Deep Inverse Design of Reconfigurable Metasurfaces for Future Communications
11 Deep Inverse Design of ReconfigurableMetasurfaces for Future Communications
John A. Hodge, Kumar Vijay Mishra and Amir I. Zaghloul
Abstract —Reconfigurable intelligent surfaces (RIS) have re-cently received significant attention as building blocks for smartradio environments and adaptable wireless channels. By alteringthe space- and time-varying electromagnetic (EM) properties, theRIS transforms the inherently stochastic nature of the wirelessenvironment into a programmable propagation channel. Conven-tionally, designing RIS to yield a desired EM response requirestrial-and-error by iteratively investigating a large possibility ofvarious geometries and materials through thousands of full-waveEM simulations. In this context, deep learning (DL) techniquesare proving critical in reducing the computational cost and timeof RIS inverse design. Instead of explicitly solving Maxwell’sequations, DL models learn physics-based relationships throughsupervised training data. Further, generative adversarial net-works are shown to synthesize novel RIS designs not previouslyseen in literature. This article provides a synopsis of DL tech-niques for inverse RIS design and optimization to yield targetedEM response necessary for future wireless networks.
Index Terms —Deep learning, beamforming, metasurfaces, re-configurable intelligent surfaces, smart radio environment.
I. I
NTRODUCTION
The emerging industrial use-cases of sixth-generation (6G)and beyond wireless networks are envisaged to include indus-trial automation, autonomous vehicles, and smart infrastruc-ture. These applications require significant improvements indata capacity, system latency, and quality-of-service reliabilityover the current 5G networks. In this context, reconfigurableintelligent surface (RIS) has been identified as a key enablingtechnology to program the smart radio environment (SRE),increase link quality, and reduce the hardware complexity [1].The RIS is made up of a metasurface (MTS) - a two-dimensional (2-D) reconfigurable electromagnetic (EM) layercomposed of a large periodic array of subwavelength scatteringelements (meta-atoms) with specially designed spatial features.Compared to electrically large arrays, the nearly passive meta-atoms offer lower cost and power consumption. The radio-frequency (RF) MTS performs customized transformations,such as beamforming, on a reflected incident wave throughmodified surface boundary conditions using Huygens’ prin-ciple. The arrangement and subwavelength structure of each
J. A. H. and A. I. Z. are with Bradley Department of Electrical andComputer Engineering, Virginia Tech, Blacksburg, VA 24061 USA. Email: { jah70, amirz } @vt.edu.K. V. M. and A. I. Z. are with United States CCDC Army Research Lab-oratory, Adelphi, MD 20783 USA. E-mail: [email protected],[email protected]. A. H. acknowledges support from Northrop Grumman Mission Systems(NGMS), Baltimore, MD, for his thesis research. K. V. M. acknowledgessupport from the National Academies of Sciences, Engineering, and Medicinevia Army Research Laboratory Harry Diamond Distinguished PostdoctoralFellowship. meta-atom and, in turn, the array of space- and time-varyingmeta-atoms determine MTS aperture field distribution andcontrol the direction and strength of reflected signal [2].In a wireless link, the RIS functions as either an electricallylarge antenna array at the endpoints or as an amplify-and-forward relay (Fig. 1). By actively controlling and optimizingthe amplitude/phase of each meta-atom across the aperture, theRIS maximizes the receive signal-to-noise ratio and providesadaptive beamforming to coherently focus the reflected signalon the receiver. Each scattering element typically includesan active tuning element, such as a varactor or PIN diode,whose bias voltage is software-controlled to change the EMresponse of the surface. The bias voltage for each meta-atom is pre-computed and modulated by a digital controlmodule employing a field programmable gate array (FPGA)[1]. Each meta-atom is controlled by tuning its EM proper-ties (susceptibility or impedance) which affects the spectralresponse of the reflected signal. This aids in producing tailoredradiation patterns for diverse functions, such as beam steering,anomalous reflection, focusing, beam splitting, absorption, anddirect modulation of the reflected signal.However, the design and optimization of RIS hardware atthe physical layer remains a formidable challenge. In general,canonical structures such as v-antennas, loaded-dipoles, split-ring resonators, are used to