• Advanced Photonics
  • Vol. 7, Issue 3, 034005 (2025)
Yasir Saifullah1,2,3,†, Nanxuan Wu1, Huaping Wang4, Bin Zheng1,2,3..., Chao Qian1,* and Hongsheng Chen1,2,3,*|Show fewer author(s)
Author Affiliations
  • 1Zhejiang University, ZJU-UIUC Institute, Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, Hangzhou, China
  • 2Zhejiang University, ZJU-Hangzhou Global Science and Technology Innovation Center, Zhejiang Key Laboratory of Intelligent Electromagnetic Control and Advanced Electronic Integration, Hangzhou, China
  • 3Zhejiang University, Jinhua Institute of Zhejiang University, Jinhua, China
  • 4Zhejiang University, Institute of Marine Electronics Engineering, Ocean College, Key Laboratory of Ocean Observation-Imaging Testbed of Zhejiang Province, Hangzhou, China
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    DOI: 10.1117/1.AP.7.3.034005 Cite this Article Set citation alerts
    Yasir Saifullah, Nanxuan Wu, Huaping Wang, Bin Zheng, Chao Qian, Hongsheng Chen, "Deep learning in metasurfaces: from automated design to adaptive metadevices," Adv. Photon. 7, 034005 (2025) Copy Citation Text show less

    Abstract

    Metasurface modeling, designs, and applications using computational approaches are by now well established as an essential pillar in photonics, physics, and materials science. The past years have witnessed tremendous advances in methodologies and technologies to unearth the intricate light–matter interaction and promote adaptive metadevices. They have pushed the studies of metasurfaces from early passive, reconfigurable modalities to the next generation of intelligent metasurfaces. In this review, we elaborate general architecture for intelligent metasurfaces, constructed by the algorithm layer, tunable metasurface layer, and application layer. We first discuss a variety of deep learning models, ranging from the fundamental neural networks inspired by computer science to sophisticated algorithms embedded with physical specialty, highlighting their potential in the forward prediction, inverse design, and spectral correlation of metasurfaces. We then discuss adaptive metadevices in the main applications of invisibility cloaks, smart vision, intelligent sensing, and wireless communication. Finally, we pinpoint current challenges and future perspectives to embrace the coming era of intelligent metasurfaces.

    Key Points

    1. Intelligent metasurfaces, as the next generation of passive and tunable metasurfaces, have recently attracted a great deal of attention due to the distinct features of decision-making, self-programming, and executing a series of successive tasks without human supervision.
    2. Intelligent metasurfaces are typically composed of three layers: intelligent algorithms, tunable metasurfaces, and applications, where tunable metasurfaces are the physical foundation, and intelligent algorithms are the internal driving force.
    3. Recent breakthroughs in deep learning have provided an essential tool for accelerating on-demand photonics design as it can alleviate the time-consuming, low-efficiency, and experience-oriented shortcomings in conventional numerical simulations.
    4. In addition to the fundamental neural networks inspired by computer science, embedding physical knowledge into neural networks can greatly improve output accuracy and relax data requirements at a low cost.
    5. Intelligent metasurfaces have facilitated numerous applications, such as intelligent invisibility cloaks, smart vision, intelligent sensing, and wireless communication.
    6. Deep learning enabled self-adaptive invisibility cloak exhibits a millisecond response time to an ever-changing incident wave and the surrounding environment.

    1 Introduction

    Pursuing the free control of electromagnetic (EM) waves is an endless goal. Its century-old development trajectory is analogous to the evolution of a species, always moving toward adapting to the changing environment. Before the twenty-first century, scientists had built up a universal framework of electromagnetism and optics and explained many anomalous scattering phenomena, such as the bright colors and distinctive eye spots on the peacock’s feathers. After that, humans started to explore how to control EM waves, and then, metamaterials and metasurfaces were born. They are artificial media comprising three-/two-dimensional arrays of subwavelength structures commonly called meta-atoms/unit cells. They have garnered notable interest for their remarkable ability to manipulate EM waves at the subwavelength scale, facilitating a variety of exciting phenomena and novel applications, such as invisibility cloaking,13 analog computing,48 quantum photonics,911 and wireless communication.1218 In particular, metasurfaces are more popular in both academia and industry due to their features of compactness, lightweight design, and low loss.1923 Reconfigurable metasurfaces epitomize a revolutionary class of metasurfaces characterized by their ability to dynamically manipulate EM waves. Reconfigurable metasurfaces employ diverse tuning mechanisms depending on the operating frequency, leveraging different physical principles to achieve dynamic control over electromagnetic properties.2427 In the microwave regime, tunability is primarily realized through electrical control using PIN diodes,28 varactors,29 and liquid crystals.30 At terahertz frequencies, free-carrier modulation in semiconductors (e.g., GaAs, Si, and Ge),3133 graphene,34 and other 2D materials (e.g., MoS2)35 is widely used, utilizing electrical gating or optical excitation for dynamic conductivity tuning. Phase-change materials, vanadium dioxide (VO2), germanium-antimony-tellurium (GST), and liquid crystal provide additional tunability via electrical, optical, or thermal stimuli from GHz to visible.3639 In the optical regime, reconfigurable metasurfaces rely on liquid crystals,37 thermo-optic effects,38 electrochemical tuning,40 and transparent conducting oxides (e.g., ITO and AZO)41,42 for dynamic refractive index modulation. Mechanical tuning through MEMS/NEMS, flexible substrates, and microfluidics enables shape reconfiguration for microwave, terahertz, and optical frequencies.4348

