{
  "abstract": "In this paper, we consider structure-preserving model reduction of port-Hamiltonian (pH) systems which extend classical Hamiltonian systems with dissipation and an input-output port. These pH systems are often used in multi-physics systems, as the interconnection of one or more \\pH systems results again in a pH system. If particularly the system matrices associated with the interconnection and/or dissipation of a pH system are state-dependent, then the evaluation of standard reduced-order models (ROMs) may depend on the dimension of the original full-order model, resulting in high computational costs. To circumvent these high costs, we propose to use structure-preserving neural networks. In particular, we perform two steps: (1) we use the generalized manifold Galerkin projection to project the pH system onto the reduced space; then (2) we train a neural network to learn the map from the reduced-order state to the reduced-order interconnection and dissipation system matrices. To ensure that the resulting ROM is again a pH system, the architecture of the neural network is chosen such that the skew-symmetry and positive semi-definiteness of the reduced-order systems matrices are maintained. In a numerical example, we consider a nonlinear mass-spring-damper system with state-dependent system matrices. The numerical results show that the proposed method achieves a significant computational speed-up compared to the original \\ROM with comparable accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30788",
  "author_total": 4,
  "authors": [
    {
      "name": "Silke Glas"
    },
    {
      "name": "Alexander Heinlein"
    },
    {
      "name": "Harald Monsuur"
    },
    {
      "name": "Hongliang Mu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/af7e7mpw0h8xx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30788",
  "fulltext_url": null,
  "id": "af7e7mpw0h8xx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30788",
  "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.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7204917266",
  "pdf_url": "https://arxiv.org/pdf/2608.30788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/af7e7mpw0h8xx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Model reduction of port-Hamiltonian systems via neural networks",
  "title_text": "Model reduction of port-Hamiltonian systems via neural networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/af7e7mpw0h8xx",
  "venue": "arXiv",
  "versions": []
}