fabricate RIS. However, meta-atoms based on these geometries usually fall short of desiredperformance, particularly when anisotropic, broadband, and/orwide-angle responses are required. Designing a user-defined,arbitrary wave-front RIS or metagrating is a challenging,labor-intensive, and long process. IN general, a new MTSdesign entails numerous rounds of manual tuning and full-wave simulations that iteratively solve Maxwell’s equationsuntil a locally optimized design is achieved [3]. Initial de-signs are typically based on physical instincts and intuitivearguments. However, the final geometric structure and materialcharacteristics are attained through iterative analyses.Recently, machine/deep learning (ML/DL) techniques haveshown unprecedented performance in problems where it isdifficult to develop an accurate mathematical model for featurerepresentation. These methods are now also transforming theabove-mentioned tedious approaches to design RIS and EMdevices. Note that this is different than using DL to performsignal processing function in RIS-aided communications (see,e.g., [4] for a survey). This paper provides an overviewof recent developments in using ML/DL for designing thephysical layer of RIS. a r X i v : . [ phy s i c s . a pp - ph ] J a n Fig. 1. The RIS architecture (center) operating at carrier frequency f c for wireless communication networks comprises meta-atoms located at below carrierwavelength ( λ ) spacing. It acts as both an endpoint transceiver and a relay. The RIS enables various beamforming functions (left column) including beamsteering, splitting, and adaptive beamforming for customized radiation patterns by manipulating the phase coding of constituent meta-atoms. It is also capableof directly modulating (right column) the surface in frequency, phase, and polarization. II. I
NVERSE
RIS D
ESIGN
Communications-based analysis of RIS without physics-based EM-compliant models is a major limitation of currentresearch. Until recently, prior works did not consider suchrealistic RIS implementations. As the parameter spaces ofmeta-atom geometry and constituent materials has grown, theconventional approaches to achieve the targeted EM responsehave become more tedious. In this context, deep learningmodels have demonstrated the ability to implicitly learnMaxwell’s equations from training data within a constraineddesign space. The ML techniques have witnessed increased usein research to create surrogate models for MTS performanceprediction, inverse design, and optimization. For an inverseMTS design problem, the input is an arbitrary design spectrumand the network finds or synthesizes a geometry to closelyapproximate the desired spectral response (Fig. 2).Major benefits of DL-based RIS design for wireless com-munications include: • EM-based surrogate models : DL constructs a nonlinearmapping between the raw input data (meta-atom design)and the desired output to approximate the MTS response. • Inverse design : Deep generative models are utilized tolearn geometric features from training data and generatenew meta-atom designs to achieve the spectral response. • Diverse EM surface representations : DL-based MTSdesign admits flexible design representation. The inputcould be either vectors of discrete parameters describingthe geometry, material, frequency, and angular designparameters or pixelated images to represent the geometryor phases of the meta-atom design. Whereas a fully-connected neural network is well-suited to process thesimple designs specified by the former representation, aconvolutional networks handle images appropriately toyield more complex MTS geometries.Table I summarizes prior works on various techniques forRIS inverse design. The non-DL methods typically compriseof several evolutionary optimization algorithms as listed below.
Fig. 2. In inverse RIS design, ML algorithms learn and generalize complexEM relationships between the physical RIS structure (left column) and spectralresponse (right column) through training data.
1) Genetic algorithm (GA):
This is an iterative globaloptimization (GO) algorithm that has been used extensively inthe design of pixelated coded MTS designs. GA is a nature-inspired algorithm that uses binary strings (chromosomes) torepresent candidate designs [5]. During the optimization, theGA selects the best subset of design candidates from theprevious generation to serve as starting points for mutationand crossover in the next design iteration. Recent GA appli-cations include coding MTS [5] which demonstrates channelresponse modification, efficient polarization conversion, andphase-graded beam steering.
