In this talk, we discuss several aspects of random field generation. From a numerical point of view, we introduce an efficient algorithm how to discretize a fractional in space operator based on a rational approximation and a sum of exponentials. We this approach we generate a wide range of random structures, including two-phase and multi-phase materials and wind flow profiles. For the mean flow, a copula based approach fitting the synthetic profile to the windrose data is used, while for the turbulent part a fractional PDE operator in space with a Gaussian white noise on the right hand side is considered. Adaptive sampling strategies are used for topology optimization under noise.

All theoretical and algorithmic results are illustrated by numerical examples illustrating the large flexibility of the proposed tools.