Current density impedance imaging with PINNs

In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization. This method constructs a physics-informed loss function by merging the regularized least-squares output functional with an underlying differential equa...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 452; p. 116120
Main Authors Duan, Chenguang, Huang, Junjun, Jiao, Yuling, Lu, Xiliang, Yang, Jerry Zhijian
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.12.2024
Subjects
CDII
EIT
Inverse problems
Neural networks
PINNs
EIT
Inverse problems
PINNs
Neural networks
CDII
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Summary:In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization. This method constructs a physics-informed loss function by merging the regularized least-squares output functional with an underlying differential equation, which describes the relationship between the conductivity and voltage. A pair of neural networks representing the conductivity and voltage, respectively, are coupled by this loss function. Then, minimizing the loss function provides a reconstruction. A rigorous theoretical guarantee is provided. We give an error analysis for CDII-PINNs and establish a convergence rate, based on prior selected neural network parameters in terms of the number of samples. The numerical simulations demonstrate that CDII-PINNs are efficient, accurate and robust to noise levels ranging from 1% to 20%.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2024.116120