{
  "abstract": "Topology optimization of electromagnetic devices is computationally formidable owing to the combinatorial on/off material distribution on unstructured finite element meshes and repeated Maxwell equation solves. This paper develops GPRL-TO, a data-driven framework addressing both difficulties through three synergistic components. First, a graph physics-informed neural network (G-PINN) reformulates the finite element mesh as a graph and predicts element-wise magnetic flux densities under embedded magnetoquasistatic constraints, with two to three orders of magnitude speedup over finite element analysis. Second, as the central methodological contribution, a physics residual-driven curiosity mechanism converts the Maxwell residual into an intrinsic reward of a reinforcement learning agent, steering exploration toward physically unreliable design regions; the residual also indicates surrogate reliability. Third, a Gumbel–Softmax relaxation with temperature annealing renders the binary design variables differentiable, so the discrete on/off decisions relax to a continuous reparameterization driven by energy-type design sensitivities evaluated on the surrogate-predicted fields, instead of adjoint solves. A layered bridge-prescribed refinement fixes an iron skeleton that closes the magnetic circuit and guarantees manufacturable multi-layer barriers by construction. On a synchronous reluctance motor rotor, the G-PINN attains a relative L2 error of 9.51%, and the layered optimization improves the objective by 16.7% while raising the saliency difference from essentially zero to +0.017165.",
  "abstract_shown": true,
  "affiliations": [
    "National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 401331, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xiaoyu Liu",
      "orcid": "0009-0001-1475-7480"
    },
    {
      "affs": [
        0
      ],
      "name": "Yihan Si"
    },
    {
      "affs": [
        0
      ],
      "name": "Wei Xiang"
    },
    {
      "affs": [
        0
      ],
      "name": "Mengxin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mzegpbxpan2y.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203649",
  "fulltext_url": null,
  "id": "6mzegpbxpan2y",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3649",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2205|Topology Optimization in Engineering"
    ]
  ],
  "openalex": "W7221094121",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/6mzegpbxpan2y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203649",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3649"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Data-Driven On/Off Topology Optimization of Electromagnetic Devices Based on Graph Physics-Informed Neural Networks and Physics-Guided Reinforcement Learning",
  "title_text": "Data-Driven On/Off Topology Optimization of Electromagnetic Devices Based on Graph Physics-Informed Neural Networks and Physics-Guided Reinforcement Learning",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/6mzegpbxpan2y",
  "venue": "Mathematics",
  "versions": []
}