Reconstruction of 3D microstructures from 2D images using a gradient-based sequential optimization approach

The prediction of macro-scale properties of materials requires study of their 3D stochastic microstructures. Since experimentally acquiring a 3D image is often infeasible, computational microstructure reconstruction approaches such as statistical functions-based and machine learning (ML) based methods are used as alternatives to generate 3D images. However, conventional statistical functions-based methods can be prohibitively slow and limiting for complex microstructure systems and large image sizes. Furthermore, the large memory required in ML-based reconstruction methods becomes a bottleneck in reconstructing large 3D microstructures. To overcome this, we propose a parallelizable optimization-based microstructure reconstruction procedure. Here, the statistical descriptors and feature maps from VGG19, a pre-trained deep neural network are combined into an overall differentiable loss function [1]. Our novel approach efficiently reconstructs a 3D microstructure by performing sequential optimization of 2D slices in each orthogonal direction. This approach requires significantly lower memory compared to the latest ML-based 3D reconstruction approaches and provides excellent scalability. Several numerical examples for the reconstruction of 3D bi-phase porous ceramic material and multi-phase polycrystalline material demonstrate the generalizability of the proposed methodology. Applications of the proposed approach include generation of a high-resolution microstructure from low-resolution micrographs, reconstruction of 3D microstructures from 2D/3D images, generation of massive datasets of material systems with targeted properties, and microstructure induced uncertainty quantification and propagation.