    Although reconfigurable metasurfaces enable dynamic tuning of optical functions, human intervention is still required for a specific task. As the next generation of tunable metasurfaces, intelligent metasurfaces have recently garnered significant attention, in large part due to the fast development of deep learning.4953Figure 1 presents the conceptual illustration of intelligent metasurfaces, where tunable metasurfaces are the physical foundation, and deep learning is the internal driving force. Their fusion is poised to give rise to radically intelligent devices that adapt to the changing EM conditions and user demand autonomously. As a data-driven approach, deep learning enables efficient metasurface design, system optimization, and automation control through hierarchical layers for data abstraction.5458 In particular, on-demand metasurface design using deep learning can address the time-consuming, low-efficiency, and experience-oriented challenges in traditional full-wave numerical simulations and physics-based methods. Meanwhile, sophisticated model structures have been suggested for enhancements to address tasks in specialized domains of computer science. To illustrate this progression, we introduce key deep learning models, ranging from foundational to advanced architectures, highlighting their roles and contributions to intelligent metasurface design. For instance, convolutional neural networks (CNNs) excel in image recognition,59 offering robust feature extraction capabilities beneficial for metamaterial design. Recurrent neural network (RNN), adept at handling sequential data, finds applications in natural language processing60 and can be adapted for time-series analysis. Generative adversarial network (GAN)54 and variational autoencoder (VAE) are pivotal for generating new images61 and exploring latent spaces, respectively, both of which are crucial for complex metasurface designs. In addition, large language models have shown promise in autonomous material research,62 demonstrating their versatility in handling complex tasks beyond traditional domains. Despite their strengths, these models also have limitations—such as the instability in GAN training and the constrained generative quality of VAEs. Nevertheless, advancements in these areas have profoundly influenced metasurface design and its applications.

    Architecture of intelligent metasurfaces. Tunable metasurfaces are the physical foundation, and deep learning is the internal driving force. With both, intelligent metasurfaces can enable a myriad of adaptive applications without human intervention.

    Figure 1.Architecture of intelligent metasurfaces. Tunable metasurfaces are the physical foundation, and deep learning is the internal driving force. With both, intelligent metasurfaces can enable a myriad of adaptive applications without human intervention.

    In this review, we provide an overview of recent findings that demonstrate the effectiveness of deep learning in the design of metasurfaces and promote adaptive metadevices, particularly in situations where conventional or empirical methods prove impractical or inefficient. We first present deep learning architectures, ranging from the fundamental neural networks inspired by computer science to sophisticated algorithms embedded with physical specialty, highlighting their potential in the design of metasurfaces. These models are capable of mapping design parameters, encompassing factors such as geometry, material, topology, and spatiotemporal arrangement, and enabling them to perform forward prediction, inverse design, and spectral correlation. We then discuss the main applications of deep learning-enabled metasurfaces in invisibility cloaks, wireless communication, smart vision, and sensing. Finally, we offer our insights on the challenges and perspectives in this field.

    2 Deep Learning for Metasurface Design

    The development history of deep learning has been long and torturous. Its origin can be traced back to 1943 when psychologist McCulloch and mathematical logician Pitts proposed the McCulloch-Pitts (MP) neural model to simulate the human brain.63 In the late 1950s, the perceptron learning algorithm was introduced. In 1986, Jeffrey Hinton proposed a backpropagation algorithm for the multi-layer perceptron, effectively solving the nonlinear classification problem and reigniting widespread interest in artificial neural networks (ANNs). In 2006, Hinton and Salakhdinov introduced the concept of deep learning. Soon afterward, deep learning algorithms gained rapid traction in academia, sparking widespread interest and quickly extending their influence to numerous research fields.6466

    In the context of metamaterials and metasurfaces, deep learning has gained attention over the past 6 years.6772 Traditional methods often rely on iterative and lengthy numerical simulations, leading to failed designs through a trial-and-error process. Thus, employing a variety of deep learning algorithms for on-demand metasurface designs has been identified as a solution to address issues related to low efficiency, time-consuming processes, and experience-oriented shortcomings. With robust nonlinear fitting and generalizability abilities, deep learning has been found to facilitate rapid forward prediction, inverse design,73,74 and spectral correlation construction.75 Notably, we will emphasize specialized deep learning algorithms embedded with local physics.

    2.1 Fundamental Deep Learning Models

    2.1.1 Multilayer perceptron (MLP)

    For deep learning tasks, key considerations include training data collection, network structure modeling, and efficient training. MLP has been widely used in metamaterial and nanophotonics design,76,77 particularly in addressing forward spectrum calculation [Fig. 2(a)]. In modern deep-learning models, MLPs often serve as bottleneck layers, which compress information and transmit key features through fewer nodes to extract meaningful features and compactly represent high-dimensional data such as images. For instance, a deep neural network trained with synthetic experiments can retrieve sub-wavelength dimensions from far-field measurements and solve geometric inverse problems.78 Furthermore, an MLP-based programmable metasurface imager has been proposed to carry out feature extraction in the analog domain.79 Liu et al. proposed a deep learning model to understand how the EM environment and their corresponding local density of optical states are determined by artificial nanophotonics.80 Although MLPs are versatile for various tasks, their fully connected architecture can lead to a large number of parameters, making them computationally expensive and prone to overfitting, especially in high-dimensional data spaces.

    Deep-learning-based metasurface design methods. (a) A traditional forward design MLP for the spectrum prediction of nanoparticles. (b) A CNN model for inverse design with customized field distributions. Two different kernel sizes can transit two different inputs to the same output shape. (c) A recurrent neural network is used to find the required series of optical responses based on the features extracted from the input nanostructure. (d) A recursive neural network that can deal with structural inputs, c represents a child node, and p represents a parent node. M represents the assembled metasurface, and m represents the metasurface component. (e) A VAE model for both inverse and forward designs between the optical responses and design geometries by setting one to both input and output reconstruction x , whereas the other one is the latent variable z before the decoder. (f) A GAN model for inverse design by generating possible patterns, approximating spectra, and evaluating accuracy. (g) Illustration of four deep transfer learning methods. (h) A deep reinforcement learning algorithm. State is the data of the detected environmental situation, and the action is the instruction to control the metasurface design. The actor network provides the design (named action in DRL), and the environment interaction provides rewards for optimization, and the next state for the next epoch training.

    Figure 2.Deep-learning-based metasurface design methods. (a) A traditional forward design MLP for the spectrum prediction of nanoparticles. (b) A CNN model for inverse design with customized field distributions. Two different kernel sizes can transit two different inputs to the same output shape. (c) A recurrent neural network is used to find the required series of optical responses based on the features extracted from the input nanostructure. (d) A recursive neural network that can deal with structural inputs, c represents a child node, and p represents a parent node. M represents the assembled metasurface, and m represents the metasurface component. (e) A VAE model for both inverse and forward designs between the optical responses and design geometries by setting one to both input and output reconstruction x , whereas the other one is the latent variable z before the decoder. (f) A GAN model for inverse design by generating possible patterns, approximating spectra, and evaluating accuracy. (g) Illustration of four deep transfer learning methods. (h) A deep reinforcement learning algorithm. State is the data of the detected environmental situation, and the action is the instruction to control the metasurface design. The actor network provides the design (named action in DRL), and the environment interaction provides rewards for optimization, and the next state for the next epoch training.

