Electromagnetic Inverse Problem Research Articles

Fourier Subspace-Based Deep Learning Method for Inverse Design of Frequency Selective Surface

Frequency selective surface (FSS) is critical for electromagnetic (EM) radiation protection due to its high spatial filtering performance, especially for active FSS. Recently, the artificial neural network (ANN) has shown great potential in solving EM inverse problems and rapid industrial design. In such an inverse model with ANN, it establishes the relationship between the given inputs of S-parameters and the desired structure parameters or material parameters. However, faced with applications where S-parameters vary in a large frequency range with different curve shapes, such as multiband microwave devices, equal interval sampling may result in high-dimensional inputs and will require a more complicated neural network. In this work, we present a Fourier subspace-based deep learning method (FS-BDLM) for FSS inverse design, where the dimension of the input is largely reduced by using Fourier subspace to represent the most salient features of the desired S-parameter performance. Compared with existing deep learning methods, the proposed technique makes inverse neural models more compact and more stable to noise contaminations. The validation of the proposed FS-BDLM is conducted both numerically and experimentally through two dual-passband FSS design examples, where the well-designed FSS is fabricated to validate the technique.

Stability for the electromagnetic inverse source problem in inhomogeneous media

Abstract This paper is concerned with the stability of the inverse source problem for Maxwell’s equations in an inhomogeneous background medium. We show that the stability estimate consists of the Lipschitz-type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The analysis employs scattering theory to obtain the holomorphic domain and an upper bound for the resolvent of the elliptic operator.

The Incident Field Optimization Method for the Electromagnetic Inverse Problems

In this letter, an incident field optimization (IO) method integrated with contrast source inversion (CSI) method and multiplicative regularized CSI (MR-CSI) method is proposed to deal with the electromagnetic inverse problems. For the conventional iterative inversion methods, the incident field is a prior knowledge and is usually obtained by the calibration process. Through the synthetic data experiments, it can be found that a small distortion of the incident field has little impact on the inversion results, but a high distortion will lead to fault inversion results or no convergence. In this letter, the incident field optimal factor, being updated during the iterative process, is introduced into the CSI and MR-CSI method, named as IO-CSI and MR–IO–CSI. The new methods have good inversion performance even with high incident field distortion. The proposed methods are applied to the Fresnel experiment data directly without the calibration procedure. Both the single-frequency and multifrequency inversion experiments demonstrate that the IO-CSI and MR–IO–CSI method can achieve good inversion results, indicating the method’s practical applicability.

Deep Neural Network with Data Cropping Algorithm for Absorptive Frequency‐Selective Transmission Metasurface

AbstractDeep neural networks (DNNs) are widely used in designing a metasurface; however, data acquisition from simulations is expensive in terms of time and effort. Inspired by image cropping, a data cropping algorithm is proposed that can significantly reduce the simulation time required in the DNN pre‐training process. The algorithm crops the simulated data and adds random data to augment the amount of the dataset. By applying the proposed target‐driven DNN, an absorptive frequency‐selective transmission (AFST) metasurface structure with a low profile and a broad transmission band is designed. A transmission band from 7.5 to 14 GHz and an absorption rate as large as 0.75 beyond the transmission band are observed. The proposed method provides an efficient strategy to design metasurfaces and a fast solution to the electromagnetic inverse design problem.

Machine-learning-assisted inverse design of scattering enhanced metasurface.

The scattering enhancement technique has shown prominent potential in various regimes such as satellite communication, Radar Cross Section (RCS) camouflage, and remote sensing. Currently, the scattering enhancement devices based on the metasurface have shown advantages in light weight and better performance. These metasurfaces always possess complex structure, it is hard to achieve through the tradition trial-and-error method which relies on the full-wave numerical simulation. In this paper, a new method combining the machine learning and the evolution optimization algorithm is proposed to design the metasurface retroreflector (MRF) for arbitrary direction incident wave. In this method, a predicting model and a generative inverse design model are constructed and trained, the predicting model is used to evaluate the fitness of each offspring in the genetic algorithm (GA), the generative model is used to initialize the first offspring of the GA by inverse generate the MRF based on the requirements of the designer. With the assistance of these two machine learning models, the evolution optimization algorithm is employed to find the optimal design of the MRF. This approach enables automatic solution of electromagnetic inverse design problems and opens the way to facilitate the optimization of other metadevices.

