{
  "abstract": "Inverse problems are predominantly solved within the optimization-driven paradigm, which formulates the problem as objective-function minimization and approaches the solution by iterative search. Though universal, it suffers from limitations in efficiency, interpretability, and multi-parameter decoupling. This paper proposes a new paradigm---Structure-Driven Inversion (SDI). Instead of iterative search, SDI identifies and exploits the intrinsic structure of the problem to construct a solution method. It has two types of structure---mathematical structure and physical structure---and two corresponding driving inversion types: Mathematical Structure-Driven Inversion (MSDI) and Physical Structure-Driven Inversion (PSDI). The current representative method of MSDI is Mathematical Structure-Driven Pseudo-Inverse Inversion (MSDPII), which constructs a pseudo-inverse in the spectral domain via unitary diagonalization. The current representative methods of PSDI are Physical Structure-Driven Waveform Inversion Imaging (PSDWII), which performs inversion through virtual-source projection, and Physical Structure-Driven Back-Propagation (PSDBP), which implements three structural projections for deep neural networks via physical-system analogy. SDI is not a rejection but a complement and extension of Optimization-Driven Inversion (ODI). To the best of the author's knowledge, no existing study has systematically presented structure-driven inversion as an independent paradigm; this paper aims to fill that gap.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16536",
  "author_total": 1,
  "authors": [
    {
      "name": "Shengchang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dednhf9kfr5ey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16536",
  "fulltext_url": null,
  "id": "dednhf9kfr5ey",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16536",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.geo-ph"
    ],
    [
      "openalex",
      "1908|Seismic Imaging and Inversion Techniques"
    ]
  ],
  "openalex": "W7213418898",
  "pdf_url": "https://arxiv.org/pdf/2609.16536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dednhf9kfr5ey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.16536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16536"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Structure-Driven Inversion: A New Paradigm for Solving Inverse Problems",
  "title_text": "Structure-Driven Inversion: A New Paradigm for Solving Inverse Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/dednhf9kfr5ey",
  "venue": "arXiv",
  "versions": []
}