{
  "abstract": "We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $φ$-finite element method ($φ$-FEM). $φ$-FEM is an unfitted method that accommodates geometric variations without body-fitted meshes, where the domain geometry is represented by the level-set function $φ$. To impose the boundary conditions, Dirichlet problems adopt the $φ$-FEM lifting so only the homogeneous displacement contribution is learned, whereas traction-driven Neumann problems additionally predict the auxiliary fields necessary for the unfitted weak formulation. Parameters are trained by minimizing squared weak-form residuals aligned with $φ$-FEM together with squared penalties on the cut-cell auxiliary equations, which removes the need for large paired datasets of converged reference solutions. When labeled reference data are available, an optional data-augmented variant (WINO+data) can further combine this physics-informed loss with a supervised term. After training, WINO outputs can seed the nonlinear $φ$-FEM solvers as neural operator warm starts (NOWS), which reduce iteration counts relative to traditional cold-started solvers. Numerical benchmarks show substantial accuracy of WINO together with total training times of about 15%-70% of those of supervised $φ$-FEM-FNO across all cases, without requiring reference-solution generation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24651",
  "author_total": 4,
  "authors": [
    {
      "name": "Bokai Zhu"
    },
    {
      "name": "Yizheng Wang"
    },
    {
      "name": "Qinghui Zhang"
    },
    {
      "name": "Timon Rabczuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72sv612c2q5bw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24651",
  "fulltext_url": null,
  "id": "72sv612c2q5bw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24651",
  "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.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7162439902",
  "pdf_url": "https://arxiv.org/pdf/2605.24651",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72sv612c2q5bw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2605.24651",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24651"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains",
  "title_text": "WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/72sv612c2q5bw",
  "venue": "arXiv",
  "versions": []
}