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

[31] TO BE OR NOT TO BE STABLE, THAT IS THE QUESTION: UNDERSTANDING NEURAL NETWORKS FOR INVERSE PROBLEMS
Evangelista, Davide
Piccolomini, Elena loli
Morotti, Elena
Nagy, James g.
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2025, 47 (01): : C77 - C99
[32] Neural Networks for Inverse Problems: the Microwave Imaging Case
Franceschini, S.
Ambrosanio, M.
Baselice, F.
Pascazio, V
2021 15TH EUROPEAN CONFERENCE ON ANTENNAS AND PROPAGATION (EUCAP), 2021,
[33] Applications of Topological Derivatives and Neural Networks for Inverse Problems
Grzanek, Marta
Szulc, Katarzyna
SYSTEM MODELING AND OPTIMIZATION, 2009, 312 : 268 - +
[34] Application of Neural Networks in Nonlinear Inverse Problems of Geophysics
E. A. Obornev
I. E. Obornev
E. A. Rodionov
M. I. Shimelevich
Computational Mathematics and Mathematical Physics, 2020, 60 : 1025 - 1036
[35] Application of Neural Networks in Nonlinear Inverse Problems of Geophysics
Obornev, E. A.
Obornev, I. E.
Rodionov, E. A.
Shimelevich, M. I.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2020, 60 (06) : 1025 - 1036
[36] Finite element neural networks for electromagnetic inverse problems
Ramuhalli, P
Udpa, L
Udpa, S
REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION, VOLS 21A & B, 2002, 615 : 728 - 735
[37] Topological derivative and training neural networks for inverse problems
Jackowska-Strumillo, L
Sokolowski, J
Zochowski, A
ARTIFICIAL NEURAL NETWORKS: FORMAL MODELS AND THEIR APPLICATIONS - ICANN 2005, PT 2, PROCEEDINGS, 2005, 3697 : 391 - 396
[38] Artificial neural networks for inverse heat transfer problems
Cortes, Obed
Urquiza, Gustavo
Hernandez, J. A.
Cruz, Marco A.
CERMA 2007: ELECTRONICS, ROBOTICS AND AUTOMOTIVE MECHANICS CONFERENCE, PROCEEDINGS, 2007, : 198 - +
[39] Artificial neural networks and inverse problems of optical diagnostics
Abrukov, Victor S.
Troeshestova, Daria A.
ISDA 2006: SIXTH INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS DESIGN AND APPLICATIONS, VOL 1, 2006, : 850 - 855
[40] Inverse-Based Approach to Explaining and Visualizing Convolutional Neural Networks
Kwon, Hyuk Jin
Koo, Hyung Il
Soh, Jae Woong
Cho, Nam Ik
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2022, 33 (12) : 7318 - 7329

← 1 2 3 4 5 →