Very often mathematical models  (given by partial or ordinary differential equations) contain parameters which are uncertain. Typical examples are conductivity coefficients in groundwater flow problems and porosity. The uncertain heterogeneity in the material can affect the system behaviour dramatically. One of the mostly used techniques to model such uncertainties is random fields. To solve resulting PDE with random fields (stochastic PDE) numerically one has to discretise the deterministic operator as well as the high-dimensional stochastic operator. There are different methods to discretise and to solve these stochastic PDEs: stochastic Galerkin, collocation, sparse grids, (quasi) MC etc.

To reduce the computational complexity the stochastic forward problem is approximated in a low-rank/sparse tensor data format.