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.

翻译：端口哈密顿系统（pHS）能够实现动力系统的结构保持建模。通过输入与输出之间的线性关系耦合pHS可定义整体pHS，该过程具有结构保持特性。然而在多物理场应用中，某些子系统无法采用物理pHS描述，原因在于（a）缺乏可用描述或（b）计算成本过高。此时可采用数据驱动方法为这类子系统构建pHS，进而以结构保持方式与其他子系统耦合。本研究提出一种针对端口哈密顿微分代数方程（DAE）系统的数据驱动辨识方法。该方法利用输入与状态空间数据估计pH-DAE的非线性势函数。我们采用（多任务）高斯过程作为底层技术，从而将现有研究范畴从仅能通过高斯过程辨识端口哈密顿常微分方程系统，扩展至微分代数方程系统。基于指标分别为一和二的pH-DAE系统，本方法已成功应用于网络设计与约束多体系统动力学两个案例。