Stochastic inference of effective material properties from crystallographic textures via Gaussian process regression

• Study on the influence of texture measurement uncertainty on homogenized effective properties. • Texture represented by Pole Density Functions modelled with Gaussian Process Regression (GPR). • The Monte Carlo instances mean differs from the GPR mean reflecting non-linearity, E ( H ( P h ) ) ≠ H ( E ( P h ) ) . • Homogenization of confidence interval of GPR diverges when error level α grows whereas empirical confidence interval of Monte Carlo samples remains stable. This work investigates the impact of measurement uncertainty in polycrystalline texture data on homogenized material properties through full-field homogenization. Crystallographic texture, represented by Pole Density Functions, is modeled through Gaussian Process (GP) regression, in which measurement error is explicitly introduced via the noise term of the GP. Two uncertainty propagation approaches are examined. In the first, deterministic descriptors derived from the GP posterior distribution, namely the posterior mean and the bounds of the 95% confidence interval, are used as texture inputs for homogenization. In the second, Monte Carlo Pole Density Function instances are sampled directly from the GP posterior distribution and propagated through homogenization. Numerical experiments on a two-dimensional thermal conduction problem use a synthetic texture. The effective properties and their variability obtained from both approaches are compared with deterministic predictions based on the error-free reference texture. The results show that sampling-based homogenization provides a more robust estimation of effective physical properties and their associated uncertainty.