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）计算的数值精度取决于多种计算参数，其中最关键的参数之一是基组大小。当基组无限大时，即达到完备基组（CBS）极限，可获得最高精度。本研究旨在寻找一种机器学习模型，将有限基组大小的计算结果外推至CBS极限。我们以63种二元固体为数据集，采用两种全电子DFT代码（exciting和FHI-aims）进行计算，这两种代码使用的基组类型截然不同。通过分位数随机森林模型，我们估计了相对于完全收敛计算的总能量修正与基组大小的函数关系。该随机森林模型对两种代码的对称平均绝对百分误差均低于25%，优于文献中的已有方法。此外，我们的方法还提供了预测区间，用于量化模型预测的不确定性。