Even-sampling methods have allowed for the evaluation of the density of states, providing access to all thermodynamic properties at once. However, these methods become highly intensive for multicomponent systems. We develop a combined Expanded Wang-Landau-Machine Learning (EWL-ML) approach to predict efficiently and accurately the thermodynamics of mixtures. We show that only a fraction of the EWL results is necessary to train a neural network and provide results in very good agreement with experiments. The resulting speed-up is expected to considerably increase the range and complexity of systems that can be studied with even-sampling methods.