    2.1.2 Convolutional neural network (CNN)

    The CNN algorithm is generally used in metamaterial designs because it can learn the features and optimize the weights of each layer independently, and enhance key characteristics of the EM response results with the most representative features. A general CNN model is shown in Fig. 2(b), which has convolution layers to get feature recognition characteristics through the convolution kernel.59,81 The convolution kernel is an operator used for feature extraction and for mapping features from input to output data in convolution layers. It has two key parameters: padding, which compensates for missing edge data, and stride, which determines the step size for moving the convolution kernel through the input data. The output feature data size is influenced by kernel size k, padding size p, and stride s. The relationship between the output shape Fo and input shape Fin of the convolution layer after applying a convolution operation is given by Fo=1+(Fink+2p/s). For example, in Fig. 2(b), if we have an input shape Fin of 5×5 as the blue square and apply a convolution layer with a kernel size k of 3×3, padding p of 0, and stride s of 1, the output shape Fo can be calculated as follows: Fo=1+(53+0/1)=3. Thus, the output feature map will have dimensions of 3×3 as the green square. CNN with multiple target optical responses can be used for inverse design metasurfaces with greater geometric complexity.15,82,83 Lin et al. used CNN as an inverse design tool to achieve high prediction accuracy of plasmonic metasurfaces, leveraging greater generalization compared with MLP.84 Jia et al. applied CNN to globally design an intelligent optical illusion with free-form metasurfaces, which significantly reduces the design parameters in conventional transformation optics-based methods.85 Unlike MLPs, CNNs reduce the parameter count through local connectivity and weight sharing, but they struggle with capturing long-range dependencies in sequential data, which limits their effectiveness in tasks requiring temporal or spatial coherence.

    2.1.3 Recurrent neural network (RNN)

    Designed for sequential data, such as language and audio signals, RNNs capture historical information up to the current time step and process correlations between data points. Unlike traditional feedforward neural networks, RNNs maintain a hidden state that carries information from previous time steps to the current one, enabling them to effectively manage sequences. Importantly, the number of model parameters does not increase as the time step increases, as each step shares the same weight and bias. The key training unit is the hidden layer, where the concept of gates controlling the information flow between nearby states is introduced into the hidden unit to alleviate gradient disappearance or gradient explosion questions, making RNNs efficient for processing long sequences. RNN has two typical models: long short-term memory (LSTM) and gated recurrent unit (GRU). The LSTM model introduces three gates and memory cells to control information transfer to the next sequential data, enabling it to remember important information over longer periods.86,87 The GRU model has only two gates to reset the hidden unit state and deal with the transferring information, whereas a reset gate plays the role of both forget and input gates in LSTM, making it computationally more efficient while still addressing the same issues. RNNs are also widely used with time series data or time-varying analog signals, suitable for modeling dynamic applications.88 Such a model has been demonstrated to rapidly identify relations between a series of optical properties and various shapes of nanoparticle arrays arranged in a lattice [Fig. 2(c)].89 In Pillai’s research, a pre-trained network is used to transmit image information to RNN in the form of features, and the powerful internal architecture of LSTM is used to identify relevant information from long sequence data.90 Yan et al. proposed a deep-learning method based on GRUs to extract spectral sequence features and achieve the inverse design of nanorod hyperbolic metamaterials and spectral prediction.91 RNNs excel at handling sequential data by maintaining hidden states, yet they suffer from vanishing gradient problems, which hinder learning long-term dependencies, prompting the development of more sophisticated architectures such as recursive neural networks.

    2.1.4 Recursive neural network

    Although RNNs are proficient at handling sequential data, they often face challenges when dealing with more intricate structures such as trees and graphs, which cannot be easily represented as simple sequences of data. To address this, recursive neural networks are used, capable of encoding the structural information of trees or graphs into vectors,92 as illustrated in Fig. 2(d). These vectors are then mapped into a semantic vector space that maintains specific properties, ensuring that vectors with similar properties are positioned closer together. This proximity enables effective recognition and processing of structured information. The input of a recurrent neural network unit is two (or more) child nodes c and the output is the parent node p encoded after the two child nodes, whereas the dimensions of the parent node are the same as each child node, forming a fully connected neural network. The vectors of the generated parent node and those of the other child nodes are then taken again at a new stage, resulting in their parent nodes being generated again. Each child node needs to be entered in turn according to the input tree structure during the input process, and the weights and biases of the recursive neural network are shared the same across all nodes. Both recurrent and recursive neural networks facilitate the sequential handling of metasurface designs, resulting in a model with fewer parameters, a lighter computational load, and enhanced performance. The application of recursive networks is still in progress, but researchers have extensively constructed models to address structural questions using recursive approaches. For instance, Yang et al. utilized this recursive idea as an iterative algorithm for generating quantitative field distributions.93 Recursive neural networks address some limitations of RNNs by structuring data hierarchically, but they require predefined tree structures, limiting their flexibility in dynamic environments where sequences may vary unpredictably.

    2.2 Advanced Deep Learning Models

    2.2.1 Deep generative models

    Generative models characterize the joint distribution of input and output variables to optimize a specific objective. By harnessing deep-learning algorithms, deep generative models can generate similar data by sampling from this distribution. In metasurface inverse design, the most widely used generative models are the VAE and the GAN.54,61,9497 A VAE includes an encoder that transforms training data into a latent space, which contains the main features of the original high-dimensional data but in a low-dimensional representation, and a decoder that reconstructs the original data from this latent space [Fig. 2(e)]. GANs consist of a generative network and a discriminative network [Fig. 2(f)]. GANs leverage neural networks to model the distance between two distributions, effectively avoiding the challenge of directly solving the likelihood function.98 Liu et al.99 proposed a framework for compositional patterns-producing networks and cooperative coevolution to address the inverse design of metamolecules in a metasurface composed of spatially varied meta-units. In contrast to recursive neural networks, deep generative models such as GANs and VAEs offer powerful frameworks for data generation, but they often require extensive training data and computational resources, making them less accessible for small-scale applications.

