Recently, studies have shown the potential of integrating field-type iterative methods with deep learning (DL) techniques in solving inverse scattering problems (ISPs). In this article, we propose a novel variational Born iterative network (VBIM-Net), to solve the full-wave ISPs with significantly improved structural rationality and inversion quality. The proposed VBIM-Net emulates the alternating updates of the total electric field and the contrast in the variational Born iterative method (VBIM) by multiple layers of subnetworks. We embed the analytical calculation of the contrast variation into each subnetwork, converting the scattered field residual into an approximate contrast variation and then enhancing it by a U-Net, thus avoiding the requirement of matched measurement dimension and grid resolution as in existing approaches. The total field and contrast of each layer’s output are supervised in the loss function of VBIM-Net, imposing soft physical constraints on the variables in the subnetworks, which benefits the model’s performance. In addition, we design a training scheme with extra noise to enhance the model’s stability. Extensive numerical results on synthetic and experimental data both verify the inversion quality, generalization ability, and robustness of the proposed VBIM-Net. This work may provide some new inspiration for the design of efficient field-type DL schemes.

Impedance matching circuits (IMCs) are crucial modules in radio frequency (RF) front-end components, devices, and systems, affecting the performance of the whole systems. However, the design process of IMCs has to require intense manual interventions with high computational costs. To alleviate this problem, a novel scheme for inversely designing IMCs is presented in this work based on neural network technology. Such IMC inverse design framework consists of two mapping-based deep neural networks (DNNs). The first one is an untrained generative adversarial network (GAN) that maps from the design requirements to the regularized S-parameters curves. The second one is an inversion network that maps from the S-parameters and the target impedance to the designed circuit parameters. With the cascaded GAN and inversion network, an efficient method for designing IMC-based filtering antenna is introduced, which takes about 1/17 the time compared to the traditional EM-based design and optimization methods. Further, three power amplifiers (PAs) with multiple IMCs are inversely-designed based on the proposed framework. In experimental demonstration, the elaborate prototypes are fabricated and measured, where the measured results fully satisfy the demand performance.

Recently, deep learning methods have attracted intensive attentions on solving inverse scattering problems (ISPs). However, different with traditional physical-model based methods, the reliability of the learning methods is low due to the low explainability of deep neural networks (DNNs). Thus, the uncertainty quantification is extremely important, which provides the “confidence level" of the reconstructed results in ISPs. In this paper, four uncertainty calibration methods are introduced to better quantify the uncertainties and improve the reconstructions in deep-learning based ISP solvers, which includes Deep-Ensemble, Drop-Block, Drop-Channel, and Loss-Balance. Different calibration methods are evaluated in terms of their impacts on the accuracies of reconstructed results in solving ISPs and how well they quantify the uncertainties of the full-wave reconstructed results, which are further compared with previously proposed uncertainty quantification methods including MC-Dropout and generative models in ISPs. Our synthetic and experimental results show that the methods of Deep-Ensemble and Drop-block can achieve better performance than other methods quantitatively in terms of uncertainty quantifications. Besides, Loss-Balance has a significant effect on the preservation of reconstruction accuracy. It is expected that the results and conclusions are helpful to better quantify uncertainties and push learning methods to a more reliable way in full-wave nonlinear reconstructions of ISPs.

Recently, deep learning approaches have shown their advantages on solving scientific problems including full-wave nonlinear inverse problems. However, these data-driven methods face severe problems, especially about the low generalization ability, which means the trained models only work for scenarios with similar training data and physical setups. In this work, we propose a multi-domain weight-sharing method (MDWS) for inverse scattering problems, which increases the generalization ability of learning approaches for both data-based and physical-based out-of-range tests. Specifically, the proposed MDWS utilizes a physical layer of Green’s function to transform between induced current domain and electrical field domain, where weight-sharing blocks having the same weights in different incidences and stages are used to decouple the network structure from measurement setups. It is shown by intensive numerical and experimental tests both qualitatively and quantitatively that the proposed MDWS apparently outperforms the benchmarked method. Further, the proposed weight-sharing architecture also provides an efficient way to build large model in electromagnetic society with much less memory and computational cost.

Recently, deep learning methods have made significant success in inverse scattering problems (ISPs). However, learning approaches that work in different spaces, such as frequency and real space, are seldom explored in solving ISPs. In this work, multiple-space deep learning schemes (MSDLSs) incorporating frequency-space and real-space processing are studied. Specifically, a network that works in low-frequency subspace is first introduced. Then, serial MSDLSs are introduced by combining frequency-space and real-space networks in a serial way to enable networks in different spaces work complementarily. Finally, to further enable dynamic interaction between multiple-space information during both training and testing stages, a parallel MSDLS is proposed. The proposed MSDLSs are presented under the framework of backpropagation scheme (BPS). It is shown by synthetic and experimental tests that the MSDLSs have a consistent improvement over BPS. It is expected that the proposed schemes will find applications on other inverse problems where an incorporation of multiple-space information is needed.

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.

Electrical impedance tomography (EIT) is an attractive technique that aims to reconstruct the unknown electrical property in a domain from the surface electrical measurements. In this work, the induced-current learning method (ICLM) is proposed to solve nonlinear electrical impedance tomography (EIT) problems. Specifically, the cascaded end-to-end convolutional neural network (CEE-CNN) architecture is designed to implement the ICLM. The CEE-CNN greatly decreases the nonlinearities in EIT problems by designing a combined objective function and introducing multiple labels. A noticeable characteristic of the proposed CNN scheme is that the input parameters are chosen as both induced contrast current (ICC) and the updated electrical field from a spectral analysis and the output is chosen as ICC, which is fundamentally different from prevailing CNN schemes. Further, several skip connections are introduced to focus on learning only the unknown part of ICC. ICLM is verified with both numerical and experimental tests on typical EIT problems, and it is found that ICLM is able to solve typical EIT problems in less than 1 second with high image qualities. More importantly, it is also highly robust to measurement noises and modeling errors, such as inaccurate boundary data.

This paper is devoted to solving a full-wave inverse scattering problem (ISP), which is aimed at retrieving permittivities of dielectric scatterers from the knowledge of measured scattering data. ISPs are highly nonlinear due to multiple scattering, and iterative algorithms with regularizations are often used to solve such problems. However, they are associated with heavy computational cost, and consequently, they are often time-consuming. This paper proposes the convolutional neural network (CNN) technique to solve full-wave ISPs. We introduce and compare three training schemes based on U-Net CNN, including direct inversion, backpropagation, and dominant current schemes (DCS). Several representative tests are carried out, including both synthetic and experimental data, to evaluate the performances of the proposed methods. It is demonstrated that the proposed DCS outperforms the other two schemes in terms of accuracy and is able to solve typical ISPs quickly within 1 s. The proposed deep-learning inversion scheme is promising in providing quantitative images in real time.