2) Particle swarm optimization (PSO):
A popular stochas-tic evolutionary computation technique, PSO is inspired bythe movement and intelligence of swarms. Recently, it hasbeen employed for shaping EM waves using pixelized codedmetasurfaces [5]. The design procedure using PSO is tiedto a full-wave EM solver and completely automatic. Thesoftware yields both microscopic meta-atom designs and themacroscopic aperture coding matrix. By changing the reflec-tion phase difference between cells, this approach has pro-duced designs of functional metasurfaces with circularly- andelliptically-shaped radiation beams and multi-beam patterns.
TABLE IS
TATE - OF - THE - ART ON
RIS
INVERSE DESIGN
Algorithm Frequency MTSlayers Data Key features DrawbacksEvolutionary optimization techniques
GA [5] - GHz ParameterVector Pixelized meta-atoms with discrete input designspace when a contiguous structure is not required Optimization from scratch for eachdesign; output structures may be toocomplex to fabricatePSO [5] . - GHz BinaryMatrix(2-D) Swarm-based GO technique for pixelized meta-atom design; outperforms GA for various EMdesigns Optimization from scratch for eachdesign with parameter tuningACO [5] - . GHz BinaryMatrix(3-D) MTS, including 3-D structures and wire grid ar-rays, with discrete design space and a contiguousstructure Optimization from scratch for eachdesign; output structures may be toocomplex to fabricate
Learning methods
ANN [6] - THz ParameterVector Performance prediction, inverse design, and opti-mization of nanophotonic particles Limited design variables; applicableto only spherical dielectric nanopar-ticlesANN [7]
THz ParameterVector Performance prediction and inverse design ofmetagratings Limited set of parametric inputs; sig-nificant training overloadDNN [8] - THz ParameterVector Inverse design of chiral and multi-layer MTS Design-specific architecture; limiteddesign spaceCNN [9] GHz BinaryMatrix(2-D) Anisotropic digital coding MTS; PSO for beam-forming Significant training overloadCNN [10] . GHz BinaryMatrix(2-D) Hybrid CNN-GA for space-time modulation ofprogrammable MTS; multi-beam steering Binary phase coding limits beam-forming performance; limited tun-abilitycDC-GAN [3] - THz ImageMatrix(2-D) Generative inverse design of transmission MTS Significant training overload; limitedto single layer designs and passivestructurescDC-GAN [11] - GHz Image(2-D) Reflective RF MTS; training set with publishedmeta-atom structures to improve learning Limited to single layer; post-processing requiredcDC-GAN [2] - GHz Image(3-D) Multi-layer MTS; RGB-style matrix to representmultiple layers No active elements; additional vali-dation requiredcDC-GAN [12] - GHz Image(3-D) Federated learning for multi-layer design Significant training overloadcDC-VAE [13] - THz 1 Image(2-D) Anisotropic MTS; encodes input into low-dimensional latent space Significant training overload; post-processing requiredTO-GAN [14] - THz 1 Image(2-D) Free-form diffractive metagrating design for se-lect wavelength-deflection angle pairs with topol-ogy refinement Additional optimization requiredGLOnet [15] - THz 1 Image(2-D) Dielectric MTS design without training sets Limited to single objective optimiza-tion; requires solving Maxwell’sequations inside training loop
Similar efforts have used a simulated annealing algorithm forthe design and optimization of a broadband diffusion MTSusing anisotropic elements for scattering reduction. In [9],binary PSO (BPSO) was used to automate the macroscropiclayout of both passive and active aperture to realize user-defined dual-beam scattering radiation patterns.
3) Ant colony optimization (ACO):
This is another swarm-based algorithm inspired by stigmergy in ant colonies in orderto search for optimal solutions to graph-based problems [5].Here, a number of artificial ants build solutions to an opti-mization problem and exchange information on their qualityusing a cooperation scheme similar to that utilized by realants. In [5], inverse MTS design is performed based on multi-objective lazy ACO (MOLACO) to synthesize 3-D nano-antenna geometries with low-loss transmission performanceand broad phase tunability. The ACO is generally most usefulfor a discrete input design space and when a contiguousstructure is required. III. DL-B
ASED I NVERSE D ESIGN AND O PTIMIZATION
The computational power and time required for evolutionaryoptimization algorithms grow exponentially with the numberof design parameters. This is mitigated by DL-based inversedesign for RIS. Prior works have employed a variety ofnetwork structures and algorithms based on the availabilityof data, RIS topology, and desired EM spectral response.
