  In this work, we investigate a model order reduction scheme for polynomial
parametric systems. We begin with defining the generalized multivariate
transfer functions for the system. Based on this, we aim at constructing a
reduced-order system, interpolating the defined generalized transfer functions
at a given set of interpolation points. Furthermore, we provide a method,
inspired by the Loewner approach for linear and (quadratic-)bilinear systems,
to determine a good-quality reduced-order system in an automatic way. We also
discuss the computational issues related to the proposed method and a potential
application of CUR matrix approximation in order to further speed-up
simulations of reduced-order systems. We test the efficiency of the proposed
methods via several numerical examples.
