TexFlow models grain orientations for better material processing prediction
TexFlow: learning crystallographic texture on SO(3) manifold via normalizing flows
Computational Engineering, Finance, and Science
Summary
Understanding how grains are oriented in materials helps predict how those materials will behave. Traditional methods don’t directly connect these orientations with manufacturing conditions. The authors created TexFlow, a tool that learns to represent orientations accurately on a special curved space called SO(3), which matches rotation data naturally. This method lets them model how grain orientations change depending on factors like temperature or stress, improving predictions about materials.
What this means in practice
- •For materials engineers: Use TexFlow to predict how grain orientations evolve under different processing conditions, aiding the design of stronger or more reliable materials.
- •For manufacturing process designers: Incorporate accurate texture models from TexFlow to optimize processing parameters like temperature and deformation for improving material properties.
Authors
Gowtham Nimmal Haribabu, Tarakram Ramgopal, Divakar Vetriveeran, Siddhant Kumar
Abstract
Crystallographic texture is an important microstructural feature that statistically describes the orientations of grains in polycrystalline materials. Conventional texture analysis relies on the orientation distribution functions and pole figures, which are essential for interpreting the texture of a given material specimen but do not, by themselves, provide a direct framework for predictive modeling of process-structure-property linkages. Data- and machine learning-based approaches offer a means to address this gap; however, a key challenge lies in developing representations and learning frameworks that account for the manifold structure of rotations. In particular, many existing machine learning techniques are designed for Euclidean data and therefore are not readily applicable to rotations in the non-Euclidean group $\text{SO}(3)$. Here we introduce TexFlow, a conditional normalizing flow framework for texture modeling that learns a probability distribution over rotations in $\text{SO}(3)$ by construction. Rotations are encoded in a six-dimensional Gram-Schmidt orthogonalization representation which is then mapped back to valid rotations $\mathbf{R}\in\text{SO}(3)$. The framework supports conditional probabilistic modeling of texture $p(\mathbf{R}|c)$, where $c$ may represent processing parameters like temperature or deformation state. To complement conventional texture-analysis visualizations, such as pole figures and sections of the orientation distribution function, we further introduce Hopf-fibration visualizations as a compact global representation of texture. TexFlow is validated on both unconditional and conditional experimental and simulated texture datasets spanning diverse material systems. We show that TexFlow can accurately capture multimodal textures and their conditional evolution, providing a data-driven framework for establishing process-texture linkages.