A. Artificial Neural Network (ANN)
The ANNs were first used to approximate light scattering bymulti-layer nanoparticles (meta-atoms) [6]. Similar to MTS,nanophotonic particles derive their frequency response fromphysical structure and the size constituent scatterers. Then,[7] used a similar technique for metagratings. The primaryapplication of ANNs in MTS design is performance approxi-mation. The feedforward ANN is trained to be a high-fidelitysurrogate model for performance prediction. Using trainingdata consisting of meta-atom physical design parameters asinputs and frequency response as labels, the ANN is trained to approximate a complex physics simulation (such as finite-element method (FEM), method of moment (MoM), or finite-difference time-domain (FDTD) simulation). Through thetraining data, the ANN learns to map the scattering function ofthe meta-atom into a continuous, higher-order space where thederivative is found analytically through propagation. In [6], atrained ANN simulated spectral responses orders of magnitudefaster than conventional full-wave simulations. The resultssuggest that the ANN was not simply fitting the data, butrather discovered the underlying structure of input-to-outputmapping to generalize the physics of the systems with thetraining set and solve problems not yet encountered.A significant drawback of this approach is that the inputs arelimited to the thicknesses of the meta-atom layers with fixedmaterials. This results in a lack of generalizability for the ANNthat vastly limits the possible meta-atom design structures.While fixing the input parameters reduces the complexity ofthe ANN architecture, it limits the design space and optimaldesigns. Another drawback of this approach is that [6] required , examples using conventional simulation methods togenerate training data. However, unlike evolutionary optimiza-tion methods such as GA or PSO, simulation of the trainingdataset is an upfront fixed cost because it only needs tobe simulated once and is then leveraged for other designs.Additionally, the simulations for training data generation arehighly parallelized unlike serial optimization techniques.Once trained, [6] shows that the ANN solves inverse designproblems more quickly than than its numerical counterpartsbecause the gradient is found analytically, through back prop-agation, rather than numerically. Similar to inverse design,the ANN also optimizes for a desired property by alteringthe cost function used for the design without training theANN. Their results that the ANN performs inverse designand optimization more accurately than traditional numericalnonlinear optimization techniques. B. Deep Neural Networks (DNN)
To model more complex meta-atom structures and increaseperformance prediction accuracy, DL has been applied to theon-demand design of chiral (a form of anisotropy) MTS [8].Here, DNN - an ANN comprised of many hidden layers tosignificantly expand learning and generalization ability - wasemployed to automatically design and optimize 3-D chiralMTS with strong anisotropic spectra at predetermined wave-lengths. The network comprised two bidirectional networksthat were constructed using partial stacking technique. Thisstudy limited the input design space (and hence the structuresobtained) and predicted the reflection spectral response at discrete frequency points for two orthogonal polarizationand the cross-polarization coupling term resulting in a -by- spectral output vector. Full-wave simulation was usedto generate the training data set for , example meta-atoms. The DNN achieved high efficiency and high-accuracyfor performance prediction and inverse design for anisotropicMTS, where the meta-atom design space is limited. C. Convolutional Neural Networks (CNN)
To improve on the lack of generalization and increaseperformance prediction accuracy, CNNs are used to designanisotropic digital coding metasurfaces. CNNs are a classof ANNs that use convolution functions to learn hierarchicalpatterns within data. These models learn generalized patternsacross many spatial scales from their input data and are widelyused on image data. In [9], a CNN predicted the reflectionphase response of binary coded meta-atoms where each meta-atom contains -by- square sub-pixels and is mirroredwith two-fold symmetry. The results show an accuracy of . of phase responses with ◦ error in the ◦ phase.A drawback of this binary coding approach is that a -by- pixel meta-atom has potential design combinations.This study generated training data by simulating randomizedpixel matrices. However, it was fundamentally inefficient inan analogous manner to GA because the training data isessentially random and does not contain the knowledge ofcanonical structures in the training data set. A significantCNN advantage is that the meta-atom shape is directly inputinto the network rather than shape-specific design parameters.The convolutional filters allow the CNN to learn the physicalstructure that leads to given EM response, leading to a broaderapplicability of the model.In [10], the element phases of a reconfigurable MTS werecomputed by a 11-layer CNN for multiple beam steeringapplications. The input was the parameter vector representingthe target beam pattern and the output was a matrix that carriedthe 1-bit codes for a programmable -element MTS. Thistechnique to obtain the phase matrices reduced the time forproducing almost similar beam patterns using conventionalmethods to a few milliseconds. D. Deep Generative Models (DGMs)
