  Density functional theory is routinely applied to predict crystal structures.
The most common exchange-correlation functionals used to this end are the
Perdew-Burke-Ernzerhof (PBE) approximation and its variant PBEsol. We
investigate the performance of these functionals for the prediction of lattice
parameters and show how to enhance their accuracy using machine learning. Our
dataset is constituted by experimental crystal structures of the Inorganic
Crystal Structure Database matched with PBE-optmized structures stored in the
materials project database. We complement these data with PBEsol calculations.
We demonstrate that the accuracy and precision of PBE/PBEsol volume predictions
can be noticeably improved a posteriori by employing simple, explainable
machine learning models. These models can improve PBE unit cell volumes to
match the accuracy of PBEsol calculations, and reduce the error of the latter
with respect to experiment by 35%. Further, the error of PBE lattice constants
is reduced by a factor of 3--5. A further benefit of our approach is the
implicit correction of finite temperature effects without performing phonon
calculations.
