Exploring VAE-driven implicit parametric unit cells for multiscale topology optimization

The simulation and optimization of metamaterial, known for their engineered properties in various applications, encounter intricate challenges due to complex microstructure interactions, extensive design spaces, and substantial computational requirements. To address these challenges, our research introduces a novel data-driven framework utilizing deep generative modeling to enhance the design process of metamaterials. Focusing on composite metamaterial with double negative coefficients of thermal expansion and Poisson's ratio, we apply an Alternative Active Phase and Objective functions (AAPO) method for deciding the initial metamaterial dataset. To enhance dataset diversity, a distortion filter is applied, broadening the range of design possibilities. Subsequently, we utilize a Variational Autoencoder (VAE), integrated with a regressor, to train on this diversified database. This training effectively maps complex unit cell geometries to a coherent latent space, simultaneously correlating them with continuous material properties. Our approach demonstrates robustness in multi-phase and multi-physics optimization as well as efficiency in generating specialized databases of unit cells. This framework is pivotal in systematically designing unit cells and multiscale systems, specifically aiming for distinct thermo-mechanical behavior targets. To mitigate the computational demands encountered during multiple design meta-materials via gradient-based topology optimization, we have integrated high-performance methods and automatic differentiation. This integration marks a significant advancement in the data-driven design of metamaterials, offering substantial practical and theoretical benefits in the field.