Learning descriptors from materials science (big) data

Abstract: Statistical learning of materials properties or functions so far starts with a largely silent, non-challenged step: the introduction of a set of descriptive parameter (a multidimensional descriptor). However, when the scientific relationship of the descriptor to the actuating mechanisms is unclear, causality of the learned descriptor-property relation is uncertain. Thus, scientific advancement, trustful prediction of new promising materials and identification of anomalies is doubtful. We discuss and analyze this issue and define requirements for a descriptor that is suited for statistical learning of materials properties and functions. We show how a meaningful descriptor can be found systematically, by means of compressed sensing techniques, which allow for an unbiased and robust model selection among many competing descriptive models. These concepts are demonstrated for solving problems in materials science: i) prediction of the relative stability of several possible crystal structures for octet binary semiconductors, and ii) prediction of the pressures at which the different crystal structures coexist, by using simple atomic input for building the feature space.
Furthermore, several problems in theoretical physics and chemistry can be recast into the expression of a given quantity via a basis set expansions at increasing accuracy. In general, it is not trivial to design a truly incremental basis set, where the optimal basis function are selected from an exhaustive pool of candidates. I show one application where a compressed-sensing based algorithm allows for the identification of a minimal basis set for variational problems in quantum chemistry, such as Hartree-Fock and Kohn-Sham Density Functional Theory.

The work is done in collaboration with J. Vybiral (Charles University, Prague), N. Menzel (FHI), C. Wang (FHI), S. Levchenko (FHI), C. Draxl (Humboldt University, Berlin), and M. Scheffler (FHI)