Goal-Oriented Compression of Random Fields

For computations one typically truncates the series after a number M terms chosen sufficiently large for an acceptable truncation error. A large value of M , however, constrains the feasibility of numerical methods for approximating u = u(ξ) or Q = Q(u(ξ)) based on stochastic Galerkin or stochastic collocation discretization. Thus, our goal is a sparse expansion (2) of a which still allows a good approximation of Q. A common choice for the basis {ψm}m∈N are the eigenfunctions of the covariance operator