Why It's Important:  The development of materials with superior properties has been a longstanding key enabler of technological advancement and a core pillar of scientific research, driving innovation across various industries and pushing the boundaries of what is possible in engineering and technology. However, the limitations of current microscopy techniques present a critical obstacle, as 3D microscopy—while essential for in-depth studies of material structures—is prohibitively expensive and time-consuming. In contrast, 2D microscopy is much more affordable and accessible, but it falls short in capturing the full complexity of a material's internal structure. The ability to construct 3D material structures from 2D microscopy images in a cost-effective manner would represent a transformative advancement in materials science, enabling faster and more efficient development of advanced materials.

 

Polycrystalline structure under microscopyOur Approach: Our approach has two primary objectives. The first goal is to develop a generative model that captures the statistical distribution of 3D microstructural features in polycrystalline materials. These features, which include the spatial arrangement of grains and crystallites, significantly influence the macroscopic properties of materials. The generative model will be constructed using existing 3D experimental data, leveraging advanced machine learning techniques, particularly Denoising Diffusion Models, to learn the complex joint probabilities of the 3D microstructures.

The second objective involves constructing 3D material structures that are statistically consistent with new 2D microscopy slices obtained from material samples. This ill-posed problem will be tackled using a Bayesian inversion approach, which will leverage the generative prior to regularize the solution space. The innovative application of Plug and Play MCMC (PnP MCMC) algorithms will allow for modular conditioning of generative models, facilitating the integration of datasets with different dimensionalities and enabling the generation of 3D structures from 2D data.

The research is expected to have a transformative impact on the design, development, and deployment of new and improved materials in advanced technologies. By enabling the accurate and efficient reconstruction of 3D material structures from 2D images, the proposed work will significantly enhance the understanding of PSP linkages and accelerate the development of materials with superior properties