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He et al. Microstructures 2023;3:2023037 https://dx.doi.org/10.20517/microstructures.2023.29 Page 13 of 24

TNN Experimental verification of the accuracy of using TNN to 2022
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inverse design interface states

MLP Efficient implementation of edge state design for specific or 2022
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GA maximum bandwidth corresponding structures

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design of metaporous materials with broadband sound absorption performance by GAN . Liu et al. used
cascaded inverse and forwarded CNN to achieve the inverse design of acoustic absorbing devices with
coiled Fabry-Perot channels, which is based on the same principle as a fully connected TNN
architecture . Jin et al. used RL to optimize a lightweight sound absorption multi-function integrated
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meta-structure with perforated fish-belly panels . Subsequently, they used this method to optimize a spiral
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plate sandwich structure that integrates lightweight, vibration reduction, and sound absorption
functions . Mahesh et al. proposed a one-dimensional CNN inverse design scheme for low-frequency
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Helmholtz resonate sound absorber . Afterward, they further constructed a TNN architecture using
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inverse and forward one-dimensional CNNs for inverse design of a similar sound-absorbing structure .
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Sound insulation is another method of controlling noise, with the objective of blocking or attenuating the
transmission of acoustic waves. It typically relies on the transmission coefficient to characterize the
performance of the sound insulation structure in blocking sound energy. For the design enabled by ML in
sound insulation meta-structures, Luo et al. provided a paradigm of fuzzy design to overcome the problem
of data inconsistency, as shown in Figure 3A . Specifically, they combine MLP with mixed Gaussian
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sampling, mapping a target transmission spectrum to multiple sets of Gaussian sampling parameters
through MLP and then linearly overlaying these Gaussian distributions to obtain a mixed Gaussian
distribution. All acoustic meta-structures corresponding to the local maximum values are alternative
structures that meet the target transmission frequency spectrum. Gurbuz et al. used a random algorithm to
generate binary images of units composed of fluid elements and solid elements and obtained the
transmission loss spectra through the finite element method . Then, by training CGAN to capture the
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potential relationship between transmission loss spectrum and unit geometry, they carried out inverse
design of the structural units to achieve the required sound insulation purpose.

Advanced control of wave propagation characteristics
Subwavelength scale metasurfaces may experience significant losses due to the presence of viscous friction
and narrow acoustic channels. The diffraction acoustic meta-grating designed based on diffraction theory
can improve the control efficiency of the acoustic metasurface. Ding et al. employed the TNN model to
achieve inverse design of non-local metasurfaces for acoustic wave diffraction characteristics . They
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explored the coupling effect between all subunits rather than nearest-neighbor coupling, demonstrating the
ability of non-local metasurfaces to reshape the acoustic field. Meanwhile, the implementation of this work
effectively demonstrates the ability of TNN to support the design of non-local coupled metasurfaces,
especially in the face of complex coupling effects that greatly increase the degree of nonlinearity. In another
work, Du et al. designed acoustic meta-grating wavelength division multiplexing by using an improved
TNN architecture . Specifically, they introduced probability sampling in the TNN architecture, which
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divides the design space into two layers instead of the traditional one layer for design parameters. Among
them, the latter layer is the design parameters of the structure, obtained by sampling from the Gaussian