Physics-informed Deep Learning to Solve Electromagnetic Scattering Problems

Wang, Jiyuan; Li, Yuzhao; Xue, Bo-Wen; Pan, Xiao‐Min

doi:10.1109/cama56352.2022.10002575

Cited by 1 publication

(1 citation statement)

References 8 publications

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“…Such integration has been shown its accuracy, reliability, and interpretability of predictions in various applications [4]- [9]. When DL is taken as a numerical solver, including a computational electromagnetic (EM) one, NNs are typically regarded as function approximators [10]- [14], functional approximators [15]- [20] or operator approximators [21], [22]. In this work, we are interested in taking NNs as function approximators where the EM data is regarded as the function with respect to the spatial coordinate.…”

Section: Introductionmentioning

confidence: 99%

Universal Approximation Theorem and Deep Learning for the Solution of Frequency Domain Electromagnetic Scattering Problems

Wang,

Pan

2024

Preprint

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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.

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