  Faithful representations of atomic environments and general models for
regression can be harnessed to learn electron densities that are close to the
ground state. One of the applications of data-derived electron densities is to
orbital-free density functional theory. However, extrapolations of densities
learned from a training set to dissimilar structures could result in inaccurate
results, which would limit the applicability of the method. Here, we show that
a non-Bayesian approach can produce estimates of uncertainty which can
successfully distinguish accurate from inaccurate predictions of electron
density. We apply our approach to density functional theory where we initialise
calculations with data-derived densities only when we are confident about their
quality. This results in a guaranteed acceleration to self-consistency for
configurations that are similar to those seen during training and could be
useful for sampling based methods, where previous ground state densities cannot
be used to initialise subsequent calculations.
