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 orbital-free density functional theory (DFT). 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 DFT where we initialise calculations with data-derived densities only when we are confident about their quality. This results in a guaranteed acceleration to selfconsistency 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.

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