Two-step deep learning for decoding elastic constants of hexagonal-symmetry materials from resonant-spectrum image

• High image-recognition ability of CNN is adopted for accurate estimation of hexagonal materials elastic constants. • The average Young’s modulus is found to serve as a primary parameter for the initial classification of the material elasticity. • We introduce the Blackmann-diagram like relationships for hexagonal materials. • Based on the hexagonal Blackmann-diagram strategy, the second step CNN allows prediction of the principal elastic constants with 5 % accuracy. • Introduction of missing modes in the dataset maintains the high accuracy up to 10 missing modes. We developed a deep learning (DL) framework based on convolutional neural networks (CNNs) to predict elastic constants of hexagonal materials by leveraging high image-recognition capability of CNNs. Resonant frequency data were converted into three-channel RGB images, referred to as ”elasticity images” for CNN training. Without mode identification, the trained models accurately predicted all five independent elastic constants. We reveal that the average Young modulus is a critical for classification of hexagonal materials based on their elasticity images. Furthermore, we extended the Blackman diagram, originally developed for cubic crystals, to hexagonal systems, enabling a substantial reduction of five-dimensional elastic-constant space. We then established a two-step DL scheme: first, classification using the average Young modulus, followed by regression of the five elastic constants in the classified average-Young-modulus class. The prediction error was approximately 5 % for the principal elastic constants and 1.5 % for the average Young modulus.