    2.2.2 Transfer learning

    Building large-scale, well-annotated datasets proves challenging due to the high costs associated with data acquisition and annotation in traditional deep learning for fields such as bioinformatics, robotics, and electromagnetic regulation. Transfer learning allows trained models to share their knowledge and experience with networks that need to be retrained to improve their performance in other scenarios and alleviate the data dilemmas.100 For each transferring question, we already have a pre-trained neural network with a known source domain for data feature characteristics and a source target for studying results with a trained function. We can employ four distinct methods depicted in Fig. 2(g) to construct a new neural network for new questions. First, through instance-based transfer learning, we reweight a portion of data in the source domain for the target domain. Second, with feature-representation transfer learning, we learn a robust feature representation in the source domain, encode this knowledge as features, and transfer it from the source to the target domain. Third, parameter-based transfer learning involves either sharing partial model parameters between the target and source domain tasks or subjecting them to the same prior distribution. Fourth, in relational knowledge transfer learning, we assume that the relationship between data in the source and target domains is the same, enabling the transfer of knowledge based on this assumed relationship. An adversarial layer, inspired by GANs, is utilized to discern the origin of features from either the source or target domain. Poor performance of this layer suggests subtle differences between the features, indicating greatly enhanced transferability. Conversely, the strong performance of this layer implies significant differences, suggesting terrible transferability.

    Transfer learning has emerged as a novel framework for fast deep learning in the field of metamaterials. Zhu et al.101 proposed a fast and accurate inverse design method for functional metasurfaces, employing transfer learning to transfer knowledge from image recognition to phase prediction. Deep transfer learning shows significant potential for large-scale metasurface designs to alleviate the data dilemma associated with high-dimensional metasurface simulation. Fan et al.102 proposed an inverse metasurface design method assisted by transfer learning, successfully extending the application from a 5 × 5 metasurface to a 20 × 20 metasurface. Zhang et al.103 demonstrated the application of heterogeneous transfer learning, applicable to variations in parameterizations, physical sizes, and entirely different geometries. Transfer learning mitigates the resource demands of deep generative models by leveraging pre-trained models, though it relies heavily on the relevance between source and target domains, potentially introducing biases if the domains differ significantly.

    2.2.3 Deep reinforcement learning (DRL)

    Deep reinforcement learning is more suitable for unsupervised learning problems [Fig. 2(h)]. Unlike traditional supervised or unsupervised algorithms, the deep reinforcement learning model learns to maximize reward by selecting appropriate actions across the entire action space, which is the set of all possible actions that an agent can take, rather than by establishing relationships between input data and target labels.104 The knowledge learned from previous optimizations assists the network in finding the best solution for the new material in fewer steps, thus greatly improving the efficiency of the design of metamaterials under the new requirements. There are other deep reinforcement learning algorithms used in metamaterial designs. For instance, by learning the optimal strategy through a dual deep Q learning network (DDQN), Rho et al.105 proposed an ultra-wideband, bionic, and perfect absorber using various materials based on the structure of moth eyes. In another approach, Lu et al.106 have combined the deep reinforcement learning algorithm soft actor-critic with a tunable metasurface, which demonstrates stable operation in the presence of multiple arbitrarily shaped obstacles, adaptively converging the incident wave to a user-defined location. Deep reinforcement learning extends transfer learning by enabling agents to learn optimal behaviors through interaction with environments, yet DRL faces challenges such as sample inefficiency and instability in training, particularly in complex, real-world scenarios.

    2.3 Deep Learning Algorithms Embedded with Physical Specialty

    A majority of existing deep learning algorithms have been adapted from computer science, often neglecting valuable insights from the physical laws that govern metasurface-related works. Harnessing these latent physical laws could significantly aid in addressing various challenging issues, including non-uniqueness and missing data. In this section, we will introduce specific, innovative, and practical ideas to tackle these real-world application problems.

    2.3.1 Non-uniqueness solution

    In metasurface inverse design, especially for global metadevices, the starting point is to establish a quality index for the design. This process introduces a non-uniqueness challenge, that is, many different metasurfaces may induce similar EM responses, which results in non-convergence of deep neural networks. To address this inevitable challenge, researchers have introduced a tandem neural network, as illustrated in Fig. 3(a), capable of relaxing one-to-many issues.107 The tandem network comprises an inverse design network and a forward simulation-like network. The forward network is pre-trained to generate the EM response based on a given metamaterial. By contrast, the inverse network is configured to design a metamaterial by giving customized standard EM responses. During the training of the entire tandem network, the weights and biases in the pre-trained forward network remain fixed, whereas those in the inverse network are continually updated to minimize the error between the input standard EM response and the output EM response. This involves using the generated metamaterial from the inverse network as the input for the forward network. Once the error approaches near-zero, it indicates that the EM response of the predicted metamaterial closely aligns with the customized one. With this algorithm, the accuracy of inverse design has significantly increased, even for metamaterials with more complex designs.29,108,109

    Specialized algorithms in metasurface design fields. (a) Illustration of a tandem neural network, setting the EM responses as the inputs and outputs while the metasurface design serves as the middle layer. (b) Demonstration of the generation-elimination framework, from a semi-known design to an optimal solution. (c) Knowledge-inherited paradigm for a metasurface inverse design. Only the SNN network should be rebuilt, and the INN related to each child’s metasurface can be inherited. (d) Two types of physics integrated algorithms: analytical model-assisted and physical adversarial networks. The right-top loss component illustrates how numerical calculation error in PDE functions or boundary conditions (BCs) helps the efficient optimization of analytical models in the same way as normal training loss. The right-bottom physical disconfirmation, which occurs when putting the network output into the principals, helps generate adversary channels to enhance scientificity and rationality.

    Figure 3.Specialized algorithms in metasurface design fields. (a) Illustration of a tandem neural network, setting the EM responses as the inputs and outputs while the metasurface design serves as the middle layer. (b) Demonstration of the generation-elimination framework, from a semi-known design to an optimal solution. (c) Knowledge-inherited paradigm for a metasurface inverse design. Only the SNN network should be rebuilt, and the INN related to each child’s metasurface can be inherited. (d) Two types of physics integrated algorithms: analytical model-assisted and physical adversarial networks. The right-top loss component illustrates how numerical calculation error in PDE functions or boundary conditions (BCs) helps the efficient optimization of analytical models in the same way as normal training loss. The right-bottom physical disconfirmation, which occurs when putting the network output into the principals, helps generate adversary channels to enhance scientificity and rationality.

