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

• URL: http://arxiv.org/abs/2303.14760v3
• Date: Thu, 1 Jun 2023 12:22:51 GMT
• Title: Extrapolation to complete basis-set limit in density-functional theory by quantile random-forest models
• Abstract summary: We find a machine-learning model that extrapolates finite basis-size calculations to the CBS limit. A quantile-random-forest model is used to estimate the total-energy correction with respect to a fully converged calculation. Our approach also provides prediction intervals, which quantify the uncertainty of the models' predictions.
• Score: 0.41104099603771493
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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