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This article deals with the data-driven prediction of the band structures of thermoelastic waves in the nano-scale phononic crystal beams considering nano-size effects. The computational intelligence methods are developed using a data-driven tool to discover the design space of phononic crystals, which are subjected to thermal shock loading. For this purpose, a rich dataset is created utilizing an analytical solution, which was previously proposed for the nonlocal coupled thermoelasticity analysis in a nano-sized phononic crystal beam. The preprocessing methods, hyperparameters optimization, and shallow and deep neural networks are used to classify and predict the bandgaps. Also, according to the created dataset and the data-driven method, the phononic crystal feature importance and behavior based on the design parameters are assessed in detail. The detailed investigation reveals the importance of the design parameters according to the deep neural network’s results. It is demonstrated by numerical results that the proposed final data-driven model can predict the characteristics of the phononic crystals pretty well. Also, the results show that the deep neural network outperforms the shallow neural network for the classification and prediction of the band structures. The final results can be a helpful tool to have a fast numerical framework for the prediction of photonic crystals’ bandgaps before the application of time-consuming accurate frameworks.

A deep learning approach based on a data-driven tool for classification and prediction of thermoelastic wave’s band structures for phononic crystals