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He et al. Microstructures 2023;3:2023037 https://dx.doi.org/10.20517/microstructures.2023.29 Page 19 of 24

The former achieves mapping from performance to features, while the latter achieves structure
reconstruction from features. 3. Combining MLP (or CNN) with GA. The former achieves performance
prediction through pre-training and then adds it to the iterative process of the latter. Another approach is
based on probabilistic strategies; the main approach is to use Gaussian sampling after the data passes
through the neural network rather than directly mapping to the structure or introducing Gaussian sampling
in the middle design layer of the TNN architecture. Compared to deterministic strategies, probabilistic
strategies have more diverse design choices.

(3) As the functional requirements of meta-structures become more critical, the design of meta-structures
based on specific goals becomes more and more complex, which makes many advanced algorithms
constantly develop and combine to meet the requirements. The support of an open-source framework
makes the development of relevant algorithms for meta-structure design easier, even for the researchers
without professional backgrounds in ML, which is an important reason for this field in a period of vigorous
development and growth.

Although the research on the combination of ML and meta-structures has aroused great interest and
attention in recent years, and many research achievements have been made, there are still many problems
that restrict further development. The main problems and future directions can be summarized as follows:

(1) Obtaining data is often difficult, especially for problems without analytical solutions or high numerical
calculation costs. Therefore, it is necessary to develop algorithms that only need small dataset training, such
as reducing the demand for source data by transfer learning. Additionally, there is currently a lack of
commonly used datasets in the field of meta-structure design. If researchers can share some datasets of
conventional meta-structures, it will be easy to achieve data migration and fusion in the future.

(2) ANNs are often seen as black boxes, wherein the input of a set of structural parameters naturally results
in the output of a corresponding set of performance parameters. Exploring what changes the data has
undergone in the process of layer-by-layer transmission, in other words, how the structural parameters
change step by step toward the performance parameters after each layer of operation, is important research
to uncover the interpretability application of neural networks in the field of meta-structures.

(3) The research on some new physical concepts, such as non-Hermite smart phononic crystals, is in full
swing in the field of meta-structures. What role ML can play in these new physical mechanisms is a
question that can be deeply explored at present.

(4) The research of meta-structure mainly involves design and manufacturing. ML can theoretically provide
excellent design results for various acoustic or mechanical requirements of targets, but most current
research lacks manufacturing and experimental verification after design. Therefore, more consideration of
manufacturing and verification is an important prerequisite for the application of this field.

(5) Multifunctional integration is an important direction of the development of meta-structures at present,
which may involve the coupling of multiple physical fields, such as acoustics, mechanics, electromagnetism,
and heat. Developing ML algorithms for multifunctional meta-structure design with multi-physical field
characteristics is not only a challenge but also a promising direction. The path planning problem of
multifunctional integrated composite meta-structure configuration in 3D printing containing continuous
fibers is one of the important reasons currently restricting the manufacturing of complex composite
structures. By introducing ML algorithms to optimize the fiber distribution direction field of continuous