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.(c) 2022 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper addresses the challenge of identifying complete, concise, and explainable quantitative microstructure representations for disordered heterogeneous material systems. It proposes a representation composed of three-point correlation functions and demonstrates that a concise subset of three-point correlations can characterize various microstructures. Bayesian optimization is used to identify such subsets from a small microstructure dataset. The proposed representation allows for the computation of material properties and the construction of predictive structure-property models with significantly less data and lower computational cost compared to purely data-driven and physics-based methods.