Generative models are unsupervised or semi-supervisedlearning models that infer a function to describe hidden struc-ture from unlabeled data. Their functions include clustering,density estimation, feature learning, and dimension reduc-tion. Whereas discriminative networks capture the relationshipbetween meta-atom geometry and spectral response from atraining set, DGMs focus on learning the properties of meta-atom geometry distributions [3, 11, 14, 15]. Major classes ofDGMs (Fig. 3) applied to MTS inverse design are as follows.
1) Generative adversarial networks (GANs):
In a GANsystem, two ANNs compete to improve each of their models:the generative network learns to create inputs indistinguishablefrom the training data while the discriminative network learnsto identify true data from the output of the generative network.GANs are promising for low-cost MTS design with complexfrequency and polarization dependent scattering responses. In[3], an input set of user-defined EM spectra is fed to GAN thatgenerates candidate patterns to match the on-demand spectrawith high fidelity. Here, DNNs are employed to approxi-mate the spectra of the MTS and perform inverse design bygenerating meta-atom structures that yield user-defined inputspectra. Once the model is trained, extensive parameter scansand trial-and-error procedures are bypassed. This conditional
Fig. 3. DGM architectures for RIS inverse design. The conventional GAN (left) lacks spectral information of the RIS structure x . The latent variable z is fedto the generator G to yield an estimated meta-atom structure ˆ x . The discriminator D then makes a decision if ˆ x is a valid design. The cGAN (second fromleft), conditioned by the reflection spectra R , shows improved performance. A simulator neural network may also be added to cGAN (center) to acceleratetraining and also predict the performance ˆ R of generated meta-atoms. The cMD-GAN (second from right) comprises of multiple discriminators, one for eachlayer. The cVAE (right) consists of an encoder-decoder network structure, where a feature extractor (FE) coupled with the recognition (Rec) network servesas the encoder to map the meta-atom structure to a lower-dimensional latent variable space. The generation model is a reconstruction (decoder) network. deep convolutional GAN (cDC-GAN) architecture uses threeinterconnected CNNs: generator, discriminator, and simulator.The simulator is a pretrained network that serves as a surrogatemodel for fast spectral performance prediction. The condi-tional generator networks accepts the desired spectral responseand a latent noise vector to output potential meta-atom designs.The discriminator serves to train the generator by evaluatingthe distance of the distributions between the geometric patternsfrom training data and generator. At the end of successfultraining, discriminator is unable to distinguish batches fromgenerator and training set. This approach is shown to exhibithigh accuracy in inverse design of meta-atoms.In [11], a deep convolutional GAN (DC-GAN) is employedto generate anisotropic RF meta-atom designs. Using a smallset of simulated spectra, the network learned the relationshipbetween the physical structure of meta-atoms and their reflec-tion spectra for vertical and horizontal polarizations. The DC-GANs generated meta-atom structures that resembled designfeatures in the training data. To speed up training, the networkwas fed with parametric variations of twelve published meta-atom designs to a full-wave EM simulator. Starting out withparametric variations of canonical meta-atoms scatterers, thenetwork picked up more efficiently than it would have fromtraining with responses of randomized pixel data.The design approach in [2] introduced the cDC-GAN-based for jointly designing several layers of tensorial RIS. Itrepresented three RIS layers with a × × red-green-blue (RGB) image matrix. The co-polarization and cross-polarization transmission responses of the resulting meta-atomdesigns (Fig. 4) differed from EM simulators by less than adB. One of the most exciting features of cDC-GAN is itsability to discover new geometries not previously found inthe literature. This suggests that the model implicitly learnedthe physical relationships of Maxwell’s equations rather thansimply interpolating from past designs. Building on this tech-niques, the federated learning approach in [12] employed aconditional multi-discriminator distributed GAN (cMD-GAN) (see Fig. 3) for multi-layer RF MTS discovery (Fig. 5).
