Generative reconstruction of 2D and 3D polycrystalline microstructures using symmetrized hyperspherical harmonics
Establishing structure-property linkages in polycrystalline materials requires representative two- (2D) and three- (3D) dimensional microstructural inputs for full-field simulations. A core objective of microstructure characterization and reconstruction is the generative synthesis of 2D and 3D microstructures that reflect a target statistical ensemble using limited 2D data as a reference. This work introduces an orientation-based differentiable microstructure characterization and reconstruction framework, implemented in MCRpy, to perform reconstructions of voxelized images. Unit quaternions in combination with symmetrized hyperspherical harmonics are utilized to derive a continuous, symmetry-invariant representation of crystallographic orientations to overcome the numerical singularities and discontinuities associated with traditional Euler-based methods. The descriptor-based reconstructions are driven by a set combining two-point spatial correlations, a novel hybrid three-point variogram, and a mean variation regularizer to capture both global texture and local interfacial topology. The framework's efficiency is demonstrated by reconstructing 3D realizations from 2D orientation data of an aluminum alloy after thermo-mechanical processing, successfully recovering both morphological features and crystallographic distribution. Systematic benchmarking indicates that second-order gradient-based optimization, utilizing the L-BFGS-B algorithm, effectively navigates the complex loss landscape to generate high-fidelity realizations with minimal residuals. This methodology provides a versatile, open-source framework for the digital synthesis of polycrystalline representative volume elements to facilitate the rapid development of microstructure-informed materials design workflows.