Physics- and data-driven active learning of neural network representations for free energy density functions of materials from statistical mechanics

Accurate free energy density representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy density model by training a neural network on DFT-informed Monte Carlo data. To optimize sampling in the high-dimensional Monte Carlo space, we present an active learning framework that integrates space-filling sampling, uncertainty-based sampling, and physics-informed sampling. Additionally, our approach includes methods such as hyperparameter tuning, dynamic sampling, and novelty enforcement. These strategies can be combined to reduce the mean squared error-either globally or in targeted regions of interest-while minimizing the number of required data points. The framework introduced here is broadly applicable to Monte Carlo sampling of a range of materials systems.