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Periodic structure is useful and powerful tool for the wave manipulation. The development of design and analysis of periodic structures using traditional methods (analysis of eigenfrequencies by the finite element method) takes quite a lot of time. Machine learning and deep learning algorithms can speed up the development and subsequent analysis of periodic structures. In this work, we consider a particular case of the propagation of torsional waves in cylindrical objects, the calculation of their dispersion curves, and methods for generating the design of a unit cell of periodic structure by a given bandgap configuration. To achieve this goal, autoencoders and diffusion models were used. A dataset of unit cell shapes and their dispersion curves were used as training data. First, the dispersion curves were analysed to form a bandgap configuration, which was then fed to the input of the neural network. The neural network generates unit cell shape as the output data. Information about dispersion curves is also very important for the analysis of periodic structures. To calculate the dispersion curves, the possibility of using deep learning methods is considered - the problem is the opposite of the previous one. According to the given form, the neural network should calculate dispersion curves. The paper presents the results of applying this method for calculating dispersion curves.