Inverse Scattering by Perfectly Electric Conducting (PEC) Rough Surfaces: An Equivalent Model With Line Sources

This paper presents a new method for the reconstruction of the perfectly electric conducting (PEC) rough surface profiles by utilizing electromagnetic waves. The inaccessible rough surface is illuminated by a tapered plane electromagnetic wave and the scattered field data are measured on a certain number of points above the surface under test. The method for the inverse electromagnetic imaging problem is based on a special representation of the scattered field in terms of a finite number of fictitious discrete line sources located along a plane below the rough surface. The current densities of these fictitious sources are obtained through the regularized solution of an ill-posed problem. Then, it is shown that the image of the rough surface can be directly retrieved by seeking the points in the space where the tangential component of the total electric field vanishes. Alternatively, a much more rigorous iterative method based on a regularized Newton algorithm is also presented. A comprehensive numerical analysis is provided to demonstrate the feasibility of the presented approach. In this context, the quantitative successes of both approaches are interpreted by considering a very sensitive ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm based error function between the actual and the reconstructed surface profiles. Regarding different scattering scenarios taken into account, the error values obtained for satisfactory reconstructions are generally in the range of 10% - 30% for both methods. It is also shown that the presented algorithms are capable of reconstructing the rough surfaces which oscillate for every λ horizontally and have a peak to peak variation 0.5λ at most.

A Wavelet-Based Compressive Deep Learning Scheme for Inverse Scattering Problems

Recently, physics-assisted deep learning schemes (DLSs) have demonstrated state-of-the-art performance for solving inverse scattering problems (ISPs). However, most learning approaches typically require a high computational overhead and a big memory footprint, which prohibits further applications. In this work, a wavelet-based compressive scheme (WCS) is proposed in solving ISPs, where the multi-subspace information is explored by wavelet bases and branched between each encoder and decoder path. It is shown that the proposed WCS can be simply adapted to commonly used DLSs, such as the back-propagation scheme (BPS) and the dominant current scheme (DCS), to reduce the computational and storage load. Specifically, benefiting from compressive and multi-resolution properties of wavelet and with the help of the factorized convolution method, more than 99.7% trainable weights are reduced in both illustrated BP-WCS and DC-WCS, whereas the performance deterioration is limited around 1% in terms of traditional BPS and DCS. Extensive numerical and experimental tests are conducted for quantitative validations. Comparisons are also made among UNet, a well-known compressive method (Mobile-UNet), and the proposed method. It is expected that the suggested compression technique would find its applications on deep learning-based electromagnetic inverse problems under source-limited scenarios.

A Multimodal Improved Particle Swarm Optimization for High Dimensional Problems in Electromagnetic Devices

Particle Swarm Optimization (PSO) is a member of the swarm intelligence-based on a metaheuristic approach which is inspired by the natural deeds of bird flocking and fish schooling. In comparison to other traditional methods, the model of PSO is widely recognized as a simple algorithm and easy to implement. However, the traditional PSO’s have two primary issues: premature convergence and loss of diversity. These problems arise at the latter stages of the evolution process when dealing with high-dimensional, complex and electromagnetic inverse problems. To address these types of issues in the PSO approach, we proposed an Improved PSO (IPSO) which employs a dynamic control parameter as well as an adaptive mutation mechanism. The main proposal of the novel adaptive mutation operator is to prevent the diversity loss of the optimization process while the dynamic factor comprises the balance between exploration and exploitation in the search domain. The experimental outcomes achieved by solving complicated and extremely high-dimensional optimization problems were also validated on superconducting magnetic energy storage devices (SMES). According to numerical and experimental analysis, the IPSO delivers a better optimal solution than the other solutions described, particularly in the early computational evaluation of the generation.

