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Metamaterials are emerging as a new paradigmatic material system to renderunprecedented and tailorable properties for a wide variety of engineeringapplications. However, the inverse design of metamaterial and its multiscalesystem 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 deepgenerative modeling. A variational autoencoder (VAE) and a regressor forproperty prediction are simultaneously trained on a large metamaterial databaseto map complex microstructures into a low-dimensional, continuous, andorganized latent space. We show in this study that the latent space of VAEprovides a distance metric to measure shape similarity, enable interpolationbetween microstructures and encode meaningful patterns of variation ingeometries and properties. Based on these insights, systematic data-drivenmethods are proposed for the design of microstructure, graded family, andmultiscale system. For microstructure design, the tuning of mechanicalproperties and complex manipulations of microstructures are easily achieved bysimple vector operations in the latent space. The vector operation is furtherextended to generate metamaterial families with a controlled gradation ofmechanical properties by searching on a constructed graph model. For multiscalemetamaterial systems design, a diverse set of microstructures can be rapidlygenerated using VAE for target properties at different locations and thenassembled by an efficient graph-based optimization method to ensurecompatibility between adjacent microstructures. We demonstrate our framework bydesigning both functionally graded and heterogeneous metamaterial systems thatachieve desired distortion behaviors.

Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems