{
  "abstract": "This article proposes and articulates structure-driven methodology as an emerging cross-domain paradigm. In contrast to the objective-driven paradigm that has dominated inverse-problem solving for over two centuries, structure-driven methodology advocates identifying and exploiting the intrinsic structure of a problem to construct the solution method directly, rather than approaching the solution through iterative search. Drawing on examples from the Liouville-variant Goldbach conjecture, the three-dimensional Kakeya conjecture, Noether's theorem, and the author's nearly four decades of geophysical inversion practice, the article illustrates the common logic of structure-driven thinking in number theory, pure mathematics, physics, and seismic imaging. The author also systematically proposes the Structure-Driven Inversion (SDI) paradigm, comprising Mathematical Structure-Driven Inversion (MSDI) and Physical Structure-Driven Inversion (PSDI). Structure-driven methodology does not negate objective-driven methodology but complements it: objective-driven is a general search strategy, whereas structure-driven is a custom direct strategy. The article concludes that the significance of this shift lies not only in efficiency gains but also in cognitive deepening---when facing complex problems, the first question is no longer ``how to solve the problem faster'' but ``what is the structure of the problem.''",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02698",
  "author_total": 1,
  "authors": [
    {
      "name": "Shengchang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5asv4am4eetre.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02698",
  "fulltext_url": null,
  "id": "5asv4am4eetre",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02698",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.HO"
    ],
    [
      "arxiv",
      "physics.geo-ph"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7220415887",
  "pdf_url": "https://arxiv.org/pdf/2610.02698",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5asv4am4eetre.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02698",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02698"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.HO",
      "subfield": "general"
    }
  ],
  "title": "Structure-Driven Methodology: An Emerging Cross-Domain Paradigm",
  "title_text": "Structure-Driven Methodology: An Emerging Cross-Domain Paradigm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/5asv4am4eetre",
  "venue": "arXiv",
  "versions": []
}