SOREPs) as electronic structure descriptors which take advantage of the natural symmetries and inherent interpretability of physical models. Using this framework, we formulate a simple SOREP and apply it to the discovery of novel transparent conducting materials (TCMs) in the Materials Cloud 3D database (MC3D) using a random forest classifier. By training only on 1% (N=222) of materials in the MC3D, the model is able to correctly label more than 75% of entries in the database which meet common screening criteria for promising TCMs.