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He et al. Microstructures 2023;3:2023037 https://dx.doi.org/10.20517/microstructures.2023.29 Page 5 of 24

TNN can obtain multiple reasonable structures as alternative solutions based on inputs. Additionally, in
order to deal with the situation of only small-scale data, researchers introduced transfer learning into meta-
structure design [86,87] . Transfer the model trained from similar data sources to the target data for retraining,
thereby reducing the demand for target data without affecting the training results.

Another solution is to rely on GAN and CGAN . In this solution, the generator of GAN takes random
[80]
[81]
vectors as input, initiates the generation of a structure, and then sends the generated structure and real
structure to the discriminator for authenticity discrimination to guide model updates. After adversarial
training of the generator and discriminator, a generator model that can generate the target structure can be
obtained. While inputting random vectors, the expected property can be input together to enable the
generator to generate structures under this condition. The combination mode of RL and meta-structure
inverse design is to regard structural parameters as agents. These agents execute the action of parameter
changes, determine feedback based on the proximity of the altered property to the design goal, and finally
explore a parameter path to achieve the goal.

As a summary, the overview diagram of ML in the field of meta-structure for forward performance
prediction and inverse structure design is shown in Figure 1. In addition, there are various types of ML
algorithms, some of which may be simple and perform well when dealing with specific problems. For
example, linear regression obtains sample distribution patterns by fitting data points as closely as possible.
Logistic regression can compress samples to a specific range through nonlinear functions, thus realizing the
classification of samples. A decision tree is a tree-structured classifier that classifies samples by representing
branches of different attributes. Multiple groups of decision trees can form a random forest, which yields
higher performance and prediction stability. However, the increase in the complexity of the model requires
more computing time. Readers can refer to relevant literature for more information [73,88,89] .

The emergence of some deep learning open-source frameworks, such as TensorFlow and PyTorch ,
[91]
[90]
helps beginners easily grasp the basic usage of ML. These frameworks are integrated through Python
packages and can be easily called, eliminating the hassle of writing low-level computational code for neural
networks. Researchers can use some shared ready-made datasets for training and learning, such as
Handwritten Digit Dataset, CIFAR10, Fashion-MNIST, and so forth. In addition, the commercial software
MATLAB also has a built-in toolbox for neural networks, which can be easily modeled through the user
interface.

APPLICATION OF ML IN META-STRUCTURES
Design of band structure in infinite meta-structures
A band structure is the most basic way to describe the acoustic/elastic wave characteristics in meta-
structure, so it is the most direct research idea to carry out the application of ML in meta-structure design
around a band structure and the wave information it carries. With the maturity of deep learning algorithms
and open-source frameworks, a large amount of design work has emerged around band structures, which
can be mainly divided into two categories: design based on complete band structures and design based on
bandgaps. Table 1 provides a brief overview of ML for the design of band structures in infinite meta-
structures.

Complete band structures
For the design of complete band structures, one type of work is to predict the corresponding band structure
[92]
of a meta-structure from a forward perspective to replace the analytical process. Liu and Yu used MLP
and radial basis function neural networks (RBF-NN) to predict the band structures of one-dimensional