  A non-intrusive model order reduction (MOR) method that combines features of
the dynamic mode decomposition (DMD) and the radial basis function (RBF)
network is proposed to predict the dynamics of parametric nonlinear systems. In
many applications, we have limited access to the information of the whole
system, which motivates non-intrusive model reduction. One bottleneck is
capturing the dynamics of the solution without knowing the physics inside the
"black-box" system. DMD is a powerful tool to mimic the dynamics of the system
and give a reliable approximation of the solution in the time domain using only
the dominant DMD modes. However, DMD cannot reproduce the parametric behavior
of the dynamics. Our contribution focuses on extending DMD to parametric DMD by
RBF interpolation. Specifically, a RBF network is first trained using snapshot
matrices at limited parameter samples. The snapshot matrix at any new parameter
sample can be quickly learned from the RBF network. DMD will use the newly
generated snapshot matrix at the online stage to predict the time patterns of
the dynamics corresponding to the new parameter sample. The proposed framework
and algorithm are tested and validated by numerical examples including models
with parametrized and time-varying inputs.
