  In this article, we discuss the numerical solution of diffusion equations on
random surfaces within the isogeometric framework. We describe in detail, how
diffusion problems on random surfaces can be modelled and how quantities of
interest may be derived. In particular, we employ a low rank approximation
algorithm for the high-dimensional space-time correlation of the random
solution based on an online singular value decomposition, cp. [7]. Extensive
numerical studies are performed to validate the approach. In particular, we
consider complex computational geometries originating from surface
triangulations. The latter can be recast into the isogeometric context by
transforming them into quadrangulations using the procedure from [41] and a
subsequent approximation by NURBS surfaces.
