Data-driven learning of 3-point correlation functions as microstructure representations

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 (100-fold smaller than the full set), and the identification of such subsets can be achieved by Bayesian optimization on a small microstructure dataset. The proposed representation can directly be used to compute material properties by leveraging the effective medium theory, allowing the construction of predictive structure-property models with significantly less data than needed by purely data-driven methods and with a computational cost 100-fold lower than the physics-based model.