Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy

[2608.27590] Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy Skip to main content Search Submit Donate Log in Condensed Matter > Materials Science arXiv:2608.27590 (cond-mat) [Submitted on 27 Aug 2026] Title: Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy Authors: Alejandro Cubillos Muñoz , Manuela Rivas , Julian Rincon View PDF HTML (experimental) 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. Comments: 15 pages, 8 figures, 3 tables Subjects: Materials Science (cond-mat.mtrl-sci) ; Machine Learning (cs.LG); Applied Physics (physics.app-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2608.27590 [cond-mat.mtrl-sci] (or arXiv:2608.27590v1 [cond-mat.mtrl-sci] for this version) https://doi.org/10.48550/arXiv.2608.27590 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Julian Rincon [ view email ] [v1] Thu, 27 Aug 2026 18:20:08 UTC (270 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.mtrl-sci < prev | next > new | recent | 2026-08 Change to browse by: cond-mat cs cs.LG physics physics.app-ph physics.comp-ph References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy#779521
• ANaLOG: Anisotropic Native-Latent Operator Guidance for Solving Inverse Problems#1115889
• Biophysics-informed deep operator learning for inverse problems with application to electrophysiological source reconstruction#625418
• Biophysics-informed deep operator learning for inverse problems with application to electrophysiological source reconstruction#623145
• Physics-Informed Non-Dimensionalisation for Neural Solvers#684012