{
  "abstract": "Inferring elastic constants from resonant ultrasound spectra is a nonlinear and typically overdetermined inverse problem based on finite spectral data. We formulate the Rayleigh-Ritz inverse problem as a constrained inverse-isospectral problem on the set of physically admissible elasticity tensors. This induces effective low-dimensional variables for the inverse map on the admissible elasticity manifold: length and elastic scales, aspect-ratio coordinates, scale-free spectral features, and stability-respecting elastic ratios. We use these variables to construct a physics-informed learning pipeline in which a regression model acts only on reduced spectral and geometric features, while scale recovery and final elastic-constant reconstruction are imposed analytically. For the full cubic benchmark, the reconstructed constants have MAE values of $20.37(35.15)$, $24.30(41.33)$, and $2.13(3.66)~\\mathrm{GPa}$ for $C_{11}$, $C_{12}$, and $C_{44}$. In the fixed-geometry benchmark, the corresponding cubic MAPE values are $4.14(3.87)\\%$, $8.31(8.50)\\%$, and $2.44(2.86)\\%$, while the isotropic values are $4.0(3.6)\\%$ and $0.4(0.3)\\%$ for the bulk and shear moduli. The inverse problem then becomes a constrained regression problem in variables adapted to the geometry, scaling, crystal symmetry, and thermodynamic stability of Hookean elasticity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27590",
  "author_total": 3,
  "authors": [
    {
      "name": "Alejandro Cubillos Muñoz"
    },
    {
      "name": "Manuela Rivas"
    },
    {
      "name": "Julian Rincon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ad6mckszs8z4w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27590",
  "fulltext_url": null,
  "id": "ad6mckszs8z4w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27590",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.app-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7204775084",
  "pdf_url": "https://arxiv.org/pdf/2608.27590",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ad6mckszs8z4w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.27590",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27590"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.app-ph",
      "subfield": "applied-instrumentation"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy",
  "title_text": "Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/ad6mckszs8z4w",
  "venue": "arXiv",
  "versions": []
}