Hyperparameters optimization of neural network using improved particle swarm optimization for modeling of electromagnetic inverse problems

AbstractOptimization of hyperparameters of artificial neural network (ANN) usually involves a trial and error approach which is not only computationally expensive but also fails to predict a near-optimal solution most of the time. To design a better optimized ANN model, evolutionary algorithms are widely utilized to determine hyperparameters. This work proposes hyperparameters optimization of the ANN model using an improved particle swarm optimization (IPSO) algorithm. The different ANN hyperparameters considered are a number of hidden layers, neurons in each hidden layer, activation function, and training function. The proposed technique is validated using inverse modeling of two meander line electromagnetic bandgap unit cells and a slotted ultra-wideband antenna loaded with EBG structures. Three other evolutionary algorithms viz. hybrid PSO, conventional PSO, and genetic algorithm are also adopted for the hyperparameter optimization of the ANN models for comparative analysis. Performances of all the models are evaluated using quantitative assessment parameters viz. mean square error, mean absolute percentage deviation, and coefficient of determination (R2). The comparative investigation establishes the accurate and efficient prediction capability of the ANN models tuned using IPSO compared to other evolutionary algorithms.

A Non-Iterative Method Combined with Neural Network Embedded in Physical Model to Solve the Imaging of Electromagnetic Inverse Scattering Problem

The main purpose of this paper is to solve the electromagnetic inverse scattering problem (ISP). Compared with conventional tomography technology, it considers the interaction between the internal structure of the scene and the electromagnetic wave in a more realistic manner. However, due to the nonlinearity of ISP, the conventional calculation scheme usually has some problems, such as the unsatisfactory imaging effect and high computational cost. To solve these problems and improve the imaging quality, this paper presents a simple method named the diagonal matrix inversion method (DMI) to estimate the distribution of scatterer contrast (DSC) and a Generative Adversarial Network (GAN) which could optimize the DSC obtained by DMI and make it closer to the real distribution of scatterer contrast. In order to make the distribution of scatterer contrast generated by GAN more accurate, the forward model is embedded in the GAN. Moreover, because of the existence of the forward model, not only is the DSC generated by the generator similar to the original distribution of the scatterer contrast in the numerical distribution, but the numerical of each point is also approximate to the original.

Women’s Contributions in Electromagnetic Inverse Problems [Women in Engineering

Science is often considered a male-dominated field. Today, women are still discouraged from entering the fields of technology, engineering, and math and, in the last two years, the COVID-19 pandemic has worsened this situation. Nevertheless, despite challenges of gender discrimination and lack of recognition in the scientific community, countless inspiring women in these fields have made historic contributions to science and helped develop a better understanding of the world around us. Many women were not recognized in their own lifetimes, but their achievements have helped generations of female scientists to come.

Convolutional neural network inversion of airborne transient electromagnetic data

ABSTRACTAs an efficient geophysical exploration technique, airborne transient electromagnetics shows strong adaptability to complex terrains and can provide subsurface resistivity information rapidly with a dense spatial coverage. However, the huge volume of airborne transient electromagnetic data obtained from a large number of spatial locations presents a great challenge to real‐time airborne transient electromagnetic interpretation due to the high computational cost. Moreover, the inherent non‐uniqueness of the inverse problem also limits our ability to constrain the underground resistivity structure. In this study, we develop an entirely data‐driven convolutional neural network to solve the airborne transient electromagnetic inverse problem. Synthetic tests show that the convolutional neural network is computationally efficient and yields robust results. Compared with the Gauss–Newton method, convolutional neural network inversion does not depend on the choices of an initial model and the regularization parameters and is less prone to getting trapped in a local minimum. We also demonstrate the general applicability of the convolutional neural network to three‐dimensional synthetic airborne transient electromagnetic responses and the field observations acquired from Leach Lake Basin, Fort Irwin, California. The efficient convolutional neural network inversion framework can support real‐time resistivity imaging of subsurface structures from airborne transient electromagnetic observations, providing a powerful tool for field explorations.

