Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy
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) GPa for C11, C12, and C44. 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.
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BibTeX
@misc{munoz2026physicsinformed,
title = {{Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy}},
author = {Alejandro Cubillos Muñoz and Manuela Rivas and Julian Rincon},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27590},
eprint = {2608.27590},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27590},
}
RIS
TY - UNPB
TI - Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy
AU - Alejandro Cubillos Muñoz
AU - Manuela Rivas
AU - Julian Rincon
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27590
UR - https://arxiv.org/abs/2608.27590
AB - 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) 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.
ER -