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

• Main Authors: Speckhard, Daniel T, Carbogno, Christian, Ghiringhelli, Luca, Lubeck, Sven, Scheffler, Matthias, Draxl, Claudia
• Format: Journal Article
• Language: English
• Published: 26-03-2023
• Subjects: Physics - Computational Physics; Physics - Materials Science; Statistics - Machine Learning
• DOI: 10.48550/arxiv.2303.14760

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.