Statistical characterization and reconstruction of heterogeneous microstructures using deep neural network

Abstract

Heterogeneous materials, whether natural or artificial, are usually composed of distinct constituents present in complex microstructures with discontinuous, irregular and hierarchical characteristics. For many heterogeneous materials, such as porous media and composites, the microstructural features are of fundamental importance for their macroscopic properties. This paper presents a novel method to statistically characterize and reconstruct random microstructures through a deep neural network (DNN) model, which can be used to study the microstructure–property relationships. In our method, the digital microstructure image is assumed to be a stationary Markov random field (MRF), and local patterns covering the basic morphological features are collected to train a DNN model, after which statistically equivalent samples can be generated through a DNN-guided reconstruction procedure. Furthermore, to overcome the short-distance limitation associated with the MRF assumption, a multi-level approach is developed to preserve the long-distance morphological features of heterogeneous microstructures. A large number of tests have been conducted to compare the reconstructed and target microstructures in both morphological characteristics and physical properties, and good agreements are observed in all test cases. The proposed method is efficient, accurate, versatile, and especially beneficial to the statistical reconstruction of 2D/3D microstructures with long-distance correlations.