Applications of Deep Learning in Electromagnetics: Teaching Maxwell's equations to machines
2: Department of Civil, Environmental, and Mechanical Engineering (DICAM), University of Trento, Italy
Deep learning has started to be applied to solving many electromagnetic problems, including the development of fast modelling solvers, accurate imaging algorithms, efficient design tools for antennas, as well as tools for wireless links/channels characterization. The contents of this book represent pioneer applications of deep learning techniques to electromagnetic engineering, where physical principles described by the Maxwell's equations dominate. With the development of deep learning techniques, improvement in learning capacity and generalization ability may allow machines to "learn" from properly collected data and "master" the physical laws in certain controlled boundary conditions. In the long run, a hybridization of fundamental physical principles with knowledge from training data could unleash numerous possibilities in electromagnetic theory and engineering that used to be impossible due to the limit of data information and ability of computation.
Electromagnetic applications of deep learning covered in the book include electromagnetic forward modeling, freespace inverse scattering, nondestructive testing and evaluation, subsurface imaging, biomedical imaging, direction of arrival estimation, remote sensing, digital satellite communications, imaging and gesture recognition, metamaterials and metasurfaces design, as well as microwave circuit modeling.
Applications of Deep Learning in Electromagnetics contains valuable information for researchers looking for new tools to solve Maxwell's equations, students of electromagnetic theory, and researchers in the field of deep learning with an interest in novel applications.
 Book DOI: 10.1049/SBEW563E
 Chapter DOI: 10.1049/SBEW563E
 ISBN: 9781839535895
 eISBN: 9781839535901
 Page count: 480
 Format: PDF

Front Matter
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1 An introduction to deep learning for electromagnetics
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This chapter provided a gentle introduction to DL, recalling the most used terms in this field as well as describing some of the most widespread architectures in the recent literature and their applications in EM.

2 Deep learning techniques for electromagnetic forward modeling
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In this chapter, we introduce the approaches of applying deep learning techniques to electromagnetic forward modeling. These approaches are divided into three types: fully datadriven forward modeling, deep learningassisted forward modeling, and physics inspired forward modeling. In fully datadriven forward modeling, the deep neural networks demonstrate powerful learning capacity and approximating ability to learn and abstract the inner physical laws from the massive training data. In deep learningassisted forward modeling, the learning tasks of the deep neural networks are simplified and made explicit based on the physical or mathematical models. Thus, the performance of the deep neural networks is further improved and the forward modeling assisted by deep learning boasts better computational efficiency and precision. The physicsinspired forward modeling focuses on the inner reasoning of the deep neural networks to enable effective deep learning models for electromagnetics. The design and training of the deep neural networks are guided, motivated, or inspired by the mathematical or physical models for better robustness and interpretability.

3 Deep learning techniques for freespace inverse scattering
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This chapter surveyed applications of deep learning techniques to freespace inverse scattering. We have divided some of the most popular deep learning approaches to inverse scattering problems into three broad categories: blackbox type of solutions, learningbased approaches to augment otherwise (traditional) iterative inverse scattering algorithms, and nonblackbox, noniterative learning approaches. This classification is not very sharp and has been used here simply to facilitate the presentation. Given the chapter length limitations and since the application of deep learning techniques for freespace inverse scattering is a quickly evolving area of research, this survey has been necessarily nonexhaustive. With the steady progress in computational hardware capabilities for processing of large amounts of data, it is expected that much progress will be made on this topic in the coming years to exploit the increasing availability of large training data sets. In addition, the use of very large numbers of hidden layers and unconventional neural network architecture is poised to open new research vistas and capabilities.

