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.

This chapter surveyed applications of deep learning techniques to free-space inverse scattering. We have divided some of the most popular deep learning approaches to inverse scattering problems into three broad categories: black-box type of solutions, learning-based approaches to augment otherwise (traditional) iterative inverse scattering algorithms, and non-black-box, non-iterative 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 free-space inverse scattering is a quickly evolving area of research, this survey has been necessarily non-exhaustive. 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.

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 non-uniqueness, 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, multi-physics measurements such as gravity, seismic, and electromagnetic (EM) data can be jointly used for comprehensively understanding the domain of investigation. The large-volume data, large-scale survey domain, as well as the complex numerical modeling process, make geophysical inversion computationally expensive. It is also common to repeat multi-physics 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 high-quality imaging with large-volume 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 learning-based inversion, we show state-of-the-art techniques in applying DL in EM inversion, including purely data-driven approaches, physics-embedded data-driven approaches and learning-assisted physics-driven approaches. We also present several DL-based 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.

This chapter presents an overview of how deep learning (DL) techniques can be exploited to solve the problem of direction-of-arrival (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 array-imperfection 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.

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 near-space 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 high-power 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 high-power 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 high-power 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.

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 high-level 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.

Throughout this book, we have seen how deep learning (DL) has recently become a very active research field in many electromagnetic (EM) engineering applications [1-4].

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 [5-8]. 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 EM-related areas.