Denoising diffusion-based synthetic generation of three-dimensional (3D) anisotropic microstructures from two-dimensional (2D) micrographs

Integrated computational materials engineering (ICME) has significantly enhanced the systemic analysis of the relationship between microstructure and material properties, paving the way for the development of high-performance materials. However, analyzing microstructure-sensitive material behavior remains challenging due to the scarcity of three-dimensional (3D) microstructure datasets. Moreover, this challenge is amplified if the microstructure is anisotropic, as this results in anisotropic material properties as well. In this paper, we present a framework for reconstruction of anisotropic microstructures solely based on two-dimensional (2D) micrographs using conditional diffusion-based generative models (DGMs). The proposed framework involves spatial connection of multiple 2D conditional DGMs, each trained to generate 2D microstructure samples for three different orthogonal planes. The connected multiple reverse diffusion processes then enable effective modeling of a Markov chain for transforming noise into a 3D microstructure sample. Furthermore, a modified harmonized sampling is employed to enhance the sample quality while preserving the spatial connection between the slices of anisotropic microstructure samples in 3D space. To validate the proposed framework, the 2D-to-3D reconstructed anisotropic microstructure samples are evaluated in terms of both the spatial correlation function and the physical material behavior. The results demonstrate that the framework is capable of reproducing not only the statistical distribution of material phases but also the material properties in 3D space. This highlights the potential application of the proposed 2D-to-3D reconstruction framework in establishing microstructure-property linkages, which could aid high-throughput material design for future studies

Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling

Acquiring reliable microstructure datasets is a pivotal step toward the systematic design of materials with the aid of integrated computational materials engineering (ICME) approaches. However, obtaining three-dimensional (3D) microstructure datasets is often challenging due to high experimental costs or technical limitations, while acquiring two-dimensional (2D) micrographs is comparatively easier. To deal with this issue, this study proposes a novel framework for 2D-to-3D reconstruction of microstructures called Micro3Diff using diffusion-based generative models (DGMs). Specifically, this approach solely requires pre-trained DGMs for the generation of 2D samples, and dimensionality expansion (2D-to-3D) takes place only during the generation process (i.e., reverse diffusion process). The proposed framework incorporates a new concept referred to as multi-plane denoising diffusion, which transforms noisy samples (i.e., latent variables) from different planes into the data structure while maintaining spatial connectivity in 3D space. Furthermore, a harmonized sampling process is developed to address possible deviations from the reverse Markov chain of DGMs during the dimensionality expansion. Combined, we demonstrate the feasibility of Micro3Diff in reconstructing 3D samples with connected slices that maintain morphologically equivalence to the original 2D images. To validate the performance of Micro3Diff, various types of microstructures (synthetic and experimentally observed) are reconstructed, and the quality of the generated samples is assessed both qualitatively and quantitatively. The successful reconstruction outcomes inspire the potential utilization of Micro3Diff in upcoming ICME applications while achieving a breakthrough in comprehending and manipulating the latent space of DGMs.