Active learning-driven inference of mesoscale material heterogeneity from acoustic resonance

Mesoscale material heterogeneity critically influences component performance but remains difficult to quantify using rapid, non-destructive approaches such as vibration sensing. Here, we establish an active learning-driven, physics-guided framework that links heterogeneity to acoustic resonance and enables inference of heterogeneity descriptors from frequency responses. Eigenmode finite element simulations define a nonlinear mapping between heterogeneity descriptors (geometry, location, and material type of dissimilar domains) and vibrational responses across deformation types (elongation, bending, and twisting). To enable efficient forward prediction, surrogate models are constructed to rapidly generate datasets of frequency response–heterogeneity pairs. Trained on these datasets, a coupled inverse–forward neural network architecture is developed to perform inverse prediction while enforcing spectral consistency. Compared to uniform sampling, active learning-guided forward modeling significantly improves data fidelity, which in turn improves the inverse prediction accuracy—increasing the average coefficient of determination ( R 2 ) from 0.75 to 0.82. Mode-specific analyses of forward prediction accuracy and sensitivity suggest that inverse prediction accuracy is governed not only by data but also by the underlying physics. Leveraging this insight, we optimally select informative modes in the input frequency response and further increase R 2 to 0.89. Our findings establish a direct link between forward-model fidelity, physics-based sensitivity, and heterogeneity identifiability.