An Algorithm to Generate Synthetic 3D Microstructures from 2D Exemplars

The inverse problem of constructing 3D microstructures from 2D data is an area of active research within the materials science community. This paper presents the implementation of a robust, computationally efficient algorithm: the Hierarchical Algorithm for the Reconstruction of Exemplars (HARE), written in Python to reconstruct 3D features in a given microstructure from up to three orthogonal 2D exemplars and using nearest-neighbor matching to reproduce feature qualities, such as shape, size, and distribution. HARE’s feature sampling implements histogram reweighting to avoid both over- and undersampling. A neighborhood voting scheme allows each pixel to provisionally affect its neighbors according to its weight. The algorithm is presently configured for two-phase materials and is being extended to accommodate multiple phases. HARE is a convenient and robust base from which to generate statistically representative synthetic microstructures for use in multi-scale modeling or machine-learning applications to support advanced manufacturing and materials discovery.