  Classical model order reduction (MOR) for parametric problems may become
computationally inefficient due to large sizes of the required projection
bases, especially for problems with slowly decaying Kolmogorov n-widths.
Additionally, Hamiltonian structure of dynamical systems may be available and
should be preserved during the reduction. In the current presentation, we
address these two aspects by proposing a corresponding dictionary-based,
online-adaptive MOR approach. The method requires dictionaries for the
state-variable, non-linearities and discrete empirical interpolation (DEIM)
points. During the online simulation, local basis extensions/simplifications
are performed in an online-efficient way, i.e. the runtime complexity of basis
modifications and online simulation of the reduced models do not depend on the
full state dimension. Experiments on a linear wave equation and a non-linear
Sine-Gordon example demonstrate the efficiency of the approach.
