manufacturing process designers

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.

Abstract: Neural operators can accelerate repeated nonlinear mechanics calculations, but their accuracy can deteriorate as operating conditions move beyond the training range. This work studies whether high-fidelity solutions acquired during use can be reused to adapt a neural operator and improve subsequent mechanics-based command selection. Two hard-magnetic soft-material systems are simulated using high-fidelity finite-element (FE) models, providing reference solutions for evaluating surrogate predictions and selected commands. A neural operator predicts deformation from known material, loading, and magnetic-field inputs, while an empirical error estimator determines which predictions may be used for command selection. Selected FE evaluations supplement these predictions, and their complete loading paths are retained for periodic updates of the neural operator and estimator. In both examples, the fixed operator loses substantial accuracy when stiffness and loading move outside the training range. Updates using 16 acquired paths recover much of the lost accuracy while preserving accuracy in the nominal regime. Under the same FE evaluation budget, the updated operators also improve command selection, although the benefit varies with the operating condition. Error estimation is less consistent, with inaccurate predictions sometimes accepted and accurate predictions rejected. These results demonstrate that reusing high-fidelity loading paths can extend the useful operating range of a neural operator. However, improved forward accuracy alone does not guarantee reliable prediction acceptance, highlighting prediction-specific error assessment as a separate requirement for trustworthy decision making.