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Abstract Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. This complete connectivity is crucial for manufacturability and structure-fluid interaction applications (e.g., fluid-filled lattices). In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units with the constraint of complete connectivity. First, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Second, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design framework is evaluated by comparing the performances of the obtained designs with those of known designs in the metamaterial database. Merits and shortcomings of the proposed framework are also discussed. 

Abstract Porous metamaterial units filled with fluid have been used in engineering systems due to their ability to achieve desired properties (e.g., effective thermal conductvity). Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units infilled with liquid. Firstly, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Secondly, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design approach is evaluated by comparing the performances of the obtained designs with those of existing designs in the training database. Merits and shortcomings of the proposed framework are also discussed.