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

Abstract: 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.