2) Conditional variational autoencoder (cVAE):
As analternative to GAN approaches, [13] presents a probabilisticDGM that solves both forward and inverse problems at thesame time. It is trained in an end-to-end manner and usesa deep convolution cVAE (cDC-VAE) architecture (Fig. 3)comprising an encoder-decoder network structure. The en-coder maps the meta-atom structure to a multivariate Gaussiandistribution in the latent space and the conditional decodernetwork inputs the reflection spectra and latent variable togenerate meta-atom designs (Fig. 3).In [13], the RIS inverse design is modeled in a proba-bilistic generative manner to investigate the complex struc-ture–performance relationship in an interpretable way andsolve the one-to-many mapping issue that is intractable indeterministic models. It developed a semi-supervised learningstrategy that allows the model to utilize unlabeled data inaddition to labeled data in an end-to-end training. The RIS de-sign and spectral response are encoded into a low-dimensionallatent space with a predefined prior distribution, from whichthe latent variables are sampled.
3) Global topology optimization networks (GLOnets):
Re-cently, GANs utilized to learn structural features of topology-optimized (TO) metagratings for inverse design [14, 15]. TOis a method of optimizing a material layout or an arrayof pixels to maximize system performance given a set ofconstraints and boundary conditions. Unlike other approaches,simulation overload for TO does not increase with the numberof RIS units. In [14], free-form diffractive metagratings weredesigned using TO-GAN. Here, DGMs were trained fromimages of periodic, TO metagratings to produce efficientscattering structures with the desired performance over a broadrange of frequencies and angles. The network employed , training examples for each angle. However, the performanceof the best structures was not robust and additional refinementwas needed to meet the desired performance. In [15], dielectricmetasurfaces optimization was performed using a physics-informed cGAN. Global optimization-based generative net- Fig. 4. Meta-atom structures generated using DC-GAN [2]. The first twelverows show the ability of the DC-GAN to regenerate canonical structures fromthe training data set. The last two rows show the ability of the DC-GAN togenerate new meta-atom geometries, exhibiting spatial features similar to thosein the training data set. works (GLOnets) are able to search the design space forthe global optimum design. Unlike other GAN approaches,GLOnets seek to fit a narrow-peaked function centered on theoptimal solution without a training set. The GLOnet generatesa distribution of meta-atoms to samples the global designspace and then shifts the distribution toward a more optimaldesign. Training requires computing forward and adjoint EMsimulations of output structures using backpropagation. In thiswork, GLOnets are shown to be successful and computation-ally efficient global TO for MTS and metagratings.IV. C
HALLENGES AND F UTURE R ESEARCH D IRECTIONS
The techniques for RIS inverse design are constantly evolv-ing. As mentioned below, reduction of design time and achiev-ing full EM-compliance remains a major challenge.
