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| Topology design ANNs for PnCs and EMs. a | The AE-based model by Li et al. [106] where topological feature indicates compressed low-dimensional vector. b | The VAE-based model by Liu et al. [109] where the pretrained generative model is the trained VAE's decoder. c | The CGAN by Gurbuz et al. [113] where "TL" (conditions) is the transmission loss of the 2D EMs and "Z" is the input random variables. d | The CGAN by Jiang et al. [87] where the target refers to dispersion curves of 2D PnCs.

| Topology design ANNs for PnCs and EMs. a | The AE-based model by Li et al. [106] where topological feature indicates compressed low-dimensional vector. b | The VAE-based model by Liu et al. [109] where the pretrained generative model is the trained VAE's decoder. c | The CGAN by Gurbuz et al. [113] where "TL" (conditions) is the transmission loss of the 2D EMs and "Z" is the input random variables. d | The CGAN by Jiang et al. [87] where the target refers to dispersion curves of 2D PnCs.

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The computer revolution coming by way of data provides an innovative approach for the design of phononic crystals (PnCs) and elastic metamaterials (EMs). By establishing an analytical surrogate model for PnCs/EMs, deep learning based on artificial neural networks (ANNs) possesses the superiorities of rapidity and accuracy in design, making up for t...

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... et al. [106] combined an AE and a MLP to design topologies of 2D PnCs, as shown in Fig. 4a. The AE was responsible for compressing 128×128 topology matrices into low-dimensional vectors and inverse restoration. The MLP was responsible for building the mapping relationship from dispersion properties to the transformed low-dimensional vectors. A targeted dispersion property was input into the MLP to output a designed ...
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... The MLP was responsible for building the mapping relationship from dispersion properties to the transformed low-dimensional vectors. A targeted dispersion property was input into the MLP to output a designed low-dimensional vector, and then the vector was input into the AE's decoder to obtain a designed topology. In the model shown in Fig. 4a, the AE is for dimensionality reduction and data restoration, and ...
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... and discrete topology information into low-dimensional and continuous latent space consisting of latent vectors, and it can restore inversely. Liu et al. [108] proposed a VAE-based model to design topologies of 2D EMs. Two ANNs, a VAE and a TNN, were used, where the VAE's decoder and the TNN were combined to design topologies, as shown in Fig. 4b. Similar to the idea of Li et al. [106], the VAE is for dimensionality reduction and data restoration, and the TNN is for the design of latent vectors. Compared with a single MLP, the TNN has a more powerful design ability. In addition, Liu et al. added two equations about frequencies and sizes into the model to simultaneously design ...
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... to design latent vectors. The GAN is also able to generate new samples, although it is more difficult to train in comparison with the VAE. A single GAN can only deal with topology information, and structural properties must be considered additionally in design. Hence, Gurbuz et al. [113] used a conditional GAN (CGAN) to design 2D EMs, as shown in Fig. 4c. The conditions in the CGAN referred to the property (transmission loss) of the ...
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... 2021), and discrete approach (Dong et al., 2017). With the development of AI technology, the topology design based on deep learning has been explored. For PnCs and EMs, there are mainly three ANNs to design topologies, including AE-, VAE-, and GAN-based model. Li et al. (2020) combined an AE and an MLP to design topologies of 2D PnCs, as shown in Fig. 4a. The AE was responsible for compressing 128 × 128 topology matrices into low-dimensional vectors and inverse restoration. The MLP was responsible for building the relation from dispersion properties to the transformed low-dimensional vectors. A targeted dispersion property was input into the MLP to output a designed low-dimensional ...
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... inverse restoration. The MLP was responsible for building the relation from dispersion properties to the transformed low-dimensional vectors. A targeted dispersion property was input into the MLP to output a designed low-dimensional vector, and then the vector was input into the AE's decoder to obtain a designed topology. In the model shown in Fig. 4a, the AE is for dimensionality reduction and data restoration, and the MLP is for design, which is a clear and reasonable design idea. However, for more complicated design problems, this model may be invalid due to the function nature of the MLP, which was discussed in the above section, and it cannot realize 'one-to-many' ...
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... and discrete topology information into low-dimensional and continuous latent space consisting of latent vectors, and it can restore inversely. Liu and Yu (2022e) proposed a VAE-based model to design topologies of 2D EMs. Two ANNs, a VAE, and a TNN, were used, where the VAE's decoder and the TNN were combined to design topologies, as shown in Fig. 4b. Similar to the idea of Li et al. (2020), the VAE is for dimensionality reduction and data restoration, and the TNN is for the design of latent vectors. Compared with a single MLP, the TNN has a more powerful design ability. In addition, Liu and Yu (2022e) added two equations about frequencies and sizes into the model to simultaneously ...
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... GAN is also able to generate new samples, although it is more difficult to train in comparison with the VAE. A single GAN can only deal with topology information, and structural properties must be considered additionally in design. Hence, Gurbuz et al. (2021) used a CGAN to design 2D EMs, as shown in Fig. 4c. The conditions in the CGAN referred to the property (transmission loss) of the structure. When the CGAN was trained, the conditions were input into the generator and the discriminator, enabling the CGAN to learn the property information besides topologies. Then, a targeted property (condition) and a random vector were input into the ...

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