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Synthetic microstructure generation algorithms have emerged as a key tool for enabling large ICME and Materials Informatics efforts. In particular, statistically conditioned generative models allow researchers to systematically explore complex design spaces encountered in microstructure design. In spite of the engineering importance of polycrystalline materials, generative frameworks for these systems remain extremely limited. This stunted development – in comparison to the N-phase microstructure generation problem – occurs because of the complexities inherent to the representation of the polycrystalline orientation fields. For example, these fields exhibit multiple crystal- and sample-level symmetries. In prior work, these difficulties have resulted in instabilities in deep generative models for polycrystalline microstructures. In this work, we propose the use of a Reduced-Order Generalized Spherical Harmonic (ROGSH) basis to address the challenge described above. The proposed approach accounts for the complex sample- and crystal-level symmetries, and produces well behaved and low dimensional representations whose space has a meaningful Euclidean measure. We then demonstrate the ROGSH basis’s remarkable ability to produce stable denoising diffusion models by using our recently established Local–Global generative framework to create visually realistic synthetic polycrystalline microstructures. Furthermore, we demonstrate that the generation process can be conditioned on both first- and second-order spatial statistics of the polycrystalline orientation fields. 

Digital twins are emerging as powerful tools for supporting innovation as well as optimizing the in-service performance of a broad range of complex physical machines, devices, and components. A digital twin is generally designed to provide accurate in-silico representation of the form (i.e., appearance) and the functional response of a specified (unique) physical twin. This paper offers a new perspective on how the emerging concept of digital twins could be applied to accelerate materials innovation efforts. Specifically, it is argued that the material itself can be considered as a highly complex multiscale physical system whose form (i.e., details of the material structure over a hierarchy of material length) and function (i.e., response to external stimuli typically characterized through suitably defined material properties) can be captured suitably in a digital twin. Accordingly, the digital twin can represent the evolution of structure, process, and performance of the material over time, with regard to both process history and in-service environment. This paper establishes the foundational concepts and frameworks needed to formulate and continuously update both the form and function of the digital twin of a selected material physical twin. The form of the proposed material digital twin can be captured effectively using the broadly applicable framework of n-point spatial correlations, while its function at the different length scales can be captured using homogenization and localization process-structure-property surrogate models calibrated to collections of available experimental and physics-based simulation data.