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.

翻译：密度泛函理论（DFT）计算的数值精度受多种计算参数影响，其中最关键参数之一是基组尺寸。当使用无限大基组时，即达到完备基组（CBS）极限，可获得最终精度。本研究旨在寻找一种机器学习模型，实现有限基组尺寸计算向CBS极限的外推。我们从63种二元固体的数据集出发，采用两种全电子DFT代码（exciting和FHI-aims）进行计算，这两种代码使用了不同类型的基组。我们利用分位数随机森林模型，估算相对于完全收敛计算的总能量修正量作为基组尺寸的函数。该随机森林模型对两种代码的对称平均绝对百分比误差均低于25%，优于文献中已有的方法。此外，我们的方法还能提供预测区间，用于量化模型预测的不确定性。