Tensor Krylov methods for model reduction of the stochastic mean of a parametric dynamical system

Uncertainties in mathematical models are often represented by stochastic parameters. We consider high dimensional single-input single-output (SISO) systems whose system matrices have affine dependencies on stochastically uncorrelated parameters. We introduce a reformulated SISO system for the mean of the stochastic output of the original parametric system. The problem is reformulated using tensors, represented in low-rank format. A two-sided tensor Arnoldi method is used for model order reduction of the high dimensional formulation. This results in a reduced model for the mean that is compared to the parametric reduced model that results from classical parametric model reduction.