    Although tandem neural networks can alleviate challenges for most one-to-many design scenarios, there remains a significant demand for inferring optical responses from various types of related optical responses. This need is particularly evident in a wide range of applications, including biological imaging, optical characterization, and material analysis. This application falls into a distinct category known as spectrum-to-spectrum design. Unlike the one-to-many problems addressed by tandem networks, spectrum-to-spectrum design poses a many-to-many challenge, as it involves non-unique metamaterials that can be associated with diverse optical responses. Chen et al. proposed a generation-elimination framework, as illustrated in Fig. 3(b), to automatically generate numerous optimal output candidates.110 The framework consists of a generation network and an elimination network. For a given input, the generative network can sample its potential space based on the VAE structure, resulting in different candidates. Subsequently, the elimination network filters out inferior candidates by merging two potential spaces. This algorithm offers interpretable insights for deep learning to analyze complex physical processes, steering clear of “brute-force” black boxes. This capability is crucial in addressing numerous challenges associated with many-to-many mapping, a common occurrence in metasurface applications.111,112

    2.3.2 Knowledge inheritance

    A knowledge inheritance paradigm has been proposed, challenging the conventional belief that neural networks are exclusively applicable to predefined and shape-specific metasurfaces.52,113 This new approach suggests that neural networks can inherit knowledge from a “parent” generation and then freely combine to form a “descendant” neural network. The knowledge inheritance neural network consists of two main components: the inheritance neural network (INN) and the assembly neural network (SNN), as illustrated in Fig. 3(c). Unlike conventional transfer learning inspired by computer science, “knowledge inheritance learning” is unique to the context of metasurfaces. The INN oversees the inverse design of individual “panel” metasurfaces, whereas the SNN acts as a coordinator, assigning tasks to each INN. When designing a specific metasurface, such as a rectangle or a diamond-shaped one, researchers initially constructed it in physical space using these seven “panel” metasurfaces. Subsequently, they synthesize the comprehensive neural network utilizing the INN equipped with different “panels.” Throughout this process, the INN is entirely inherited and retained, requiring researchers only to dynamically adjust the SNN for efficient metasurface inverse design. This research opens new possibilities for leveraging inherited features, reclaiming pre-trained knowledge, and significantly reducing the design dimension.

    2.3.3 Mathematics and physics integration

    Distinct from conventional signal processing and image recognition, metasurfaces are moderately governed by certain mathematical equations and physical laws that can be harnessed to enhance training efficiency. Figure 3(d) illustrates two typical routes. One of the most common methods is to use analytical models to evaluate the loss, providing valuable guidance for gradient backpropagation and weight updating. The other method is to incorporate physical laws into neural networks, which helps to significantly reduce errors with smaller data volumes. In recent years, researchers have proposed a series of more reliable networks called physical-informed neural networks (PINNs).114,115 The basic principle is to incorporate Maxwell’s equations or other partial differential equations into the neural network as loss functions, simultaneously driven by data and mathematics. Generally speaking, in Fig. 3(d), the numerical equations such as differential equations and the boundary conditions help measure the calculation error and join the optimization part of traditional deep learning,116118 which makes the output of the network more accurate. Note that the only difference between the forward and inverse problem with PINN is the addition of an additional loss term upredictionureal, which represents the difference between the predicted response and the wanted one. The physical interpretability of network outputs can be enhanced by integrating physical laws, such as Kramers–Kronig relations, which connect the real and imaginary parts of complex analytic functions. These universally applicable laws inspire the creation of a physical adversarial channel in training by identifying self-contradictions in the network output. By embedding physical modules and using self-contradiction about the output, the physics-grounded latent space can restore the system’s fundamental properties. This allows for meaningful alterations in generation or prediction and the exploration of counterfactual scenarios. Incorporating contradictions between the network outputs and the disconfirmation in such Kramers–Kronig relation or other physical principles in training helps establish this adversary channel by detecting internal contradictions in the output.119 Although rare and challenging, such studies are crucial for advancing physically assisted training, with a more rational and scientific output than a numerically similar output only.

    3 Deep-Learning-Based Adaptive Metadevices

    The integration of deep learning into tunable metasurfaces results in adaptive metadevices that are capable of adapting to changing conditions autonomously. In this section, we discuss the applications of deep learning-enabled metasurfaces in intelligent invisibility cloaks, wireless communication, smart vision, and intelligent sensing.

    3.1 Intelligent Invisibility Cloaks

    The captivating idea of attaining invisibility has fascinated humanity for centuries. In practical terms, invisibility, or the cloaking effect, aims to cancel the electromagnetic field scattered by an object by placing it inside a cover (cloak) that renders the entire setup undetectable to electromagnetic sensors.120132 Numerous experiments have demonstrated the concept of invisibility cloaks at microwave,1,123,125,133,134 terahertz,111,135,136 and optical frequencies.2,122,124,129,137143 Historically, metamaterials have been employed for cloaking through the design methodology of transformation optics, allowing precise control over the propagation of EM waves. Transformation optics-based cloak guides the incident wave around the hidden object, effectively concealing the object.144,145 Transformation cloak is a sophisticated method of realizing invisibility, its practical applications are limited because it requires materials with extreme constitutive parameters. In addition, various cloaking methods have been proposed, such as carpet cloak,138,139,142,146 scattering cancelation-based cloak,134,147 active cloak,148 natural light cloak,149 metasurface skin cloak,2 surface-wave transformation cloak,150 3D metasurface cloak,151 DC remote cloak,152 and hybrid invisibility cloak153 [Fig. 4(a)]. With the recent advancements in reconfigurable metasurfaces, tunable cloaks have been reported in the literature.108,155157

    Intelligent metasurfaces for invisibility cloaks and wireless communication. (a) Timeline of invisibility cloaks. (b) Schematic illustration of intelligent self-adaptive metadevices integrated with perception-decision-execution.3 (c) Deep-learning-assisted self-adaptive microwave cloak. (d) Photograph of the intelligent invisible drone.154 (e) Simulation results of cloaked/bare drone. Panel (c) is adapted with permission from Ref. 3, Springer Nature Limited. Panels (d) and (e) are adapted with permission from Ref. 154.

