CONVOLUTIONAL NEURAL NETWORKS IN PHASE SPACE AND INVERSE PROBLEMS

被引：1

作者：

Uhlmann, Gunther ^{[1
,2
]}

Wang, Yiran ^{[3
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Hong Kong Univ Sci & Technol, Inst Adv Study, Clear Water Bay, Hong Kong, Peoples R China

[3] Emory Univ, Dept Math, Atlanta, GA 30322 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2020年 / 80卷 / 06期

关键词：

convolutional neural networks; inverse problems; MULTILAYER FEEDFORWARD NETWORKS; PROGRESSING WAVES; SINGULARITIES; EQUATIONS;

D O I：

10.1137/19M1294484

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study inverse problems consisting of determining medium properties using the responses to probing waves from the machine learning point of view. Based on the analysis of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network to reconstruct the coefficients of nonlinear wave equations that model the medium properties. Furthermore, for given approximation accuracy, we obtain the depth and number of units of the network and their quantitative dependence on the complexity of the medium.

引用

页码：2560 / 2585

页数：26

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