title: Prediction uncertainty of density functional approximations for properties of crystals with cubic symmetry.
abstract: 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.
authors.affiliation: †Laboratoire de Chimie Physique, UMR8000, CNRS, F-91405 Orsay, France.|‡Laboratoire de Chimie Physique, UMR8000, Univ. Paris-Sud, F-91405 Orsay, France.
authors.forename: Pascal
authors.initials: P
authors.lastname: Pernot
authors.affiliation: §Department of Chemistry and NIS Center, University of Torino, Via P. Giuria 7, I-10125 Torino, Italy.
authors.forename: Bartolomeo
authors.initials: B
authors.lastname: Civalleri
authors.affiliation: ∥Department of Chemical and Geological Sciences, University of Modena and Reggio-Emilia, Via Campi 183, I-41125 Modena, Italy.
authors.forename: Davide
authors.initials: D
authors.lastname: Presti
authors.affiliation: ⊥Laboratoire de Chimie Théorique, UMR7616, CNRS, F-75005 Paris, France.|#Laboratoire de Chimie Théorique, UMR7616, UPMC Univ Paris 06, F-75005 Paris, France.
authors.forename: Andreas
authors.initials: A
authors.lastname: Savin