Identification of Port-Hamiltonian Differential-Algebraic Equations from Input-Output Data

Many models of physical systems, such as mechanical and electrical networks, exhibit algebraic constraints that arise from subsystem interconnections and underlying physical laws. Such systems are commonly formulated as differential-algebraic equations (DAEs), which describe both the dynamic evolution of system states and the algebraic relations that must hold among them. Within this class, port-Hamiltonian differential-algebraic equations (pH-DAEs) offer a structured, energy-based representation that preserves interconnection and passivity properties. This work introduces a data-driven identification method that combines port-Hamiltonian neural networks (pHNNs) with a differential-algebraic solver to model such constrained systems directly from noisy input-output data. The approach preserves the passivity and interconnection structure of port-Hamiltonian systems while employing a backward Euler discretization with Newton's method to solve the coupled differential and algebraic equations consistently. The performance of the proposed approach is demonstrated on a DC power network, where the identified model accurately captures system behaviour and maintains errors proportional to the noise amplitude, while providing reliable parameter estimates.