  Machine-learning methods are nowadays of common use in the field of material
science. For example, they can aid in optimizing the physicochemical properties
of new materials, or help in the characterization of highly complex chemical
compounds. An especially challenging problem arises in the modeling of
chemically disordered solid solutions, for which some properties depend on the
distribution of chemical species in the crystal lattice. This is the case of
defect properties of uranium-plutonium mixed oxides nuclear fuels. The number
of possible configurations is so high that the problem becomes intractable if
treated with direct sampling. We thus propose a machine learning approach,
based on generative modeling, to optimize the exploration of this large
configuration space. A probabilistic, semi-supervised approach using Mixture
Density Network is applied to estimate the concentration of thermal defects in
(U, Pu)O2. We show that this method, based on the prediction of the density of
states of formation energy of a defect, is computationally much more
cost-efficient compared to other approaches available in the literature.
