Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems
Abstract
We present a data-driven approach to identifying linear index-1 differential-algebraic pH systems (pH-DAEs) based on input-output measurements. In comparison to the identification of port-Hamiltonian (pH) systems, the algebraic constraint and the index condition pose additional challenges. First, we establish a structure-preserving formulation of the considered pH-DAE class and derive an implicit midpoint discretization that preserves the algebraic constraints and discrete dissipation inequality. We formulate the identification problem as a regularized least-squares minimization problem subject to the pH-DAE dynamics. Exploiting the index-1 structure, we reduce the constrained problem to an unconstrained optimization problem over the system parameters while preserving the port-Hamiltonian structure. Next, we derive an adjoint-based formulation to efficiently evaluate the gradient of the resulting reduced cost functional. This enables us to use gradient-based optimization methods for parameter estimation. Under suitable assumptions on the admissible parameter set, the existence of a minimizer is established. Numerical experiments demonstrate that the proposed approach can identify surrogate pH-DAE systems that accurately reproduce the input-output behavior of reference systems. Further investigations show the approach's potential for identifying reduced-order surrogate models. Cross-validation with independent input signals confirms the predictive capability of the identified models.
Related
- Nonlinear differential-algebraic systems with dissipative port-Hamiltonian structure
- Mathematical modeling, simulation and optimization via (port-Hamiltonian) differential-algebraic equations
- A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs
- Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs
- Bilinearity Preserving Algebraic Flux Correction
BibTeX
@misc{zwerschke2026structurepreserving,
title = {{Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems}},
author = {Tom Zwerschke and Matthias Ehrhardt and Michael Günther and Claudia Totzeck},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07187},
eprint = {2609.07187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems
AU - Tom Zwerschke
AU - Matthias Ehrhardt
AU - Michael Günther
AU - Claudia Totzeck
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07187
UR - https://arxiv.org/abs/2609.07187
AB - We present a data-driven approach to identifying linear index-1 differential-algebraic pH systems (pH-DAEs) based on input-output measurements. In comparison to the identification of port-Hamiltonian (pH) systems, the algebraic constraint and the index condition pose additional challenges. First, we establish a structure-preserving formulation of the considered pH-DAE class and derive an implicit midpoint discretization that preserves the algebraic constraints and discrete dissipation inequality. We formulate the identification problem as a regularized least-squares minimization problem subject to the pH-DAE dynamics. Exploiting the index-1 structure, we reduce the constrained problem to an unconstrained optimization problem over the system parameters while preserving the port-Hamiltonian structure. Next, we derive an adjoint-based formulation to efficiently evaluate the gradient of the resulting reduced cost functional. This enables us to use gradient-based optimization methods for parameter estimation. Under suitable assumptions on the admissible parameter set, the existence of a minimizer is established. Numerical experiments demonstrate that the proposed approach can identify surrogate pH-DAE systems that accurately reproduce the input-output behavior of reference systems. Further investigations show the approach's potential for identifying reduced-order surrogate models. Cross-validation with independent input signals confirms the predictive capability of the identified models.
ER -