4 Deep learning techniques for nondestructive testing and evaluation
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In this chapter, we analyzed some applications of deep learning methods to electromagnetic NDT&E and tried to show how deep neural networks can be adapted to different scenarios involving electromagnetic probing waves ranging from the quasistatic regime to microwave. In particular, CNN have been deeply exploited when the treated signals behave "as images" such as in the case of ECT and MFL inspections where real and imaginary parts of the impedance variation as well as the magnetic flux density are probed. Furthermore, time domain signals as in PECT or GPR measurements have been addressed, too, by employing LSTMRNN and/or through CNN explicitly adapted for the purpose (e.g., pixelwise inversion). Our analysis underlined that specifically tailored deep neural architectures have obtained a better prediction performances than pretrained networks based on stateoftheart architectures. In fact, the systematic lack of large shared datasets containing labeled measurements of realistic acquisitions makes it difficult to properly benchmark and improve such backbone architectures. Moreover, the difficulties in collecting labeled measurements for defect parameters (e.g., the defect geometry) downsize the practical applications of deep learning models mostly to classification problems.
The survey performed in this chapter has also highlighted that the application of deep learning in NDT&E is also going toward the acceleration of numerical forward solvers for NDT&E modeling and simulations in a fully modeldriven approach. It is believed that the ability of DL methods to handle problems having large cardinality (e.g., NDT&E parameters such as large number of defect classes, and defect geometry description) will boost the research and its application to time consuming statistical studies (see, e.g., [160,161]). Moreover, our analysis showed that the use of numerical solvers proves useful in designing the most suitable DL schemas as well as in improving the prediction accuracy when a low amount of measurements is available. Finally, a large amount of works in the literature showed that exploitation of deep learning algorithms directly on embedded systems (e.g., FPGA hardware) is already possible without an appreciable degradation in prediction performance.

5 Deep learning techniques for subsurface imaging
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Geophysical subsurface imaging is an effective tool for understanding the Earth's internal structures. It is widely used in ecological and hydrological applications, oil and gas industry, etc. The exploration is usually done with remote sensing tools. Sensors record the secondary field induced by distant targets. One needs to see through countless rocks with various properties to distinguish the buried targets. Many obstacles exist in data collection. For example, the sources and receivers may be insufficient to illuminate the region of interest. The energy of the scattered field may attenuate to be undetectable, and the measuring environment can be very noisy.
Due to the imperfect measurement, subsurface data inversion has strong nonuniqueness, i.e., multiple models may fit the same field data. To obtain a geologically reasonable model, one needs to constrain the inversion with prior knowledge. Additionally, multiphysics measurements such as gravity, seismic, and electromagnetic (EM) data can be jointly used for comprehensively understanding the domain of investigation. The largevolume data, largescale survey domain, as well as the complex numerical modeling process, make geophysical inversion computationally expensive. It is also common to repeat multiphysics inversion many times to obtain a reliable geological model, which aggravates the computational burden.
The past few years have witnessed a popularity of deep learning (DL) techniques thanks to the development of modern computing hardware, big data storage and efficient computing methods. Geophysical inversion can benefit from this progress. The advanced computing power permits fast and highquality imaging with largevolume datasets. Besides, experience of interpretation can be trained into a DL model, which enables the fusion of prior knowledge and inversion seamlessly.
This chapter aims to overview the frontiers of DL as applied to subsurface imaging. The detailed implementations will not be introduced; instead, we hope to provide readers with a broad view of DL as applied to geophysical inversion. We mainly focus on EM methods, the depth of investigation ranging from hundreds to thousands of meters. After briefly reviewing the history of learningbased inversion, we show stateoftheart techniques in applying DL in EM inversion, including purely datadriven approaches, physicsembedded datadriven approaches and learningassisted physicsdriven approaches. We also present several DLbased methods for seismic data inversion that may benefit the EM community. We further discuss different approaches of constructing training datasets. At last, we conclude the state of DL in EM subsurface imaging and show outlooks.

6 Deep learning techniques for biomedical imaging
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In this chapter, we have discussed the physics of the common medical imaging techniques that are applied in the electromagnetic spectrum: electrical impedance tomography (EIT), magnetic resonance imaging (MRI), microwave imaging (MWI), and computed tomography (CT) scan. The EIT and MWI imaging techniques based on the electromagnetic theory and Maxwell's equations are specifically investigated with detail physics and imaging algorithms (BIM and DBIM) flowcharts. Then we explained the basic theories and structures of the machine learning and deep learning methods, and discussed their applications in medical imaging within the last decade. Particularly, we discussed the most recent deep learning network applications in medical imaging diagnosis, segmentation, and reconstruction. Furthermore, more advanced applications that combine the electromagnetic physicsbased imaging methods with deep learning networks for imaging improvements are discussed in details through four recent EIT and MWI imaging studies published.

