Exploring structure–property relationships in sparse data environments using mixture-of-experts models

The mixture-of-experts (MoE) framework, which enables collaborative utilization of multiple models specialized in distinct tasks toward a new task, is especially useful for materials science problems involving sparse data where simultaneous learning from multiple complementary sources is desired. We develop deep neural network (NN)-based MoE models for predicting elastic constants of cubic metal-halide perovskites (MHPs) using other pretrained models and stiffness tensor data determined using density functional theory simulations. Beyond benchmarking the MoE models, their latent feature space is extracted through the penultimate layer of the NNs and analyzed to create structure–property maps revealing complex relationships involving elasticity and site chemistry in cubic MHPs. Finally, the utility of MoE for predicting sparse engineering scale mechanical properties is demonstrated by developing predictive models for Vickers hardness and fracture toughness of inorganic crystals. This study thus highlights MoE as a promising technique for tackling sparse data problems in materials science.