Physics-Informed Supervised Residual Learning for Electromagnetic Modeling

Abstract

In this study, physics-informed supervised residual learning (PhiSRL) is proposed to enable an effective, robust, and general deep learning framework for 2D 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 non-stationary iterative scheme of the fixed-point iteration method, stationary and non-stationary 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 $\sim 10^{-4}$ (SiPhiResNet) and $\sim 10^{-7}$ (NiPhiResNet). Numerical results further verify the generalization ability of PhiSRL.

arXiv commentThis preprint has been published in IEEE Transactions on Antennas and Propagation on 01 March 2023. Please cite the final published version as [T. Shan et al., "Physics-Informed Supervised Residual Learning for Electromagnetic Modeling," in IEEE Transactions on Antennas and Propagation, vol. 71, no. 4, pp. 3393-3407, April 2023, doi: 10.1109/TAP.2023.3245281]

References in corpus (18)

• Adam: A Method for Stochastic Optimization
• Very Deep Convolutional Networks for Large-Scale Image Recognition
• DeepXDE: A deep learning library for solving differential equations
• DGM: A deep learning algorithm for solving partial differential equations
• Deep Learning in Video Multi-Object Tracking: A Survey
• Deep neural network solution of the electronic Schrödinger equation
• Hamiltonian Neural Networks
• Stable Architectures for Deep Neural Networks
• Accelerating Eulerian Fluid Simulation With Convolutional Networks
• Neural Relational Inference for Interacting Systems
• PDE-Net: Learning PDEs from Data
• Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations
• MgNet: A Unified Framework of Multigrid and Convolutional Neural Network
• Symplectic Recurrent Neural Networks
• Convolutional Neural Networks combined with Runge-Kutta Methods
• To Fall Or Not To Fall: A Visual Approach to Physical Stability Prediction
• Neural Born Iteration Method For Solving Inverse Scattering Problems: 2D Cases
• Deep Residual Learning and PDEs on Manifold

Cited by in corpus (3)

• VBIM-Net: Variational Born Iterative Network for Inverse Scattering Problems
• Multi-frequency Neural Born Iterative Method for Solving 2-D Inverse Scattering Problems
• A Novel Highly Parallelizable Machine-Learning Based Method for the Fast Solution of Integral Equations for Electromagnetic Scattering Problems