Extrapolation to the complete basis-set limit in density-functional theory using statistical learning

Daniel T. Speckhard

doi:10.1103/PhysRevMaterials.9.013801

Extrapolation to the complete basis-set limit in density-functional theory using statistical learning

2025-01-13

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Daniel T. Speckhard *

DOI：10.1103/PhysRevMaterials.9.013801

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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 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 for periodic crystal structures. 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 and a symbolic regression approach using the SISSO model are 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. SISSO outperforms the random forest model for the exciting code. Our approach also provides prediction intervals, which quantify the uncertainty of the models' predictions.

Extrapolation to the complete basis-set limit in density-functional theory using statistical learning

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