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

共 50 条

[21] Space Efficient Quantization for Deep Convolutional Neural Networks
Zhao, Dong-Di
Li, Fan
Sharif, Kashif
Xia, Guang-Min
Wang, Yu
JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY, 2019, 34 (02) : 305 - 317
[22] Quantifying Degradations of Convolutional Neural Networks in Space Environments
Altland, Emily
Castellanos, Jonathan
Detwiler, Joshua
Fermin, Paolo
Ferra, Raquel
Kelly, Conor
Latoski, Casey
Ma, Tiffany
Maher, Thomas
Kuzin, Julia Mahon
Mohammadian, Ali
Abdalla, Abdelrahman Said
Headley, William C.
Michaels, Alan J.
2019 IEEE COGNITIVE COMMUNICATIONS FOR AEROSPACE APPLICATIONS WORKSHOP (CCAAW), 2019,
[23] Face Space Representations in Deep Convolutional Neural Networks
O'Toole, Alice J.
Castillo, Carlos D.
Parde, Connor J.
Hill, Matthew Q.
Chellappa, Rama
TRENDS IN COGNITIVE SCIENCES, 2018, 22 (09) : 794 - 809
[24] Space Efficient Quantization for Deep Convolutional Neural Networks
Dong-Di Zhao
Fan Li
Kashif Sharif
Guang-Min Xia
Yu Wang
Journal of Computer Science and Technology, 2019, 34 : 305 - 317
[25] Grounding Psychological Shape Space in Convolutional Neural Networks
Bechberger, Lucas
Kuhnberger, Kai-Uwe
SOFTWARE ENGINEERING AND FORMAL METHODS: SEFM 2021 COLLOCATED WORKSHOPS, 2022, 13230 : 86 - 106
[26] Effective Version Space Reduction for Convolutional Neural Networks
Liu, Jiayu
Chiotellis, Ioannis
Triebel, Rudolph
Cremers, Daniel
MACHINE LEARNING AND KNOWLEDGE DISCOVERY IN DATABASES, ECML PKDD 2020, PT II, 2021, 12458 : 85 - 100
[27] Shallow Convolutional Neural Networks for Pattern Recognition Problems
Gorokhovatskyi, Oleksii
Peredrii, Olena
2018 IEEE SECOND INTERNATIONAL CONFERENCE ON DATA STREAM MINING & PROCESSING (DSMP), 2018, : 459 - 463
[28] DEEP CONVOLUTIONAL NEURAL NETWORKS IN SEISMIC EXPLORATION PROBLEMS
Vasyukov, A. V.
Nikitin, I. S.
Stankevich, A. S.
Golubev, V. I.
INTERFACIAL PHENOMENA AND HEAT TRANSFER, 2022, 10 (03) : 61 - 74
[29] Deep convolutional neural networks for eigenvalue problems in mechanics
Finol, David
Lu, Yan
Mahadevan, Vijay
Srivastava, Ankit
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2019, 118 (05) : 258 - 275
[30] NETT: solving inverse problems with deep neural networks
Li, Housen
Schwab, Johannes
Antholzer, Stephan
Haltmeier, Markus
INVERSE PROBLEMS, 2020, 36 (06)

← 1 2 3 4 5 →