{
  "abstract": "Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy--angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$--$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03329",
  "author_total": 1,
  "authors": [
    {
      "name": "Lidia J. Gomes Da Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9h8sfye1gxm7f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03329",
  "fulltext_url": null,
  "id": "9h8sfye1gxm7f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03329",
  "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.HE"
    ],
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7208760515",
  "pdf_url": "https://arxiv.org/pdf/2609.03329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9h8sfye1gxm7f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03329"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.HE",
      "subfield": "high-energy-astrophysics"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration",
  "title_text": "Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/9h8sfye1gxm7f",
  "venue": "arXiv",
  "versions": []
}