Far-field to Near-field Data Relations for the Inverse Electromagnetic Scattering Problem

This paper considers (in general form) the problem of recovering information (size and material parameters) about the scattering object from far-field measurements. The order of solution and functions of each equation for the fields inside and outside the scattering object are discussed. Using well-known mathematical theorems, a simple equation has been derived that connects the far-field data on one side to the near-field data on the other side. Consequently, this equation has been used in an optimization procedure to find the parameters of the dielectric cylinder.

Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration

In this paper, the structure analysis of the direct sampling method (DSM) in the 3D electromagnetic inverse scattering problem in both near-field and far-field configurations is carried out. Even though the DSM is known to be a robust, fast, and efficient non-iterative type algorithm to estimate support and shape of unknown inhomogeneities from the knowledge of scattered data in the 2D scalar electromagnetic case, the choice of a proper test polarization dipole since the data are vectorial in the 3D vector case is to be dealt with, since indeed key to the success of 3D DSM. Here we carefully analyze the indicator function of DSM using the asymptotic formula of the scattered field under a small volume hypothesis of well-separated inhomogeneities. Thanks to it, an analytic formula of the 3D DSM indicator function is established. The already proposed heuristic method to choose the polarization test dipole is theoretically justified, and new methods developed for better efficiency. Numerical simulations from synthetic and experimental data validate the theoretical results.

Multi-Angular Electroretinography (maERG): Topographic Mapping of the Retinal Function Combining Real and Virtual Electrodes.

The full-field electroretinogram (ffERG) is an objective tool to assess global retinal function, though as it is currently done, it is unable to localize sources of retinal dysfunction or damage. To overcome this, we have developed a new way to record multiple spatial derivations of the ERG using the rotating capability of the eye, thus creating "virtual electrodes". We have termed this the multi-angular ERG (or maERG). With only 3 real electrodes and 11 varying gaze positions, we create 33 "virtual electrodes". We created a realistic electrophysiological and anatomical eye model (i.e., forward model) to reconstruct the retinal activity (i.e., inverse problem) from the 33 virtual electrodes. We simulated 2 pathological scenarios (central and peripheral scotomas), which were compared to their respective theoretical source configurations using an Area under Receiver Operator Characteristic curve metric. Our simulations show that the low-resolution brain electromagnetic tomography algorithm (LORETA) is the best method tested to reconstruct retinal sources when compared to the Minimum Norm Estimate algorithm. Furthermore, a signal to noise ratio of 50 dB is needed to accurately reconstruct the retina's functional map. Our proposed maERG recording method, combined with our solution to the electromagnetic inverse problem enables us to reconstruct the functional map of the human retina. We believe that this new functional retinal imaging technique will permit earlier detection of retinal malfunction and consequently optimize the clinical monitoring of patients affected with retinopathies.

Terahertz refractive index-based morphological dilation for breast carcinoma delineation

This paper reports investigations led on the combination of the refractive index and morphological dilation to enhance performances towards breast tumour margin delineation during conserving surgeries. The refractive index map of invasive ductal and lobular carcinomas were constructed from an inverse electromagnetic problem. Morphological dilation combined with refractive index thresholding was conducted to classify the tissue regions as malignant or benign. A histology routine was conducted to evaluate the performances of various dilation geometries associated with different thresholds. It was found that the combination of a wide structuring element and high refractive index was improving the correctness of tissue classification in comparison to other configurations or without dilation. The method reports a sensitivity of around 80% and a specificity of 82% for the best case. These results indicate that combining the fundamental optical properties of tissues denoted by their refractive index with morphological dilation may open routes to define supporting procedures during breast-conserving surgeries.

