Page 167 - Read Online

He et al. Microstructures 2023;3:2023037 https://dx.doi.org/10.20517/microstructures.2023.2 Page 3 of 24

Natural solid materials typically exhibit positive elastic and shear moduli, which are related by Poisson's
ratio, typically falling between 0 and 0.5. The mechanical meta-structures designed through origami and
[47]
[46]
[45]
kirigami structures , chiral structures , lattice structures , honeycomb structures , and other methods
[44]
can constrain and adjust the overall elastic deformation, thus exhibiting unconventional equivalent
characteristics, such as negative stiffness, negative compression, negative Poisson's ratio, multi-stability, and
so forth. Mechanical meta-structures greatly enrich the way of regulating statics performance and provide
support for the design and application of engineering vibration suppression, impact resistance, energy
absorption, and structural protection devices.

The process of analyzing the wave or mechanical properties of a certain meta-structure is a forward
problem, which can be easily realized through theoretical, experimental, or commercial software analysis.
However, designing structures with specific properties considering practical application backgrounds can
essentially be attributed to inverse problems . The traditional strategy for solving inverse problems usually
[48]
relies on trial and error supported by experimental and computational modeling techniques, which require
a significant amount of time and resource costs. Subsequently, some heuristic optimization methods that
relied on global search were developed, such as genetic algorithms (GA) , simulated annealing
[49]
algorithms , particle swarm optimization algorithms , and so forth. These methods can effectively
[51]
[50]
identify the meta-structure parameters corresponding to the target property and can be modified to adapt to
different goals. However, their performance generally depends on the specific problem, usually lacking
stability and being prone to falling into local optima.

With the deepening of artificial intelligence (AI) research, the improvement of computer hardware
performance, and the emergence of open-source deep learning frameworks, machine learning (ML)
algorithms have been rapidly developed and widely applied, and advanced methods, such as deep neural
networks (DNNs) and reinforcement learning (RL), have emerged. The development of ML has shown a
strong ability to circumvent the shortcomings of traditional methods, leading to an interdisciplinary
revolution, including biology , finance , materials science , computational chemistry , computational
[53]
[52]
[55]
[54]
mechanics , etc. Certainly, the meta-structure design scheme based on intelligent algorithms has become
[56]
an important core to break through the bottleneck of inverse problems and promote the development of the
field. In the past several years, some review articles have introduced the latest progress of ML-enabled meta-
structure design from different aspects, for instance, the progress of ML-enabled nanophotonics and
photonic devices in an all-round way [57-66] . Furthermore, Khatib et al. introduced the progress in the field of
[67]
designing electromagnetic meta-structures by ML . Jiao et al. discussed the advent and prospects of ML in
the field of mechanical meta-structures . Jin et al. introduced some basic ML algorithm principles and
[68]
reviewed intelligent on-demand design of phononic metamaterials . Subsequently, Muhammad et al. and
[69]
Liu et al. successively updated the progress of ML in phononic crystals and metamaterial [70,71] . From the
works in recent years, the field of integrating ML in the design of acoustic, elastic, and mechanical meta-
structures has developed rapidly, but there is still a lack of comprehensive review that directly takes design
objectives as the classification standard, which is helpful to understand the latest progress of various inverse
design problems in this field.

In this review, we draw attention to a series of recent results on ML inverse design of acoustic, elastic, and
mechanical meta-structures from the perspective of design objectives. We first introduce the background of
the development of ML and how basic algorithms can be combined with meta-structures for inverse design.
Then, we summarize the latest progress from three aspects: design of band structure in infinite meta-
structures, design of wave propagation characteristics in finite meta-structures, and design of static
characteristics in mechanical meta-structures. Finally, we summarize the current status of this cutting-edge