Interpolatory model order reduction by tensor Krylov methods

High dimensional models with parametric dependencies can be challenging to simulate. The computational e↵ort usually increases exponentially with the dimension of the parameter space. To keep the calculations feasible, one can use parametric model order reduction techniques. Multivariate Pad methods match higher order moments of the Laplace variable as well as the parameters. Interpolatory reduced models interpolate the exact transfer function for di↵erent parameter values. In this paper we use tensor Krylov techniques to reduce the parametric model, combining both moment matching and interpolatory model reduction in the parameter space. If a low rank tensor formulation is possible, this approach is competitive with classic parametric model reduction. Furthermore, we look at models containing stochastic parameters and construct a model that outputs the mean over these parameters within the domain of interest. This model for the mean is set up using well known quadrature techniques from numerical integration. We compare the reduced model for the mean with the parametric reduced model.