{
  "abstract": "Constraint-satisfying initial data for binary black holes require the repeated solution of a nonlinear elliptic boundary-value problem throughout the physical parameter space. We present a para\\-metric, differentiable initial-data model that combines sparse-grid spectral interpolation with Newton refinement over a family of binary configurations. Interpolation is used only to provide warm starts for the underlying elliptic solver, rather than to replace it. A small number of Newton iterations refines each interpolated solution to a discrete, row-equilibrated constraint residual $\\|R\\|_\\infty\\le10^{-10}$, independent of the interpolation error, so that every returned initial-data set satisfies the discretized constraint to that tolerance. Our JAX implementation provides analytic derivatives with respect to the physical parameters, enabling gradient-based parameter targeting, optimization, and sensitivity analysis. We demonstrate the method for quasi-circular binary-black-hole initial data using conformally flat Bowen--York punctures by constructing four-dimensional aligned-spin and eight-dimensional general-spin models. The resulting initial data are validated against TwoPunctures, and the method is applied to certified targeting of the physical Arnowitt--Deser--Misner mass and angular momentum and to effective-potential eccentricity reduction using a dedicated separation--tangential-momentum model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10173",
  "author_total": 2,
  "authors": [
    {
      "name": "Frederik De Ceuster"
    },
    {
      "name": "Tjonnie G. -F. Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ssng5anhz2jn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10173",
  "fulltext_url": null,
  "id": "8ssng5anhz2jn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10173",
  "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",
      "astro-ph.IM"
    ],
    [
      "arxiv",
      "gr-qc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.10173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ssng5anhz2jn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10173"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "A Differentiable Parametric Model of Binary-Black-Hole Initial Data: I. Conformally flat Bowen-York punctures",
  "title_text": "A Differentiable Parametric Model of Binary-Black-Hole Initial Data: I. Conformally flat Bowen-York punctures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/8ssng5anhz2jn",
  "venue": "arXiv",
  "versions": []
}