AI and the World's Hard Problems · Chemistry & materials · arXiv · 2026-10-21
TexFlow: learning crystallographic texture on SO(3) manifold via normalizing flows
Crystallographic texture, which statistically describes the orientations of grains in polycrystalline materials, is conventionally analyzed with orientation distribution functions and pole figures, but these do not by themselves support predictive modeling of process-structure-property linkages, and rotations living on the non-Euclidean group SO(3) limit the use of standard machine learning methods. TexFlow is a conditional normalizing flow that learns probability distributions over rotations in SO(3) through a six-dimensional Gram-Schmidt orthogonalization representation, supports conditional modeling p(R|c) where c can be processing parameters like temperature or deformation state, and introduces Hopf-fibration visualizations of texture. Validated on both experimental and simulated datasets, it accurately captures multimodal textures and their conditional evolution, providing a data-driven framework for process-texture linkages.