Direct determination of elastic constants of hexagonal materials without inverse calculation based on deep learning using resonant spectrum images

This study proposes a deep learning (DL) approach for determining five independent elastic constants of hexagonal-symmetry materials from specimen’s free vibration resonant frequencies without inverse calculation. Conventional RUS (resonant ultrasound spectroscopy) method determines elastic constants by solving an inverse problem that requires accurate initial guesses to avoid convergence to incorrect local minima. Here, we propose a novel two-step DL framework for predicting the complete set of independent elastic constants of hexagonal materials directly from resonance spectra. The method first coarsely predicts the average Young’s modulus using a convolutional neural network (CNN) trained on three-layer images constructed from resonance spectra, thereby enabling focused data selection. In the second step, a regression network is applied—guided by the initially decoded average Young’s modulus—to predict all five independent elastic constants of the hexagonal system. Validation on 42 existing materials demonstrates that the proposed method achieves average errors of approximately 5% for the diagonal elastic constants and 1.5% for the average Young’s modulus.