Xiao-Min Pan

A deep learning scheme is proposed to solve the electromagnetic (EM) scattering problems where the profile of the dielectric scatterer of interest is incomplete. As a compensation for the incompletion of the profile, a limited amount of scattering/prescribed data are provided, which in principle contain sufficient information associated with the missing part of the profile. The existing solvers can hardly solve this type of problems. On one hand, the well-developed forward solvers have no mechanism to accept the scattering data to recover the unknown part of the profile. On the other hand, the existing solvers for inverse problems cannot retrieve the complete profile with an acceptable accuracy from the limited amount of scattering data, even when the available part of the profile can be fed into the solvers. To overcome the difficulty, the EM forward scattering from an incompletely known dielectric scatterer is derived in this work. A deep learning scheme is then developed where the forward and inverse scattering problems can be solved simultaneously. Numerical experiments are conducted to demonstrate the performance of the proposed DL-based scheme in terms of two-dimensional (2-D) EM scattering problems.

This work develops a solver based on the neural networks, where the discrete form of integral equations is embedded to address both forward and inverse dynamic electromagnetic scattering problems. Since the input is the real-valued coordinates while the output is the complex-valued fields, our proposed solver distinguishes itself from existing neural network solvers. Different network structures to handle the phase information contained in the complex-valued numbers are investigated. Improvements are developed to enhance the performance of the proposed solver. Numerical simulations for two-dimensional electromagnetic scattering in both forward and inverse problems were conducted to validate the proposed solver.

A deep learning scheme is proposed to solve the electromagnetic (EM) scattering problems where the profile of the dielectric scatterer of interest is incomplete. As a compensation, a limited amount of scattering data is provided, which is in principle containing sufficient information associated with the missing part of the profile. The existing solvers can hardly realize the compensation if the known part of the profile and the scattering data are combined straightforwardly. On one hand, the well-developed forward solvers have no mechanism to accept the scattering data, which can recover the unknown part of the profile if properly used. On the other hand, the existing solvers for inverse problems cannot retrieve the complete profile with an acceptable accuracy from the limited amount of scattering data, even when the available part of the profile can be fed into the solvers. This work aims to handle the difficulty. To this end, the EM forward scattering from an incompletely known dielectric scatterer is derived. A scheme based on DL is then proposed where the forward and inverse scattering problems are solved simultaneously. Numerical experiments are conducted to demonstrate the performance of the proposed DL-based scheme for both two-dimensional (2-D) and three-dimensional (3-D) EM scattering problems.

Recent advances in radar automatic target recognition (RATR) techniques utilizing deep neural networks have demonstrated remarkable performance, largely due to their robust generalization capabilities. To address the challenge for applications with polarimetric HRRP sequences, a dual-polarization feature fusion network (DPFFN) is proposed along with a novel two-stage feature fusion strategy. Moreover, a specific fusion loss function is developed, which enables the adaptive generation of comprehensive multi-modal representations from polarimetric HRRP sequences. Experimental results demonstrate that the proposed network significantly improves performance in radar target recognition tasks, thus validating its effectiveness. The PyTorch implementation of our proposed DPFFN is available at https://github.com/xmpan/DPFFN.

Unlike the universal approximation theorems for functions mapping from a real-valued (RV) vector to a RV number or from a complex-valued (CV) vector to a CV number, in the field of electromagnetism, we need to approximate functions mapping from a RV vector to a CV number when we consider the electric field as a function of the spatial coordinate in the frequency domain. Typically, CV numbers contain phase information. When such phase information is handled properly, the performance of the neural networks (NNs) can be improved. This work derives a universal approximation theorem for functions mapping from a RV vector to a CV number. A deep NN, named as HV-DL, is designed accordingly, which consists of a RV input layer, a RV module containing two branches, a CV module and a CV output layer. The proposed universal approximation theorem is verified by numerical experiments on the HV-DL solution of the two-dimensional (2-D) electric field integral equation (EFIE). To integrate the underlying physics of electromagnetic scattering into the proposed HV-DL, the loss function is computed according to the EFIE.

The utilization of physics-informed deep learning (PI-DL) methodologies provides an approach to augment the predictive capabilities of deep learning (DL) models by constraining them with known physical principles. We utilize a PI-DL model called the deep operator network (DeepONet) to solve two-dimensional (2D) electromagnetic (EM) scattering problems. Numerical results demonstrate that the discrepancy between the DeepONet and conventional method of moments (MoM) is small, while maintaining computational efficiency.

Inverse scattering problems (ISPs) with a limited aperture have higher nonlinearity owing to the fewer measurement data, which bring more challenges in the application of full-wave quantitative imaging. To solve the ISPs with limited aperture, an unrolling algorithm of subspace-based optimization method under physical contraction integral equation (CIE-SOM), named CIE-SOM-NET, is proposed. The CIE model reduces nonlinearity, enabling CIE-SOM-NET to achieve better results in addressing regression problems. The proposed algorithm is composed of several sub-modules, and each sub-module is constructed with a small convolutional neural network (CNN) and an operator of the least square method, which are utilized to update the induced current and the modified contrast function. In addition, a weighted loss function, which is composed of the consistency function of the induced current, the scattered field, and the relative permittivity, is defined to constrain the training process in the physical CIE model. Compared to traditional iterative inversion methods, the proposed CIE-SOM-NET exhibits several merits in terms of imaging accuracy and computational cost. The proposed method also achieves better stability and robustness compared to the initial SOM-NET. Several numerical examples validate that the proposed CIE-SOM-NET has excellent inversion performance in the case of limited aperture.

For photonic applications, the inverse design method plays a critical role in the optimized design of photonic devices. According to its two ingredients, inverse design in photonics can be improved from two aspects: to find solutions to Maxwell’s equations more efficiently and to employ a more suitable optimization scheme. Various optimization algorithms have been employed to handle the optimization: the adjoint method (AM) has become the one of the most widely utilized ones because of its low computational cost. With the rapid development of deep learning (DL) in recent years, inverse design has also benefited from DL algorithms, leading to a new pattern of photon inverse design. Unlike the AM, DL can be an efficient solver of Maxwell’s equations, as well as a nice optimizer, or even both, in inverse design. In this review, we discuss the development of the AM and DL algorithms in inverse design, and the advancements, advantages, and disadvantages of the AM and DL algorithms in photon inverse design.

An improved block-diagonal preconditioner (IBDP) is developed for the FFT accelerated the volume integral equation formulation based on equivalent volumetric currents (FFT-JVIE). A comparative study on the realistic models is carried out among the IBDP, BDP, the previously developed analytical preconditioner (AnP) and the circulant-based preconditioners (CBP).

Deep learning (DL) equipped iterators are developed to accelerate the iterative solution of electromagnetic scattering problems. In proposed iterators, DL blocks consisting of U-nets are employed to replace the nonlinear process of the traditional iterators, i.e., the conjugate gradient (CG) method and generalized minimal residual (GMRES) method. New implementations of the complex-valued batch normalization in the U-net are proposed and investigated in terms of the DL equipped iterators. Numerical results show that the DL equipped iterators outperforms their traditional counterparts in terms of computational time under the comparable accuracy since the phase information of the currents, fields and permittivity are properly handled.