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cross-disciplinary field and discuss potential future development prospects.

BACKGROUND OF ML
AI is committed to enabling machines to acquire and expand human intelligence. The development of AI
can be traced back to the proposal of this concept at the Dartmouth Conference in 1956, but related
research has already begun earlier. It has gone through periods of symbolism, connectionism, and
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behaviorism . Early researchers constructed expert systems by feeding human experience into machines
through programming, which is a symbolic approach. Although expert systems perform well in
environments with strong logic, such as mathematical deduction, this approach cannot obtain new
knowledge beyond input, and human intelligence is acquired through autonomous learning rather than
direct input. Therefore, researchers turned to exploring ways to enable machines to autonomously acquire
knowledge starting in the 1980s, a concept known as ML . At this time, connectionism represented by an
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artificial neural network (ANN) algorithm ushered in the peak of development. Artificial neurons were
proposed in 1943 , followed by the development of a variable strength criterion for inter-unit connections,
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which led to the formation of a perceptron model . In 1986, the success of the back-propagation training
algorithm enabled the multilayer perceptron (MLP) model to have nonlinear processing capability . On
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this basis, researchers began to explore the deepening of neural network models. Recurrent neural networks
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(RNN) with time series prediction function and convolutional neural networks (CNN) with image
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processing function were successively proposed. The deepening of the model has brought about an
explosive increase in training difficulty, but this dilemma has been effectively overcome with the
improvement of computer computing power. Since 2006, research on ANNs has entered the era of deep
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learning , and the emergence of many open-source deep learning frameworks has greatly reduced the
learning cost of algorithms. Over the past decade, a large number of DNN models have emerged, such as
generative adversarial networks (GAN) , condition GANs (CGAN) , tandem neural networks (TNN) ,
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and so forth. RL, originating from behaviorism , has gradually emerged in the context of the flourishing
development of deep learning. The basic principle is that the agent takes different actions to change its own
state and corrects its behavior based on environmental feedback, thereby selecting the optimal strategy to
achieve the goal. RL is seen as the future development direction of AI and has achieved great success in
fields such as Go programs and autonomous driving .
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The advantage of DNNs lies in their ability to learn potential laws implicitly from data, especially for
nonlinear mapping problems with unclear or complex physical mechanisms, and the design of meta-
structures belongs to such problems. Unlike the process of calculating property from structural parameters
in a forward problem, inverse design, which involves extrapolating the property back to the structure, often
finds it difficult to obtain analytical solutions based on clear functional relationships. However, with the
nonlinear processing ability of data-driven neural networks, the design parameters of the structure can be
quickly obtained by taking the target property as input.

For situations where high-dimensional data or image data are used as property inputs, CNNs are often used
to reduce the number of connections between neurons, thereby reducing the computational complexity of
the computer. Autoencoders (AE) can be used to extract features from high-dimensional property data for
further wave or mechanical analysis. In the inverse design meta-structure paradigm, there may be a problem
that one property corresponds to multiple sets of structural parameters, which leads to the convergence
failure of neural network training.

The proposal of TNN effectively solves this problem by freezing the training parameters of the pre-trained
forward network and cascading it after the inverse network . The subsequently developed probabilistic
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