    Figure 4.Intelligent metasurfaces for invisibility cloaks and wireless communication. (a) Timeline of invisibility cloaks. (b) Schematic illustration of intelligent self-adaptive metadevices integrated with perception-decision-execution.3 (c) Deep-learning-assisted self-adaptive microwave cloak. (d) Photograph of the intelligent invisible drone.154 (e) Simulation results of cloaked/bare drone. Panel (c) is adapted with permission from Ref. 3, Springer Nature Limited. Panels (d) and (e) are adapted with permission from Ref. 154.

    However, state-of-the-art methods and existing invisibility cloaks share a common limitation: they function only in a predefined EM illumination and a stationary background. Overcoming this limitation would usher in a new era of invisibility cloaks capable of adapting to dynamic, unpredictable environments in real-world applications.158 For the first time, Qian et al. proposed a self-adaptive microwave cloak based on a tunable metasurface and powered by deep learning. To achieve a self-adaptive intelligent cloak, three key components—perception, decision-making, and action—have been mimicked by an electromagnetic detector, a deep learning algorithm, and tunable metasurfaces, respectively [Fig. 4(b)]. Equipped with a trained artificial neural network (ANN), the metasurface cloak can rapidly respond, achieving millisecond-scale adaptability to the continually changing incident wave and surrounding background, all without human intervention [Fig. 4(c)].3 However, for real-world applications, an invisibility cloak must maintain invisibility across diverse terrains, such as grasslands, sand, and sea. Nevertheless, achieving this requires overcoming numerous challenges, from fundamental physical principles to advanced intelligent algorithms and integration into an all-in-one system. Each scenario, whether desert, sea, or air, presents unique scattering characteristics that can compromise the cloaking effect. To achieve this goal, a self-adaptive invisible drone has been proposed at microwave frequencies that is equipped with sensing, decision, and execution modules to maintain invisibility amid diverse backgrounds [Fig. 4(d)]. A stochastic-evolution learning has been introduced that can automatically align with the optimal solution through maximum probabilistic inference.154 For an obliquely incident wave, the bare drone produces strong scattering, whereas the cloaked drone absorbs [Fig. 4(e)]. Another challenge in the large-scale intelligent cloak is that the decision space expands exponentially with the increase in degrees of freedom. This makes dataset collection and algorithm modeling increasingly burdensome. Therefore, developing an efficient computational method for a 3D large-scale cloak is crucial. To overcome these challenges, Wang et al. proposed a 3D large-scale intelligent cloaked vehicle at microwave frequencies, based on hybrid inverse design and full-polarization tunable metasurfaces, capable of achieving real-time invisibility in ever-changing environments.159 The next generation of intelligent cloaks has advanced cloaking research toward more practical scenarios, including dynamic backgrounds, moving targets, and multi-terrain invisibility.

    3.2 Wireless Communication

    The sixth-generation (6G) of mobile communication aims to offer extensive broadband coverage, seamless sensing capabilities, and intelligent connectivity for various applications such as smart cities, autonomous driving, and smart factories. However, achieving ultra-massive connections in 6G poses challenges due to the need for significant spectrum and energy resources. Intelligent metasurfaces have revolutionized wireless transceiver design by significantly reducing hardware costs and boosting efficiency. In the communication community, the terms commonly used for intelligent metasurfaces are “reconfigurable intelligent surface” (RIS)13,14,160162 and “intelligent reflecting surface” (IRS),163165 with most operating at RF frequencies. A conceptual illustration of RIS-based wireless communication is presented in Fig. 5(a). RISs can reflect incident beams in off-specular directions, offering substantial improvement in received power, especially when the line of sight is obstructed by objects. Integrating RISs into existing wireless systems is considered a revolutionary approach to realizing a smart wireless environment.166 This aims to achieve various goals, including coverage extension,167 channel capacity optimization,168 energy efficiency,12 and physical layer security.169

    Intelligent-metasurface-based adaptive metadevices. (a) The concept of RIS-assisted wireless communication. (b) Schematic illustration of the metasurface-based dual-channel wireless communication system. (c) A metalens for augmented reality. (d) Schematic illustration of deep-learning-based metasurface holograms. (e) Neuro-metamaterials-based object recognition system. (f) Schematic illustration of the metasurface-based LiDAR system.

    Figure 5.Intelligent-metasurface-based adaptive metadevices. (a) The concept of RIS-assisted wireless communication. (b) Schematic illustration of the metasurface-based dual-channel wireless communication system. (c) A metalens for augmented reality. (d) Schematic illustration of deep-learning-based metasurface holograms. (e) Neuro-metamaterials-based object recognition system. (f) Schematic illustration of the metasurface-based LiDAR system.

    For direct wireless communication, the digital information sequence is encoded onto the time-space-coding intelligent metasurface at the physical layer, eliminating the necessity for digital-to-analog conversion and mixing processes.170,171 For instance, a wireless communication scheme based on space–time-coding metasurface has been proposed for dual-channel direct data transmissions. The transmitting and receiving processes of the dual-channel wireless communication system based on the metasurface are shown in Fig. 5(b). The concept of massive backscatter communication has been proposed, which relies on modulation of the propagation environment through a programmable metasurface.172 Moreover, a dual-band metasurface-based wireless communication system has been proposed to offer additional physical channels for information security.173

    With the rapid development of deep learning, many advances have been made in integrating deep learning with metasurfaces for wireless communication applications. For dynamic wireless channel management and autonomous adaptation to user requirements, the idea of homeostatic metasurfaces has been proposed.174 Neuro-metasurfaces reduce reliance on traditional RF components and eliminate the need for iterative computations and human intervention. Furthermore, an intelligent metasurface system has been proposed to perform both target tracking and wireless communications.15 In addition, the dual-polarized DPM, integrated with a pre-trained ANN, facilitates intelligent beam tracking and wireless communications.15 Reinforcement learning (RL) has been applied to drive programmable metasurfaces for on-site wireless link control.175 A proof-of-concept system demonstrated that RL-driven metasurfaces significantly enhance wireless link quality across various scenarios, regardless of transmitter and receiver positions.

