{
  "abstract": "Port-Hamiltonian (pH) systems provide a general framework for modeling a broad class of physical dynamical systems, including systems with dissipation. Constructing accurate and robust data-driven reduced-order models for general pH systems is challenging. In this work, we focus on an important subclass of pH systems satisfying reciprocity, a property arising naturally in a variety of models. Rather than seeking to preserve the full pH structure, we exploit the additional symmetry provided by reciprocity to develop an efficient data-driven reduced-order modeling approach. We show that every minimal realization of a reciprocal system is self-adjoint with respect to a generally indefinite inner product and can, up to a similarity transformation preserving the pH structure, be represented in a Krein space with a signature inner product. This observation motivates a Galerkin projection onto a tangential rational Krylov subspace with respect to the corresponding indefinite inner product. Although the resulting projection involves full-order state solutions and the unknown inner product, we show that its reduced mass and stiffness matrices can be constructed directly from transfer-function data through a Loewner formulation. We then propose a greedy data-driven procedure that adaptively selects both interpolation frequencies and tangential directions. At every iteration, the frequency is chosen according to the largest transfer-function approximation error, while the tangential direction is selected from a dominant singular direction of the corresponding matrix-valued residual. Numerical experiments for wave propagation in lossy media demonstrate improved approximation efficiency compared with block adaptive interpolation. We further apply the method to spectral mass gauging of a three-dimensional propellant tank to provide an accurate estimate of the tank volume through Weyl's law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04065",
  "author_total": 2,
  "authors": [
    {
      "name": "Anarzhan Abilgazy"
    },
    {
      "name": "Mikhail Zaslavsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m7tjx9axhg98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04065",
  "fulltext_url": null,
  "id": "7m7tjx9axhg98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04065",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m7tjx9axhg98.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Adaptive data-driven reduced-order models for reciprocal MIMO port-Hamiltonian dynamical systems",
  "title_text": "Adaptive data-driven reduced-order models for reciprocal MIMO port-Hamiltonian dynamical systems",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/7m7tjx9axhg98",
  "venue": "arXiv",
  "versions": []
}