7 Deep learning techniques for direction of arrival estimation
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This chapter presents an overview of how deep learning (DL) techniques can be exploited to solve the problem of directionofarrival (DOA) estimation, and also provides a solution to this problem using a feasible and efficient hierarchical deep neural network (DNN). The chapter begins with a general introduction to existing DOA estimation and DL techniques in Section 1.1, then formulates the DOA estimation problem mathematically under different conditions in Section 1.2, and summarizes the most common DL frameworks that have been applied to DOA estimation in Section 1.3, including mainly their neural network configurations and the most widely used strategies for algorithm implementation. Section 1.4 presents a hierarchical DNN framework to solve the DOA estimation problem, and carries out simulations to demonstrate its predominance in generalization over previous machine learning (ML)based methods, and in arrayimperfection adaptation over conventional parametric methods. Finally, this chapter ends in Section 1.5 by providing some clues on several future research trends of this area.

8 Deep learning techniques for remote sensing
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Due to the wide swath and acceptable cost, remote sensing (RS) techniques have been widely applied in extensive applications, such as land cover land use (LCLU), flood detection, urbanization monitoring. A number of airborne and spaceborne missions are conducted to acquire remote sensing data  ALOS, TerraSARX, Sentinel1, Sentinel2, GEDI, UAVSAR, Landsat, to name a few. They carried different types of sensors that differ from each other in terms of resolution, penetration ability, and imaging mechanism, thus are suitable for different applications scenarios. Accordingly, it calls for specifically designed models for different types of data.
With the accumulation of years of the vast amount of data, how to effectively use them especially in an automatic manner to serve for practical applications becomes a challenge. Deep learning (DL), which has achieved great success in other tasks in the computer vision field, is employed as a powerful tool for dealing with remote sensing data [16]. Previous studies reviewed the basic deep learning models and their applications in remote sensing data regarding either the data types [2,4] or the task types [1,3,5,6]. They mainly align the remote sensing tasks with the computer vision tasks. In this chapter, however, we revisit several hot topics that come from the fields of target recognition, land cover and land use (LCLU), weather forecasting, and forest monitoring, introduce how various deep learning models are employed and fitted into these specific tasks.

9 Deep learning techniques for digital satellite communications
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Satellite communication (SatCom) has been in rapid evolution during the last decades. The rapid growth of space industry is making satellite technologies available to more companies and private customers. However, despite the technology improvements, the capacity of SatCom systems is still subject to the limitations presented by physical communication channels. In fact, signals travelling from the earth surface to nearspace artificial satellites are strongly attenuated by long propagation distances, and deteriorated by atmospheric and extraterrestrial noise. At the same time, compensating for noise and attenuation is only possible at the cost of increasing the power consumption or reducing the data rate of the transmitting devices. Hence, SatCom systems need intelligent strategies for the allocation of power and bandwidth resources [1].
Thankfully, machine learning (ML) can be employed to automate resource allocation, as described in Section 9.2. In particular, deep learning (DL) techniques, which exploit artificial neural networks, are suitable to perform such complex tasks in sophisticated SatCom systems. For a proper resource allocation, the receiver in a communication system has to be informed about characteristics of the channel and the operating conditions of transmitting devices, such as propagation losses and operating point of highpower amplifiers. However, carrying such information reduces the serviceable capacity of the channel, as described in Section 9.2. Instead, a DL model can be employed to directly extract this information from the signal samples incoming at the SatCom receiver, thus preserving communication link capacity.
In particular, this chapter specifically focuses on the characterisation of noise and nonlinear distortion in digital satellite communication links, which is of paramount importance to ensure the desired performance of modern SatCom systems, as described in Sections 9.3 and 9.4. The noise is due to the propagation of the transmitted signals in the channel, while the distortion is mainly caused by nonlinear highpower amplifiers used at the transmitter. The goal is to efficiently estimate these quantities directly at the receiver of a SatCom system via suitable DL techniques. Two independent DL strategies are proposed for the estimation of noise and distortion from received signals. First, a convolutional autoencoder is presented in Section 9.5 for noise estimation. Next, a deep convolutional classifier is described in Section 9.6 to evaluate the distortion introduced by highpower amplifiers. Both strategies achieve high accuracy when tested on suitable application examples of SatCom systems. Furthermore, results indicate that the trained DL models can be used simultaneously on signals that are affected by channel noise and amplifier distortion.
More generally, this chapter illustrates how DL models can be used to extract the value of system parameters or transmitting conditions from samples of an electric signal. Hence, the use of these strategies can be extended to other domains, such as electromagnetic compatibility or signal integrity, where it is valuable to estimate unknown system conditions from detected signals.