1) Hybrid physics-based models:
New approaches areneeded to increase the computational efficiency and reduce theamount of training required for DL-based RIS design. Hybridmodels, where training set is supplemented by physics-basedanalytical models, reduce the amount of required training data
Fig. 5. Two three-layer meta-atom designs (upper left) generated from cMD-GAN in [12]. The top (red), middle (green), and bottom (blue) layers aremetallic traces separated by dielectric spacers. The image matrices are post-processed to remove the background noise. The upper right shows desiredinput RF transmission response vectors (dashed lines) and the full-waveverification using the Ansys HFSS finite element method solver (solid lines)of generated design for - GHz when illuminated by a plane wave atnormal incidence. The blue and maroon lines represent the respective x and y co-polarized transmission responses. Similarly, the green and purple linesrepresent the cross-polarized responses for x and y polarized signals. Thebottom row shows a composite of each layer of generated meta-atoms for athree-layer RIS. and increase learning efficiency. Analytical RF circuit-basedmodels are available to predict the performance of severalcanonical meta-atom designs. To speed up the training datageneration, these analytical circuit-based models could be usedto supplement the training data set and reduce iterations oftime-consuming full-wave EM simulations. It may also befeasible to create innovative DL design and optimization ar-chitectures that utilize physics-based analytical models withinthe ANN architecture.
2) Other learning techniques:
Transfer learning (TL) is atechnique for expediting and improving the learning of a newtask by using a previously trained neural network weights andbias as the initialization for the new ANN. Since all ANNsfor meta-atom performance prediction and inverse design areimplicitly learning Maxwell’s equations, it is sensible that anetwork trained for one meta-atom design or frequency bandis scaled and transferred to a related design. Deep Q-networks(DQNs) have also been studied to increase the efficiency ofMTS holograms and automated multi-layer RIS design.
3) Improved data representation:
More complex input datastructures and representations are increasingly studied forDL-based RIS. While this article focused on discrete inputparameters and image data structures are RIS design represen-tations, graphical and sequential data structures have recentlybeen proposed as alternatives. The graphical model has beenused to represent EM systems with near-field coupling (as incoupled resonators). In this arrangement, graph nodes containresonator attributes, such as material, geometry, and location,and graph nodes represent the near-field coupling factors.These graphical data structures are processed using graphicalneural networks (GNNs). Similarly, sequential data structuresare useful for representing time-sequence data in dynamic EMsystems (as in RIS filters) and are learned using recurrentneural networks (RNNs).V. S
UMMARY
We surveyed DL-based techniques for designing RIS hard-ware to be deployed for future wireless communications.When the design space and scale of the RIS arrays in-creases, learning-based architectures outperform evolutionaryoptimization techniques for both surrogate performance mod-eling and inverse design. The DL inverse design is flexible inadmitting a variety of RIS unit structures. The DGMs are themost useful because of their ability to generate new designsnot previously seen in the published literature. While activeresearch and techniques in this area are still evolving, DL isa promising solution for the inverse design of RIS.R
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John A. Hodge (S’12-M’14) obtained M.S. in electrical engineering fromVirginia Tech and a dual undergraduate degree in electrical & computerengineering and physics from Duke University. Currently, John is a Ph.D.candidate in electrical engineering at Virginia Tech, under the guidance ofDr. Amir Zaghloul. From 2012 to 2014, he studied electromagnetics andantennas as a graduate research assistant at the U.S. Army Research Lab(ARL) in Adelphi, MD. John’s Ph.D. dissertation focuses on reconfigurablemetasurface antennas for communications and radar applications. He is therecipient of several student paper awards. John is also a senior principal RFdesign engineer at Northrop Grumman in Baltimore, Maryland, where he isinvolved in the design of wideband phased arrays.
Kumar Vijay Mishra (S’08-M’15-SM’18) obtained a Ph.D. in electrical engi-neering and M.S. in mathematics from The University of Iowa in 2015, M.S.in electrical engineering from Colorado State University in 2012, B. Tech. summa cum laude (Gold Medal, Honors) in electronics and communicationengineering from the National Institute of Technology, Hamirpur, India in2003. He is currently U. S. National Academies Harry Diamond DistinguishedFellow at the United States Army Research Laboratory; Technical Adviserto Hertzwell, Singapore; and honorary Research Fellow at SnT, University ofLuxembourg. He is the recipient of several fellowships and best paper awards.He has been an Associate Editor (Radar Systems) of IEEE Transactions onAerospace and Electronic Systems since 2020.