This paper solves a long-standing problem in resonant ultrasound spectroscopy (RUS) for cubic solids through the use of two-dimensional deep learning (DL). By means of inverse methods, conventional RUS can determine all independent elastic constants of a crystalline solid specimen by comparing measured and calculated free-vibration resonance frequencies. However, to avoid invalid local minima in the inverse process, good initial guesses of the elastic constants must be available. Here, we propose a DL scheme to remedy this problem, which utilizes an input elasticity image composed of three layers obtained from resonance frequency data. After network training, this scheme is executed in two steps: DL processing by a neural network to output elastic constants in a Blackman diagram classification, followed by the use of a regression network around the classified point in this diagram for more accurate determination. By means of simulations, we demonstrate that this DL scheme yields the principal elastic constants within an error of approximately $5\mathrm{\%}$ without any inverse processing even in the unfavorable case of five missing modes for 111 existing cubic crystals.

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• Acoustics
• Elastic modulus
• Elasticity
• Inverse problems
• Mechanical & acoustical properties
• Deep learning
• Resonance techniques
• Ultrasound spectroscopy