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

arXiv: https://arxiv.org/abs/2303.14760 · HTML: https://mlsanity.com/paper/2303.14760/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 23 references that are in the map.
- First posted on arXiv 26 Mar 2023.

## Builds on (most cited first, 1 of 1)

- [Neural Architecture Search for Energy Efficient Always-on Audio Models](https://mlsanity.com/paper/2202.05397/) (2022)

## Abstract (arXiv)

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.