  We present global predictions of the ground state mass of atomic nuclei based
on a novel Machine Learning (ML) algorithm. We combine precision nuclear
experimental measurements together with theoretical predictions of unmeasured
nuclei. This hybrid data set is used to train a probabilistic neural network.
In addition to training on this data, a physics-based loss function is employed
to help refine the solutions. The resultant Bayesian averaged predictions have
excellent performance compared to the testing set and come with well-quantified
uncertainties which are critical for contemporary scientific applications. We
assess extrapolations of the model's predictions and estimate the growth of
uncertainties in the region far from measurements.