Uniqueness and increasing stability in electromagnetic inverse source problems

In this paper we study the uniqueness and the increasing stability in the inverse source problem for electromagnetic waves in homogeneous and inhomogeneous media from boundary data at multiple wave numbers. For the unique determination of sources, we consider inhomogeneous media and use tangential components of the electric field and magnetic field at the boundary of the reference domain. The proof relies on the Fourier transform with respect to the wave numbers and the unique continuation theorems. To study the increasing stability in the source identification, we consider homogeneous media and measure the absorbing data or the tangential component of the electric field at the boundary of the reference domain as additional data. By using the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, Huygens' principle and bounds for initial boundary value problems, increasing (with larger wave numbers intervals) stability estimate is obtained.

A Hybrid Quantum-Behaved Particle Swarm Optimization Algorithm for Solving Inverse Scattering Problems

A hybrid inversion approach based on the quantum-behaved particle swarm optimization (QPSO) method is presented in this article to solve electromagnetic inverse problems. Inverse scattering problems are ill-posed and are often transformed into optimization problems by defining a suitable cost function, which can be minimized by evolutionary algorithms. This article is aimed at assessing the effectiveness of a customized QPSO in reconstructing 2-D dielectric scatterers. The bottleneck that restricts the application of the evolutionary algorithm in large-scale optimization problems is its computational cost. In this article, the diffraction tomographic image is used as an initial guess for the QPSO. Moreover, a weighted mean best position according to the fitness values of the particles is introduced to expand the contribution of excellent particles on population evolution. This hybrid approach, denoted as HQPSO, makes full use of the complementary advantages of linear reconstruction algorithms and stochastic optimization algorithms and is, thus, able to ensure accuracy and improve computational efficiency. Numerical experiments for different types of dielectric objects are performed with synthetic and experimental inverse-scattering data.

Cauchy-Gaussian pigeon-inspired optimisation for electromagnetic inverse problem

The optimisation of electromagnetic inverse problems could be attributed to a constraint nonlinear programming problem. Loney's solenoid problem is one of the electromagnetic inverse benchmarks in the magnetic field. Parameters such as the structure and medium are necessary to be designed based on the required magnetic properties. In this paper, an improved variant of pigeon-inspired optimisation (PIO) algorithm based on Cauchy distribution and Gaussian distribution, named Cauchy-Gaussian pigeon-inspired optimisation (CGPIO), is proposed to solve electromagnetic inverse problems. The PIO algorithm is a bio-inspired swarm intelligence optimisation algorithm, which imitates the homing process of pigeons. To improve the convergence efficiency of the basic PIO algorithm, two operators including Cauchy distribution and Gaussian distribution are utilised. Comparative results show the suitability and superiority of CGPIO algorithm for electromagnetic optimisation.

Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging

In this paper, a comparison of stochastic optimization algorithms is presented for the reconstruction of electromagnetic profiles in through-the-wall radar imaging. We combine those stochastic optimization approaches with a shape-based representation of unknown targets which is based on a parametrized level set formulation. This way, we obtain a stochastic version of shape evolution with the goal of minimizing a given cost functional. As basis functions, we consider in particular Gaussian and Wendland radial basis functions. For the optimization task, we consider three variants of stochastic approaches, namely stochastic gradient descent, the Adam method as well as a more involved stochastic quasi-Newton scheme. A specific backtracking line search method is also introduced for this specific application of stochastic shape evolution. The physical scenery considered here is set in 2D assuming TM waves for simplicity. The goal is to localize and characterize (and eventually track) targets of interest hidden behind walls by solving the corresponding electromagnetic inverse problem. The results provide a good indication on the expected performance of similar schemes in a more realistic 3D setup.