    3.3 Smart Vision

    Optical metasurfaces—engineered surfaces with subwavelength-scale unit cells that exhibit tailored light–matter interactions—have emerged as a pivotal area of research in photonics. This field has advanced rapidly due to the unique capabilities of metasurfaces, including the unprecedented miniaturization of optical systems, the ability to manipulate light’s amplitude, phase, and polarization at subwavelength scales, and the potential for dynamic reconfigurability through external stimuli. Owing to their high integration and multifunctionality, optical metasurfaces have been effectively integrated with imaging technologies. The incorporation of deep learning in meta-optics enables smart vision across various applications, including metalens, VR/AR displays, 3D imaging, and holographic displays.176 Advancements in metasurface design, driven by sophisticated fabrication, have created ultrathin, lightweight, and flat metalenses.177,178 Characterized by a high numerical aperture and freedom from spherical aberrations, metalenses have successfully achieved diffraction-limited focusing with subwavelength resolution. Chromatic aberration caused by wavelength dispersion poses another challenge for metalenses. Researchers have used multilayer metalenses to address multiple figures of merit simultaneously. A deep neural network-based inverse design method has achieved broadband achromatic metalens.179

    Metasurfaces integrated with deep learning hold significant potential as crucial components in near-eye displays, capable of replacing traditional optics and introducing innovative functionalities. This paves the way for the advancement of next-generation AR and VR technologies. VR engenders entirely immersive virtual environments by delivering digital images to users, whereas AR enables viewers to engage with a mixed-reality realm by overlaying virtual information onto real-world scenes [Fig. 5(c)]. For example, a physics-driven deep-neural-network-based multicolor metasurface beam deflector has been proposed for near-eye displays.180 Moreover, a general inverse design framework has been proposed,181 facilitating the creation of large-scale, high-performance meta-optics for the future of virtual reality. Holographic displays, which utilize light diffraction to create three-dimensional images in space, allow real objects and holographic images to coexist seamlessly [Fig. 5(d)]. In a proof-of-concept experiment, a metasurface encoded phase masks for two images and projected them onto the desired focal plane using different angles of left circularly polarized light.182

    Polarization imaging is particularly effective in enhancing the clarity and detail of target objects, particularly in environments where conventional imaging falls short. Traditional polarization imaging systems rely on complex arrangements of optical elements such as prisms and waveplates and often suffer from low polarization contrast ratios. By contrast, the polarization-dependent metasurface nanoantennas offer a superior solution, providing significantly higher polarization contrast ratios and more efficient imaging performance. For instance, a deep-learning-based all-dielectric metasurface has been designed for colorimetric polarization-angle detection.183 Metasurface-driven spectral imaging technology is an emerging field in optical imaging that can achieve high-resolution and high-sensitivity spectral imaging in microimaging systems, paving the way for the development of compact spectrometers. A tunable metasurface-based real-time ultraspectral imaging chip has been demonstrated for imaging brain hemodynamics.184 Computational imaging is an innovative method that blends physics and algorithms to capture high-dimensional optical information about a scene. For instance, an optical encryption scheme has been introduced, incorporating metasurface images as keys in the encoding and decoding processes for single-pixel imaging (SPI) encryption.185

    3.4 Intelligent Detection and Sensing

    Advancements in object recognition have led to diverse applications including security and surveillance systems as well as devices that enhance accessibility for the visually impaired. The pervasive integration of intelligent systems into contemporary society relies on intelligent EM sensing technologies, which should swiftly perceive and identify objects and gestures. Metasurfaces, with their exceptional ability to manipulate electromagnetic waves at subwavelength scales, have emerged as a transformative platform for intelligent sensing across microwave, terahertz, and optical frequencies. In the microwave regime, metasurfaces integrated with deep learning and neural networks have enabled dynamic object recognition, efficient scene information acquisition, and real-time human activity monitoring, significantly reduced computational latency, and enhanced sensing capabilities. For a dynamic object-recognition system, a neuro-metamaterial has been proposed [Fig. 5(e)],186 which can identify the objects without human intervention. Furthermore, a tunable metasurface transceiver, trained as the physical layer in an ANN, has been demonstrated to improve the efficient acquisition of task-relevant scene information.187 A diffractive neural network has been proposed using a multilayer passive metasurface array, which is capable of estimating the information of arrival (IOA) across diverse frequency bands and incident angles.188 Moreover, a deep-learning-based intelligent metasurface has been proposed to obtain high-resolution full-scene images and recognize human body language and respiration in real-time.49 By integrating tunable metasurfaces with deep learning, intelligent EM sensing has been demonstrated with low latency and computational burden.189 Terahertz metamaterial biosensors combine terahertz time-domain spectroscopy with metamaterial sensing to provide a sensitive detection platform for a variety of targets, including biological molecules, proteins, and cells.190,191

    Light detection and ranging (LiDAR) technology192 is recognized as a pivotal sensor technology for autonomous vehicles and robots. At optical frequencies, a passive metasurface-based LiDAR system has been developed,193 offering a wide field of view and high framerate, thus enabling the simultaneous capture of peripheral and central imaging zones [Fig. 5(f)]. A metasurface-based scanning LiDAR has been proposed, which can overcome the limitations of 3D sensors with a wide field of view.194 Image processing relies on spatial, temporal, and spatiotemporal differentiation techniques for edge-based enhancement, crucial in fields such as microscopy and computer vision. Metasurfaces enable advanced optical differentiation, achieving broadband edge detection,195 phase-contrast imaging,196 and high-resolution 2D spatial differentiation, seamlessly integrating into imaging systems for efficient analog processing.197 Moreover, the application of deep learning has streamlined the design of epsilon-near-zero (ENZ) layers, improving optical differentiation and edge detection capabilities.198 Furthermore, a compact gas sensor platform has been developed, seamlessly integrating liquid crystals and holographic metasurfaces, autonomously detecting volatile gases, and delivering visual holographic alarms.199

    Beyond these developments, infrared metasurfaces have shown remarkable potential in biosensing. By leveraging multi-resonant designs, these metasurfaces can resolve molecule-specific information with exceptional precision, unlocking new possibilities for understanding complex biological systems.200 Furthermore, an infrared nanoplasmonic metasurface integrated with deep learning has been proposed for applications in biomolecular interactions research.201 These advancements underscore the versatility of metasurfaces in enabling intelligent, adaptive, and efficient sensing solutions across the electromagnetic spectrum.

