Black box vs gray box: Comparing GAP and GPrep-DFTB for ruthenium and ruthenium oxide

The increasing popularity of machine learning (ML) approaches in computational modeling, most prominently ML interatomic potentials, opened possibilities that were unthinkable only a few years ago—structure and dynamics for systems up to many thousands of atoms at an ab initio level of accuracy. Strictly referring to ML interatomic potentials, however, a number of modeling applications are out of reach, specifically those that require explicit electronic structure. Hybrid (“gray box”) models based on, e.g., approximate, semi-empirical ab initio electronic structure with the aid of some ML components offer a convenient synthesis that allows us to treat all aspects of a certain physical system on the same footing without targeting a separate ML model for each property. Here, we compare one of these [Density Functional Tight Binding with a Gaussian Process Regression repulsive potential (GPrep-DFTB)] with its fully “black box” counterpart, the Gaussian approximation potential, by evaluating performance in terms of accuracy, extrapolation power, and data efficiency for the metallic Ru and oxide RuO₂ systems, given exactly the same training set. The accuracy with respect to the training set or similar chemical motifs turns out to be comparable. GPrep-DFTB is, however, slightly more data efficient. The robustness of GPRep-DFTB in terms of extrapolation power is much less clear-cut for the binary system than for the pristine system, most likely due to imperfections in the electronic parametrization.