  This paper considers the open challenge of identifying complete, concise, and
explainable quantitative microstructure representations for disordered
heterogeneous material systems. Completeness and conciseness have been achieved
through existing data-driven methods, e.g., deep generative models, which,
however, do not provide mathematically explainable latent representations. This
study investigates representations composed of three-point correlation
functions, which are a special type of spatial convolutions. We show that a
variety of microstructures can be characterized by a concise subset of
three-point correlations, and the identification of such subsets can be
achieved by Bayesian optimization. Lastly, we show that the proposed
representation can directly be used to compute material properties based on the
effective medium theory.
