Microstructure Characterization and Reconstruction (MCR) allows for (i) generating a plausible 3D computational domain from 2D information like a microscopy image, (ii) generating a set of statistical volume elements from a single representative example and (iii) augmenting microstructure datasets by sampling and interpolating in the descriptor space and subsequently reconstructing the corresponding structures.

The classical approach lies in quantifying the microstructure morphology in terms of statistical descriptors and subsequently solving an optimization problem in the space of possible microstructures. For this purpose, the recent software MCRpy [1] enables flexible combinations of descriptors, loss functions and optimizers and therefore implements a spectrum of reconstruction approaches ranging from the classical Yeong-Torquato algorithm to recent, gradient-based formulations [2, 3, 4].

As an alternative, machine learning methods have been applied and adapted to microstructure reconstruction recently [5, 6]. These methods are presented and compared to the descriptor-based approach.

Finally, hybrid methods are presented that incorporate arbitrary descriptors in machine learning models.

[1] Seibert, Raßloff, Kalina, Ambati, Kästner, Microstructure Characterization and Reconstruction in Python: MCRpy, IMMJ, 2022
[2] Seibert, Ambati, Raßloff, Kästner, Reconstructing random heterogeneous media through differentiable optimization, COMMAT, 2021
[3] Seibert, Raßloff, Ambati, Kästner, Descriptor-based reconstruction of three-dimensional microstructures through gradient-based optimization, Acta Materialia, 2022
[4] Seibert, Raßloff, Kalina, Gussone, Bugelnig, Diehl, Kästner, Two-stage 2D-to-3D reconstruction of realistic microstructures: Implementation and numerical validation by effective properties, CMAME, 2023
[5] Düreth, Seibert Rücker, Handford, Kästner, Gude, Conditional diffusion-based microstructure reconstruction, MTCOMM, 2023
[6] Zhang, Seibert, Otto, Raßloff, Ambati, Kästner, DA-VEGAN: Differentiably Augmenting VAE-GAN for microstructure reconstruction from extremely small data sets, (submitted), 2023