Targeting the partition function of chemically disordered materials with a generative approach based on inverse variational autoencoders

Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an excessive amount of configurations or do not ensure that the configuration space has been properly covered. In this work, we propose a novel approach where generative machine learning is used to yield a representative set of configurations for accurate property evaluation and provide accurate estimations of atomic-scale properties with minimal computational cost. Our method employs a specific type of variational autoencoder with inverse roles for the encoder and decoder, enabling the application of an unsupervised active learning scheme that does not require any initial training database. The model iteratively generates configuration batches, whose properties are computed with conventional atomic-scale methods. These results are then fed back into the model to estimate the partition function, repeating the process until convergence. We illustrate our approach by computing point-defect formation energies and concentrations in (U, Pu)O2 mixed-oxide fuels. In addition, the ML model provides valuable insights into the physical factors influencing the target property. Our method is generally applicable to explore other properties, such as atomic-scale diffusion coefficients, in ideally or non-ideally disordered materials like high-entropy alloys.