  Port-based network modeling of multi-physics problems leads naturally to a
formulation as port-Hamiltonian differential-algebraic system. In this way, the
physical properties are directly encoded in the structure of the model. Since
the state space dimension of such systems may be very large, in particular when
the model is a space-discretized partial differential-algebraic system, in
optimization and control there is a need for model reduction methods that
preserve the port-Hamiltonian structure while keeping the (explicit and
implicit) algebraic constraints unchanged. To combine model reduction for
differential-algebraic equations with port-Hamiltonian structure preservation,
we adapt two classes of techniques (reduction of the Dirac structure and moment
matching) to handle port-Hamiltonian differential-algebraic equations. The
performance of the methods is investigated for benchmark examples originating
from semi-discretized flow problems and mechanical multibody systems.
