  We present an adaptive sampling strategy for the optimization-based structure
preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P.
and Voigt, M. (2020). Structure preserving model order reduction by parameter
optimization, Preprint arXiv:2011.07567]. This strategy reduces the
computational demand and the required a priori knowledge about the given full
order model, while at the same time retaining a high accuracy compared to other
structure preserving but also unstructured MOR algorithms. A numerical study
with a port-Hamiltonian benchmark system demonstrates the effectiveness of our
method combined with its new adaptive sampling strategy. We also investigate
the distribution of the sample points.
