  Port-Hamiltonian systems (pHS) allow for a structure-preserving modeling of
dynamical systems. Coupling pHS via linear relations between input and output
defines an overall pHS, which is structure preserving. However, in multiphysics
applications, some subsystems do not allow for a physical pHS description, as
(a) this is not available or (b) too expensive. Here, data-driven approaches
can be used to deliver a pHS for such subsystems, which can then be coupled to
the other subsystems in a structure-preserving way. In this work, we derive a
data-driven identification approach for port-Hamiltonian differential algebraic
equation (DAE) systems. The approach uses input and state space data to
estimate nonlinear effort functions of pH-DAEs. As underlying technique, we us
(multi-task) Gaussian processes. This work thereby extends over the current
state of the art, in which only port-Hamiltonian ordinary differential equation
systems could be identified via Gaussian processes. We apply this approach
successfully to two applications from network design and constrained multibody
system dynamics, based on pH-DAE system of index one and three, respectively.
