From Texture Comparison to Inverse Materials Design

Crystallographic texture, which is the statistical distribution of grain orientations in a polycrystalline material is a key microstructural feature governing mechanical behavior, particularly anisotropy in metals. During manufacturing processes such as rolling, forming, or heat treatment, textures evolve continuously, and even subtle changes can lead to significant variations in elastic and plastic properties. For materials engineers and process designers, this creates a fundamental challenge: how can texture evolution be quantified in a way that is both physically meaningful and suitable for data-driven design and inverse optimization?

Traditional approaches to comparing textures typically rely on algebraic differences between their mathematical representations. While computationally efficient, these measures neglect the geometry of orientation space and therefore fail to reflect how textures actually evolve under deformation. As a consequence, physically similar textures may appear distant, while dissimilar ones may be treated as close. This limitation becomes particularly problematic in inverse design settings, where distances between microstructures guide process optimization, and learning-based exploration of design spaces.

This research addresses this challenge by systematically investigating distance measures for crystallographic textures, with a particular focus on optimal-transport-based approaches such as the Earth Mover’s Distance. By interpreting texture comparison as a transport problem, these distances quantify the minimal effort required to transform one orientation distribution into another, naturally embedding the geometry of orientation space into the metric.

From Texture Comparison to Inverse Materials Design
Representation of the ODF with 100 orientations by two-dimensional pole figures for the Miller’s indices (001), (110), and (111) with a resolution of 64 × 64 pixels as well as by orientation histograms for number of bins J = 512 and soft-assignment l = 3. The rows show the initial texture at process step 0, the representations at process step 10, and the representations at the final process step 19, respectively.

Beyond distance comparison, the work demonstrates how these improved distance concepts can be embedded in machine-learning workflows that link texture to mechanical response. Different representations of texture (Orientation histograms, generalized spherical harmonics, and image-based pole-figure representations) are evaluated in terms of their ability to predict elastic and plastic anisotropy. The results show that representations preserving richer orientation information enable more accurate and robust property prediction, while simpler descriptors remain viable when computational efficiency is required. Importantly, the choice of representation and distance measure directly influences how learning algorithms perceive similarity in microstructure space.

From an inverse-design perspective, this work provides a critical missing component: a reliable notion of distance in texture space. Such distances are essential when navigating high-dimensional microstructural design spaces, whether for optimization, surrogate modeling, or generative design.

Contact:

Prof. Dr. Stefan Sandfeld

Tel.: +49 241/927803-11
E-mail: s.sandfeld@fz-juelich.de

Last Modified: 29.01.2026