MATHICSE Technical Report: Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. We detail how to treat unbalanced cases, where the surrogates to be combined have a different number of poles. If the frequency surrogates are constructed by minimal rational interpolation, frequency and parameters can both be sampled in a greedy fashion, by employing a fully non-intrusive "look-ahead" strategy. We explain how our proposed technique can be applied even in a high-dimensional setting, by employing locally-refined sparse grids to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced matching, as well as with a large number of parameters.