{
  "abstract": "Inferring an Allen-Cahn constitutive force from images requires more than an accurate optimizer: nonlinear observation noise alters the mean of force features, shared noise couples instruments to the response, and a temporal balance borrowed from another solver can remain biased even on clean data. We develop observation-aware, noise-adjusted moment equations that address these effects before inversion. The surface-tension-calibrated constitutive transformer (SCCT) couples the resulting moments to a positive Bernstein inverse and can adapt its prior and precision from images and moments. A conditional stability bound separates moment residuals from prior error. Synthetic tests show that correcting the estimating equation matters more than increasing regularizer flexibility; the benefit of learned adaptation is smaller and depends on the training comparison. Forces inferred from planar movies predict unseen planar and three-dimensional evolutions. A ring-cage breakup shows why diffuse-interface accuracy distinguishes forces even when their topological predictions agree, while external surface tension sets the energy scale separately.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02672",
  "author_total": 2,
  "authors": [
    {
      "name": "Soobeen Jung"
    },
    {
      "name": "Hyunju Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cn40vjz64b38d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02672",
  "fulltext_url": null,
  "id": "cn40vjz64b38d",
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  "landing_url": "https://arxiv.org/abs/2610.02672",
  "language": null,
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  "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.NA"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7220442061",
  "pdf_url": "https://arxiv.org/pdf/2610.02672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cn40vjz64b38d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Inferring constitutive forces from noisy Allen-Cahn movies with moment equations",
  "title_text": "Inferring constitutive forces from noisy Allen-Cahn movies with moment equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/cn40vjz64b38d",
  "venue": "arXiv",
  "versions": []
}