Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy
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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
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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
arXiv-issued DOI via DataCite (pending registration)
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