    Although DL offers significant advantages in terms of design speed, scalability, and the ability to handle complex, multi-objective optimizations, the performance improvements in terms of device specifications (e.g., efficiency, resolution, sensitivity) are often incremental. The true value of DL lies in its ability to explore unconventional design spaces and achieve functionalities that are difficult or impossible with traditional methods. However, for many applications, the hype around DL may not always translate into groundbreaking improvements, and its use should be justified by the specific design challenges and computational trade-offs involved.

    4 Conclusions and Future Directions

    Over the past decade, research on intelligent metasurfaces has widely extended from efficient metasurface design, system optimization, and automation control to more sophisticated intelligent metadevices that can adapt autonomously to changing EM conditions and user demands. In particular, deep-learning-based on-demand metasurface design can tackle the challenges inherent in traditional full-wave numerical simulations and physics-based methods, such as time-consuming processes, low efficiency, and reliance on experiential approaches. We have highlighted recent advancements in intelligent metasurface design and explored potential applications, including intelligent invisibility cloaks, smart vision, intelligent sensing, and wireless communication. A deep-learning-enabled microwave cloak can autonomously adapt to ever-changing incident waves and the surrounding environment. With the addition of deep learning in meta-optics, smart vision has become possible in various applications such as VR/AR displays, wearable sensors, remote sensing, Internet of Things (IoT), and vision for autonomous cars, enabled by LiDAR devices for 3D imaging and point-cloud illumination, as well as holographic display. Various approaches are emerging to bring the vision of smart radio environments to life. Among these, the utilization of RISs stands out as a promising solution to meet the demanding requirements of future wireless networks. Nevertheless, several open challenges persist in tunable metasurface design and applications. For tunable metasurface research, tunability at the meta-atom scale is desirable for many applications; therefore, more efficient designs for tunable metasurfaces are required. Furthermore, more accurate modeling is required to account for meta-atom coupling,202 especially in the absence of periodic boundary conditions. Meta-optics-based optical neural network computing holds the potential to overcome the constraints of computational power and speed. The collaboration between deep learning and meta-optics is poised to propel the research and development of advanced optical chips, fostering the integration of the next generation of optical systems and devices.

    In the tide of deep learning development, the limit of inverse design is pushed by this data-driven relationship, highlighting excellent fitting and generalization abilities. However, when returning to real EM inverse design fields, despite some deep learning algorithms reducing time and resource costs through increasingly sophisticated computer technologies, researchers cannot overlook the confusion and waste caused by non-uniqueness and uncertainty questions. The methods mentioned above in Sec. 2.2 can only select the best solution from all generated probabilities but cannot provide a convincing physical explanation that proves the chosen output to be accurate. Furthermore, there is difficulty in reusing the dataset and network for different metamaterials and applications, as well as in generating a new specialized model from a common and well-trained one. In practice, rather than a well-thought-out design in the lab, the unsatisfactory nature of fast training and self-adaptation demands leaves ample room for improvement in the high-speed, realistic implementation of smart cities and world explorations.

    This decade is poised for the rapid development of intelligent metamaterials, with researchers paving the way for real-time, adaptive, and extensible paths to multifunctional and cutting-edge meta-device designs. First, researchers urge to solve the knowledge reuse requirements and build a bridge between simple lab-scene experiments and complex reality applications. Then, leveraging the substantial computational capabilities of deep learning, which considers unpredictable nonlocal couplings and multiple scatterings, metasurfaces can be designed with increased parametric freedom and tunable properties, enabling broader applicability. Consequently, solutions for cloaking, sensing, communication, and other fields, offering wide-bandwidth, large-angle, and full-polarization capabilities for variable scenes, become readily accessible. Moreover, increased physical involvement enhances the reliability and interpretability of network outputs, leading to accurate solutions for inverse design. By utilizing the intricate autocorrelation between responses of the same device in different incident conditions, such as lower or higher frequency bandwidths, as an additional constraint in network model optimization, future research can break free from the data-driven limit of the black box effect. With these advancements, the potential applications of deep-learning-based metadevices expand in more complex research fields, allowing for arbitrarily customized manipulation of EM waves in the real world and intricate structural designs for plasmonic and quantum realms.

    Yasir Saifullah is a postdoctoral fellow at Jinhua Institute of Zhejiang University. He received his PhD from Fudan University and was a postdoctoral fellow at Shenzhen University from 2021 to 2023. His research interests include intelligent metasurfaces, metadevices, and their applications. He is a member of IEEE and Optica.

    Chao Qian is an assistant professor at the Zhejiang University–University of Illinois at Urbana-Champaign Institute. He received his PhD from Zhejiang University and was a visiting PhD student at Caltech from 2019 to 2020. His research focuses on metamaterials/metasurfaces, electromagnetic scattering, inverse design, and deep learning. He has published more than 70 papers in high-profile journals, including Nature Photonics, Nature Communications, Science Advances, Physical Review Letters, etc. He serves as associate editor for Progress in Electromagnetic Research (PIER).

    Hongsheng Chen is a professor and dean of the College of Information Science and Electronic Engineering, Zhejiang University. He received his BSc and PhD degrees from Zhejiang University, and was a visiting professor at MIT’s Research Laboratory of Electronics from 2013 to 2014. In 2014, he was honored with the distinguished Cheung-Kong Scholar award. His research focuses on metamaterials, invisibility cloaking, transformation optics, and topological electromagnetics. He is topical editor for Journal of Optics, Deputy Editor-in-Chief of Progress in Electromagnetics Research, and serves on the editorial boards of Scientific Reports, Electromagnetic Science, and Nanomaterials. He is an IEEE fellow.

    Biographies of the other authors are not available.

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    Yasir Saifullah, Nanxuan Wu, Huaping Wang, Bin Zheng, Chao Qian, Hongsheng Chen, "Deep learning in metasurfaces: from automated design to adaptive metadevices," Adv. Photon. 7, 034005 (2025)
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