Extrapolation to complete basis-set limit in density-functional theory by quantile random-forest models

Abstract: The numerical precision of density-functional-theory (DFT) calculations depends on a variety of computational parameters, one of the most critical being the basis-set size. The ultimate precision is reached with an infinitely large basis set, i.e., in the limit of a complete basis set (CBS). Our aim in this work is to find a machine-learning model that extrapolates finite basis-size calculations to the CBS limit. We start with a data set of 63 binary solids investigated with two all-electron DFT codes, exciting and FHI-aims, which employ very different types of basis sets. A quantile-random-forest model is used to estimate the total-energy correction with respect to a fully converged calculation as a function of the basis-set size. The random-forest model achieves a symmetric mean absolute percentage error of lower than 25% for both codes and outperforms previous approaches in the literature. Our approach also provides prediction intervals, which quantify the uncertainty of the models' predictions.