  Machine learning methods and uncertainty quantification have been gaining
interest throughout the last several years in low-energy nuclear physics. In
particular, Gaussian processes and Bayesian Neural Networks have increasingly
been applied to improve mass model predictions while providing well-quantified
uncertainties. In this work, we use the probabilistic Mixture Density Network
(MDN) to directly predict the mass excess of the 2016 Atomic Mass Evaluation
within the range of measured data, and we extrapolate the inferred models
beyond available experimental data. The MDN not only provides mean values but
also full posterior distributions both within the training set and extrapolated
testing set. We show that the addition of physical information to the feature
space increases the accuracy of the match to the training data as well as
provides for more physically meaningful extrapolations beyond the the limits of
experimental data.
