  This work proposes a new framework of model reduction for parametric complex
systems. The framework employs a popular model reduction technique dynamic mode
decomposition (DMD), which is capable of combining data-driven learning and
physics ingredients based on the Koopman operator theory. In the offline step
of the proposed framework, DMD constructs a low-rank linear surrogate model for
the high dimensional quantities of interest (QoIs) derived from the (nonlinear)
complex high fidelity models (HFMs) of unknown forms. Then in the online step,
the resulting local reduced order bases (ROBs) and parametric reduced order
models (PROMs) at the training parameter sample points are interpolated to
construct a new PROM with the corresponding ROB for a new set of target/test
parameter values. The interpolations need to be done on the appropriate
manifolds within consistent sets of generalized coordinates. The proposed
framework is illustrated by numerical examples for both linear and nonlinear
problems. In particular, its advantages in computational costs and accuracy are
demonstrated by the comparisons with projection-based proper orthogonal
decomposition (POD)-PROM and Kriging.