10 Deep learning techniques for imaging and gesture recognition
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Nowadays, intelligent electromagnetic (EM) sensing, as a powerful allweather allday examination technique [16], is everincreasingly demanded to probe people in daily lives in a way not to infringe on visual privacy, in particular, to recognize where people are, how their physiological states, what they are doing, what they want to express by their body signs, etc. We here mean by intelligence that sensing systems can adaptively organize the taskoriented sensing pipeline (data acquisition plus processing) without the human intervene. Although three kinds of EM sensing schemes of realaperture [1013], syntheticaperture [2], and codingaperture [79] have been proposed by now, they are hindered from many practical utilizations because of tradingoff many critical factors effecting the costperformanceindex, especially when dealing with the socalled data crisis. To tackle this formidable challenge, recently, we have proposed the concept of hybridcomputingbased intelligent sensing by synergizing artificial materials (AMs; specifically, reprogrammable metasurfaces [1420]) for flexible wave manipulation thereby analogy data compression on physical level with artificial intelligences (AMs; specifically, deep learning strategies [2124]) for powerful data manipulation on digital level [2529]. In this chapter, we discuss three recent progress: intelligent metasurface imager [31], variationalautoencoder (VAE)based intelligent integrated metasurface sensor [32], and freeenergy (FE)based intelligent integrated metasurface sensor [33]. We mean by the integration that for a scene of interest and given hardware constraints, the settings of data acquisition and processing are simultaneously learned as a unique whole entity.

11 Deep learning techniques for metamaterials and metasurfaces design
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In this chapter, we have reviewed various approaches to apply deep learning techniques into the inverse design of metamaterials and metasurfaces, including the discriminative learning approach, generative learning approach, reinforcement learning approach, deep learning and optimization hybrid approach. The deep learning techniques play an important role in two aspects of inverse designs. First, deep learning can provide an accurate and efficient approximation of a complicated function costly to evaluate. Second, deep learning can extract and generate the highlevel features of geometries in a hierarchical and compact manner. These two important characteristics of deep learning poses a great potential for the future design tools of metamaterials and metasurfaces. Deep learning is bound to become a pivotal tool in the inverse design of metamaterials and metasurfaces.

12 Deep learning techniques for microwave circuit modeling
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This chapter provides a description of deep learning as applied to microwave circuit modeling. Microwave circuit modeling is an important area of computeraided design for fast and accurate microwave design and optimization. In recent years, rapid development of modern electronic devices/systems and wireless communications requires various customized microwave circuits. Subsequently, the modeling of microwave circuits becomes more complex and more challenging due to the demand for higher functionality, better reliability, and shorter design cycle. As a result, there is a need for more accurate, more effective, and more efficient modeling techniques for microwave circuits. To address this issue, deep learning has been introduced into the area of microwave circuit modeling. Deep learning is a class of machine learning that utilizes artificial neural networks with many layers to learn the complex inputoutput relationships. It has been highly successful in solving complex and challenging problems such as pattern recognition and classification. The powerful learning ability also makes it a suitable choice for modeling the complex inputoutput relationship of microwave circuits. Researchers have investigated a variety of important applications utilizing the ability of deep learning to perform microwave circuit modeling.

13 Concluding remarks, open challenges, and future trends
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Throughout this book, we have seen how deep learning (DL) has recently become a very active research field in many electromagnetic (EM) engineering applications [14].
DL algorithms are sophisticated machine learning (ML) techniques that try to mimic human brains to learn how to accurately solve a given task with extraordinary efficiency, robustness, and reliability [58]. However, their application to EM problems is nowadays in its very early stages and their development is significantly less mature than in other fields (e.g., speech, image, and text recognition).
In this concluding chapter, we try to summarize the main pros and cons of DL, together with the main challenges that still need to be solved in such an emerging research field. Finally, some future trends are briefly discussed as well, hopefully fostering future research in using this very powerful paradigm to address paramount challenges in many EMrelated areas.

Back Matter
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