Research

Ø  Solving Combined Field Integral Equations with Physics-informed Graph Residual Learning for EM Scattering of 3D PEC Targets

In this study, physics-informed graph residual learning (PhiGRL) is proposed as an effective and robust deep learning-based approach for 3D electromagnetic (EM) modeling. Extended from physics-informed supervised residual learning (PhiSRL), PhiGRL emulates the computation of fixed-point iteration method to iteratively modify a candidate solution until convergence by applying graph neural networks (GNNs) to predict modifications. The application of GNNs enables PhiGRL to adaptively deal with unstructured data and varying unknown numbers in 3D EM modeling where most off-the-shelf deep learning techniques are inapplicable. PhiGRL is first applied to solve the combined-field integral equations (CFIE) of basic 3D perfect electric conductor (PEC) targets, including spheroids, conical frustums, and hexahedrons, in both supervised and unsupervised learning manners. Its generalization abilities on different incident frequencies and target shapes are then verified separately. Numerical results show that PhiGRL can achieve good numerical precision with a significant reduction in computation time (online prediction). PhiGRL is further migrated to simulate more complicated 3D PEC targets through transfer learning, including missilehead- and airplane-shaped targets. This study explores the possibility of applying deep learning together with EM physics for 3D EM modeling.

Ø  Physics-Informed Supervised Residual Learning for Electromagnetic Modeling

In this study, physics-informed supervised residual learning (PhiSRL) is proposed to enable an effective, robust, and general deep learning framework for 2-D electromagnetic (EM) modeling. Based on the mathematical connection between the fixed-point iteration method and the residual neural network (ResNet), PhiSRL aims to solve a system of linear matrix equations. It applies convolutional neural networks (CNNs) to learn updates of the solution with respect to the residuals. Inspired by the stationary and nonstationary iterative scheme of the fixed-point iteration method, stationary and nonstationary iterative physics-informed ResNets (SiPhiResNet and NiPhiResNet) are designed to solve the volume integral equation (VIE) of EM scattering. The effectiveness and universality of PhiSRL are validated by solving VIE of lossless and lossy scatterers with the mean squared errors (MSEs) converging to ∼ 10−4 (SiPhiResNet) and ∼ 10−7 (NiPhiResNet). Numerical results further verify the generalization ability of PhiSRL. 

Ø  Physics-Informed Supervised Residual Learning for 2-D Inverse Scattering Problems

In this communication, we propose a new physicsconstrained approach to solve 2-D inverse scattering problems (ISPs) by extending physics-informed supervised residual learning (PhiSRL) with Born approximation (BA). By embedding the fixed-point iteration method in residual neural network (ResNet), PhiSRL aims to solve ISPs iteratively by applying the convolutional neural networks (CNNs) to learn the update rules of reconstructions. PhiSRL is employed to invert lossy scatterers by introducing BA to linearize ISPs and further reduce the computational burden of forward modeling. Both numerical and experimental results validate the effectiveness of the proposed approach.

Ø  Neural Born Iterative Method for Solving Inverse Scattering Problems: 2D Cases

In this article, we propose the neural Born iterative method (NeuralBIM) for solving 2-D inverse scattering problems (ISPs) by drawing on the scheme of the physics-informed supervised residual learning (PhiSRL) to emulate the computing process of the traditional Born iterative method (TBIM). NeuralBIM uses independent convolutional neural networks (CNNs) to learn the alternate update rules of two different candidate solutions regarding the residuals. Two different schemes are presented in this article, including the supervised and unsupervised learning schemes. With the dataset generated by the method of moments (MoM), supervised NeuralBIM is trained with the knowledge of the total fields and contrasts. Unsupervised NeuralBIM is guided by the physics-embedded objective function founding on the governing equations of ISPs, which results in no requirement of the total fields and contrasts for training. Numerical and experimental results further validate the efficacy of NeuralBIM.

Ø  Coding Programmable Metasurfaces Based on Deep Learning Techniques

Programmable metasurfaces have recently been proposed to dynamically manipulate electromagnetic (EM) waves in both temporal and spatial dimensions. With active components integrated into unit cells of the metasurface, states of the unit cells can be adjusted by digital codes. The metasurface can then construct complex spatial and temporal electromagnetic beams. Given the main parameters of the beam, the optimal codes can be computed by nonlinear optimization algorithms, such as genetic algorithm, particle swarm optimization, etc. The high computational complexity of these algorithms makes it very challenging to compute the codes in real time. In this study, we applied deep learning techniques to compute the codes. A deep convolutional neural network is designed and trained to compute the required element codes in milliseconds, given the requirement of the waveform. The average accuracy of the prediction reaches more than 94 percent. This scheme is validated on a 1-bit programmable metasurface and both experimental and numerical results agree with each other well. This study shows that machines may “learn” the physics of modulating electromagnetic waves with the help of the good generalization ability in deep convolutional neural networks. The proposed scheme may provide us with a possible solution for real-time complex beamforming in antenna arrays, such as the programmable metasurface.

Ø  Application of Multitask Learning for 2-D Modeling of Magnetotelluric Surveys: TE Case

In this article, multitask learning is applied to forward modeling of 2-D magnetotellurics (MT) to predict the apparent resistivity and impedance phase of MT data. Multitask learning can learn multiple objectives simultaneously based on the shared representation, thereby improving efficiency and accuracy. The loss function is carefully designed by weighing multiple objective functions based on homoscedastic uncertainty, and the structural similarity regularization term is applied to ensure the texture of the obtained apparent resistivity and impedance phase. The proposed convolutional neural network can make accurate predictions with an average relative error of apparent resistivity and impedance phase less than 1.2% and 0.2%, respectively. The generalization ability of the proposed network is verified by applying it to cases with more complex resistivity distributions than training samples. This article shows the potential for fast and accurate computation of two highly correlated physical quantities in electromagnetic fields.

Ø  Phase Synthesis of Beam-Scanning Refectarray Antenna Based on Deep Learning Technique

In this work, we investigate the feasibility of applying deep learning to phase synthesis of reflectarray antenna. A deep convolutional neural network (ConvNet) based on the architecture of AlexNet is built to predict the continuous phase distribution on reflectarray elements given the beam pattern. The proposed ConvNet is sufficiently trained with data set generated by array-theory method. With radiation pattern and beam direction arrays as input, the ConvNet can make real-time and fairly accurate predictions in milliseconds with the average relative error below 0.7%. This paper shows that deep convolutional neural networks can \learn" the principle of reflectarray phase synthesis due to their inherent powerful learning capacity. The proposed approach may provide us a potential scheme for real-time phase synthesis of antenna arrays in electromagnetic engineering.

Ø  Study on a Fast Solver for Poisson’s Equation Based on Deep Learning Technique

Fast and efficient computational electromagnetic simulation is a long-standing challenge. In this article, we propose a data-driven model to solve Poisson’s equation that leverages the learning capacity of deep learning techniques. A deep convolutional neural network (ConvNet) is trained to predict the electric potential with different excitations and permittivity distribution in 2-D and 3-D models. With a careful design of cost function and proper training data generated from finite-difference solvers, the proposed network enables a reliable simulation with significant speedup and fairly good accuracy. Numerical experiments show that the same ConvNet architecture is effective for both 2-D and 3-D models, and the average relative prediction error of the proposed ConvNet model is less than 3% in both 2-D and 3-D simulations with a significant reduction in computation time compared to the finite-difference solver. This article shows that deep neural networks have a good learning capacity for numerical simulations. This could help us to build some fast solvers for some computational electromagnetic problems.