Quantifying accuracy of stochastic methods of reconstructing complex materials by deep learning.

Time and cost are two main hurdles to acquiring a large number of digital image I of the microstructure of materials. Thus, use of stochastic methods for producing plausible realizations of materials' morphology based on one or very few images has become an increasingly common practice in their modeling. The accuracy of the realizations is often evaluated using two-point microstructural descriptors or physics-based modeling of certain phenomena in the materials, such as transport processes or fluid flow. In many cases, however, two-point correlation functions do not provide accurate evaluation of the realizations, as they are usually unable to distinguish between high- and low-quality reconstructed models. Calculating flow and transport properties of the realization is an accurate way of checking the quality of the realizations, but it is computationally expensive. In this paper a method based on machine learning is proposed for evaluating stochastic approaches for reconstruction of materials, which is applicable to any of such methods. The method reduces the dimensionality of the realizations using an unsupervised deep-learning algorithm by compressing images and realizations of materials. Two criteria for evaluating the accuracy of a reconstruction algorithm are then introduced. One, referred to as the internal uncertainty space, is based on the recognition that for a reconstruction method to be effective, the differences between the realizations that it produces must be reasonably wide, so that they faithfully represent all the possible spatial variations in the materials' microstructure. The second criterion recognizes that the realizations must be close to the original I and, thus, it quantifies the similarity based on an external uncertainty space. Finally, the ratio of two uncertainty indices associated with the two criteria is considered as the final score of the accuracy of a stochastic algorithm, which provides a quantitative basis for comparing various realizations and the approaches that produce them. The proposed method is tested with images of three types of heterogeneous materials in order to evaluate four stochastic reconstruction algorithms.