Model Releases
Physics-informed learning for the inverse problem in resonant ultrasound spectroscopy
arXiv:2608.27590v1 Announce Type: cross Abstract: Inferring elastic constants from resonant ultrasound spectra is a nonlinear and typically overdetermined inverse problem based on finite spectral data
arXiv:2608.27590v1 Announce Type: cross 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 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.
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Source: arXiv cs.LG | 2026-08-31