Piecewise polynomial nonlinear model reduction

We present a novel, general approach towards model-order reduction (MOR) on nonlinear systems that combines good global and local approximation properties. The nonlinear system is first approximated as piecewise polynomials over a number of regions, following which each region is reduced via polynomial model-reduction methods. Our approach, dubbed PWP, generalizes recent piecewise linear approaches and ties them with polynomial-based MOR, thereby combining their advantages. In particular, reduced models obtained by our approach reproduce small-signal distortion and intermodulation properties well, while at the same time retaining fidelity in large-swing and large-signal analyses, e.g., transient simulations. Thus our reduced models can be used as drop-in replacements for time-domain as well as frequency-domain simulations, with small or large excitations. By exploiting sparsity in system polynomial coefficients, we are able to make the polynomial reduction procedure linear in the size of the original system. We provide implementation details and illustrate PWP with an example.