Customized Gaussian process for representing polycrystalline texture

Abstract

A customized Gaussian Process Regression (GPR) model is developed to reconstruct Pole Density Functions in texture analysis. The model integrates spherical-periodic distance measures with conventional stationary kernels, adapting the GPR framework to capture localized texture features. A key contribution is the introduction of a log-linear data transformation, which enforces the non-negativity of both interpolated function values and stochastic intervals, ensuring physically meaningful reconstructions. To assess the model’s effectiveness, a systematic investigation examines the impact of distance measures, kernel selection, and hyperparameter optimization using synthetic texture datasets, provided as part of this work, with evaluations focusing on reconstruction accuracy, feature preservation, and uncertainty quantification in comparison to the conventional spherical harmonics approach. GPR with a log-linear transformation, geodesic distance, and a Matérn $\nu$=5/2 kernel, shows promise in achieving higher accuracy than traditional spherical harmonics for reconstructing non-negative pole density functions, while additionally providing confidence intervals for uncertainty quantification.