Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a novel data-driven metamaterial design framework based on deep generative modeling. A variational autoencoder (VAE) and a regressor for property prediction are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous, and organized latent space. We show in this study that the latent space of VAE provides a distance metric to measure shape similarity, enable interpolation between microstructures and encode meaningful patterns of variation in geometries and properties. Based on these insights, systematic data-driven methods are proposed for the design of microstructure, graded family, and multiscale system. For microstructure design, the tuning of mechanical properties and complex manipulations of microstructures are easily achieved by simple vector operations in the latent space. The vector operation is further extended to generate metamaterial families with a controlled gradation of mechanical properties by searching on a constructed graph model. For multiscale metamaterial systems design, a diverse set of microstructures can be rapidly generated using VAE for target properties at different locations and then assembled by an efficient graph-based optimization method to ensure compatibility between adjacent microstructures. We demonstrate our framework by designing both functionally graded and heterogeneous metamaterial systems that achieve desired distortion behaviors.
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