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We theoretically investigate the plasmonic properties of mid-infrared graphene-based metamaterials and apply deep learning of a neural network for the inverse design. These artificial structures have square periodic arrays of graphene plasmonic resonators deposited on dielectric thin films. Optical spectra vary significantly with changes in structural parameters. Our numerical results are in accordance with previous experiments. Then, the theoretical approach is employed to generate data for training and testing deep neural networks. By merging the pre-trained neural network with the inverse network, we implement calculations for inverse design of the graphene-based metameterials. We also discuss the limitation of the data-driven approach.