Pernot Pascal, Civalleri Bartolomeo, Presti Davide, Savin Andreas
†Laboratoire de Chimie Physique, UMR8000, CNRS, F-91405 Orsay, France.
‡Laboratoire de Chimie Physique, UMR8000, Univ. Paris-Sud, F-91405 Orsay, France.
J Phys Chem A. 2015 May 28;119(21):5288-304. doi: 10.1021/jp509980w. Epub 2015 Feb 10.
The performance of a method is generally measured by an assessment of the errors between the method's results and a set of reference data. The prediction uncertainty is a measure of the confidence that can be attached to a method's prediction. Its estimation is based on the random part of the errors not explained by reference data uncertainty, which implies an evaluation of the systematic component(s) of the errors. As the predictions of most density functional approximations (DFA) present systematic errors, the standard performance statistics, such as the mean of the absolute errors (MAE or MUE), cannot be directly used to infer prediction uncertainty. We investigate here an a posteriori calibration method to estimate the prediction uncertainty of DFAs for properties of solids. A linear model is shown to be adequate to address the systematic trend in the errors. The applicability of this approach to modest-size reference sets (28 systems) is evaluated for the prediction of band gaps, bulk moduli, and lattice constants with a wide panel of DFAs.
一种方法的性能通常通过评估该方法的结果与一组参考数据之间的误差来衡量。预测不确定性是对方法预测结果可信度的一种度量。其估计基于未由参考数据不确定性解释的误差的随机部分，这意味着要评估误差的系统分量。由于大多数密度泛函近似（DFA）的预测都存在系统误差，因此标准性能统计量，如绝对误差的平均值（MAE或MUE），不能直接用于推断预测不确定性。我们在此研究一种后验校准方法，以估计固体性质的DFA的预测不确定性。结果表明，线性模型足以处理误差中的系统趋势。对于带隙、体模量和晶格常数的预测，使用广泛的DFA对该方法在中等规模参考集（28个系统）上的适用性进行了评估。
