  An adaptive parametric reduced-order modeling method based on interpolating
poles of reduced-order models is proposed in this paper. To guarantee correct
interpolation, a pole-matching process is conducted to determine which poles of
two reduced-order models correspond to the same parametric pole. First, the
pole-matching in the scenario of parameter perturbation is discussed. It is
formulated as a combinatorial optimization problem and solved by a branch and
bound algorithm. Then, an adaptive framework is proposed to build repository
ROMs at adaptively chosen parameter values, which well represent the parameter
domain of interest. To achieve this, we propose techniques including a
predictor-corrector strategy and an adaptive refinement strategy, which enable
us to use larger steps to explore the parameter domain of interest with good
accuracy. The framework also consists of regression as an optional
post-processing phase to further reduce the data storage. The advantages over
other parametric reduced-order modeling approaches are, e.g., compatibility
with any model order reduction method, constant size of the parametric
reduced-order model with respect to the number of parameters, and capability to
deal with complicated parameter dependency.
