{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07187",
  "author_total": 4,
  "authors": [
    {
      "name": "Tom Zwerschke"
    },
    {
      "name": "Matthias Ehrhardt"
    },
    {
      "name": "Michael Günther"
    },
    {
      "name": "Claudia Totzeck"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ex69v28j7wba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07187",
  "fulltext_url": null,
  "id": "2ex69v28j7wba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07187",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Control Systems and Identification"
    ]
  ],
  "openalex": "W7212040863",
  "pdf_url": "https://arxiv.org/pdf/2609.07187",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ex69v28j7wba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07187",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07187"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems",
  "title_text": "Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2ex69v28j7wba",
  "venue": "arXiv",
  "versions": []
}