{"title":"Universal Approximation Theorem and Deep Learning for the Solution of Frequency-Domain Electromagnetic Scattering Problems","authors":"Ji-Yuan Wang;Xiao-Min Pan","doi":"10.1109/TAP.2024.3476915","DOIUrl":null,"url":null,"abstract":"Unlike the universal approximation theorems for functions mapping from a real-valued (RV) vector to an 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 an 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 an RV vector to a CV number. A deep NN, named HV-DL, is designed accordingly, which consists of an RV input layer, an 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 2-D electric field integral equation (EFIE). To integrate the underlying physics of electromagnetic (EM) scattering into the proposed HV-DL, the loss function is computed according to the EFIE.","PeriodicalId":13102,"journal":{"name":"IEEE Transactions on Antennas and Propagation","volume":"72 12","pages":"9274-9285"},"PeriodicalIF":4.6000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Antennas and Propagation","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10719669/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
Unlike the universal approximation theorems for functions mapping from a real-valued (RV) vector to an 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 an 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 an RV vector to a CV number. A deep NN, named HV-DL, is designed accordingly, which consists of an RV input layer, an 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 2-D electric field integral equation (EFIE). To integrate the underlying physics of electromagnetic (EM) scattering into the proposed HV-DL, the loss function is computed according to the EFIE.
期刊介绍:
IEEE Transactions on Antennas and Propagation includes theoretical and experimental advances in antennas, including design and development, and in the propagation of electromagnetic waves, including scattering, diffraction, and interaction with continuous media; and applications pertaining to antennas and propagation, such as remote sensing, applied optics, and millimeter and submillimeter wave techniques