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design with either maximum bulk modulus, maximum shear modulus, or minimum Poisson's ratio using
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CNN . The dataset of their work is generated by the topology optimization framework based on the
energy homogenization method and periodic boundary conditions.

To optimize the structure to obtain a 2D structure with the best mechanical properties, CNN is often
combined with GAN or GA. Tan et al. reported a model in which deep convolutional GANs (DCGAN) are
used to generate candidates adhering to geometric constraints, while CNN associates microstructures with
properties . After training, combine the two models for inverse design microstructural materials with
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specific mechanical properties. Garland et al. demonstrated the design of structural lattice metamaterial
combining CNN and GA to meet the constraints of additive manufacturing, as shown in Figure 4B . In
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addition, Wang et al. and Chang et al. also used this design paradigm to realize the inverse design of shell-
based mechanical metamaterial and auxetic metamaterial with zero Poisson’s ratio, respectively [140,141] .
Tian et al. proposed the combination of CNN and GAN to achieve customized Poisson's ratio meta-
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structure design . CNN is trained to predict the global Poisson's ratio response of a given meta-structure,
while GAN realizes the structural inverse design of the anticipated Poisson's ratio response through
adversarial training.

In addition, some works have been done to design and optimize specific mechanical properties of one-
dimensional or three-dimensional (3D) meta-structures. Liu et al. demonstrated a design work of curved
beams based on MLP and optimization methods, as shown in Figure 4C . The mechanical properties of
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curved beams are characterized by stiffness, forward snapping force, and backward snapping force and are
controlled by thickness distributions. They first trained MLP to predict the mechanical properties of curved
beams with variable thickness and then put the trained MLP model into the optimization cycle proposed by
Gu et al., as mentioned above, to optimize the thickness distribution with the best mechanical
properties . Challapalli et al. demonstrated the GAN-based inverse design framework for optimizing
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lightweight lattice structures, as shown in Figure 4D . The basic idea of this framework is to add initial
conditions, boundary conditions, and forward regression to the real data distinguished by discriminators to
obtain structural units with excellent performance. The new dataset is then used for GAN training, and the
process is iterated repeatedly to obtain the structure with the best mechanical performance.

CONCLUSION AND OUTLOOK
In this review, we have discussed the combination and synchronous development of ML and meta-structure
and reviewed the recent flexible applications of ML algorithms in the fields of acoustics, elastic, and
mechanical meta-structures from the aspects of band structures, wave propagation characteristics, and static
characteristics. Through analysis, we have come to the following main conclusions:

(1) The forward performance prediction of meta-structures can usually rely on analytical formulas or
simulation software. The purpose of introducing ML is to save time and computing resources or to provide
a forward computing part for some combined inverse design schemes. The inverse design of meta-
structures is difficult to deal with analytically. DNNs with strong nonlinear modeling capabilities effectively
solve this problem and can directly serve as alternative models for inverse problems. In addition, RL can
also serve as an inverse design algorithm in meta-structures to explore structures that meet customized
performance goals in the parameter space.

(2) A crucial issue in the inverse design process is how to alleviate data inconsistency. There are two main
ideas. One approach is based on deterministic strategies, with representative approaches being: 1. TNN
architecture with inverse and forward network concatenation. 2. Combining MLP (or CNN) with an AE.