Fig. 1 The proposed approach for generating complex porous metamaterial unit samples with complete connectivity in both solid and pore phases More about this image found in The proposed approach for generating complex porous metamaterial unit sampl...

Fig. 2 ( a ) The process of increasing the radius of search from nodes until they get connected. ( b ) Remaining isolated clusters will get connected based on their distances. ( c ) The process of connecting the pore phase's nodes i and j using Manhattan distance and rerouting: (1) Nodes i a... More about this image found in ( a ) The process of increasing the radius of search from nodes until they ...

Fig. 3 Diversity of the training samples: several examples of metamaterial unit samples in the created database More about this image found in Diversity of the training samples: several examples of metamaterial unit sa...

Fig. 4 Heat transfer simulation in abaqus: ( a ) the input porous metamaterial unit, the temperature gradient, and the heat flus on the surfaces of the sample, and ( b ) histogram of the simulated heat conductivity values k x , k y , and k z from X , Y , and Z direct... More about this image found in Heat transfer simulation in abaqus: ( a ) the input porous metamaterial u...

Fig. 5 Three strategies of integrating a regressor with a deep generative model: ( a ) parallel processes, ( b ) sequential integration, and ( c ) latent space-mediated integration More about this image found in Three strategies of integrating a regressor with a deep generative model: (...

Fig. 6 ( a ) Baseline VGAE model. ( b )–( d ) Three VGAE-based generative models based on sequential integration or latent space-mediated integration strategy. More about this image found in ( a ) Baseline VGAE model. ( b )–( d ) Three VGAE-based generative models b...

Fig. 7 VGAE-based design approach More about this image found in VGAE-based design approach

Fig. 8 Optimal design candidates obtained by ( a ) VGAE-based design approach and ( b ) cVAE-based design approach More about this image found in Optimal design candidates obtained by ( a ) VGAE-based design approach and ...

Fig. 9 ( a ) The proposed cVAE-based generative model, ( b ) the proposed CGVAE-based generative model, and ( c ) the cVAE-based design approach More about this image found in ( a ) The proposed cVAE-based generative model, ( b ) the proposed CGVAE-ba...

Fig. 10 ( a ) Loss history of CGVAE model. ( b ) Histogram of the distribution of volume fraction by sampling on the latent space of CGVAE under condition c = V F solid = 0.7 . More about this image found in ( a ) Loss history of CGVAE model. ( b ) Histogram of the distribution of v...

Fig. 1 Comparison of the configuration between ( a ) single-split and ( b ) multi-split cases. The location of branching is indicated by a box encompassing source or junction nodes. More about this image found in Comparison of the configuration between ( a ) single-split and (...

Fig. 2 Class of problems considered in this article. The systems include a tank, a pump, valve(s), CPHXs in parallel and series, a LLHX, and a sink. More about this image found in Class of problems considered in this article. The systems include a tank, a...

Fig. 3 Workflow diagram illustrating the steps involved in the code execution. Starting with the given Data , Head Load , and Config Number , the base graph and physics graph are generated. The OLOC problem is then defined and solved to obtain the objective function value (thermal endurance wit... More about this image found in Workflow diagram illustrating the steps involved in the code execution. Sta...

Fig. 4 Graph-based model for multi-split architectures studied in this article. Here, fluid nodes are represented by circles, wall nodes by squares, and thermal power is indicated by directional lines (distinguished according to the legend). More about this image found in Graph-based model for multi-split architectures studied in this article. He...

Fig. 5 Notional example to illustrate the elements of thermal physics included in this system model. Here, a node (circle) represents a temperature and an edge (directional line) represents a thermal power flow. More about this image found in Notional example to illustrate the elements of thermal physics included in ...