Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes
This work addresses the challenge of modeling subsystems in multiphysics applications where physical port-Hamiltonian descriptions are unavailable or too expensive, enabling structure-preserving coupling.
The paper tackled the problem of identifying port-Hamiltonian differential algebraic equation (DAE) systems from data, using Gaussian processes to estimate nonlinear effort functions, and successfully applied it to network design and constrained multibody system dynamics examples.
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.