中文版 | English
Title

A data-driven model reduction method for parabolic inverse source problems and its convergence analysis

Author
Corresponding AuthorZhang, Wenlong; Zhang, Zhiwen
Publication Years
2023-08-15
DOI
Source Title
ISSN
0021-9991
EISSN
1090-2716
Volume487
Abstract
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems with uncertain data efficiently. Our method consists of offline and online stages. In the offline stage, we explore the low-dimensional structures in the solution space of parabolic partial differential equations (PDEs) in the forward problems with a given class of source functions and construct a small number of proper orthogonal decomposition (POD) basis functions to achieve significant dimension reduction. Equipped with the POD basis functions, we can solve the forward problems extremely fast in the online stage. Thus, we develop a fast algorithm to solve the optimization problem in parabolic inverse source problems, which is referred to as the POD method. Moreover, we design an a posteriori algorithm to find the optimal regularization parameter in the optimization problem using the proposed POD method without knowing the noise level. Under a weak regularity assumption on the solution of the parabolic PDEs, we prove the convergence of the POD method in solving the forward parabolic PDEs. In addition, we obtain the error estimate of the POD method for parabolic inverse source problems. Finally, we present numerical examples to demonstrate the accuracy and efficiency of the proposed method. Numerical results show that the POD method provides considerable computational savings over the finite element method while maintaining the same accuracy.(c) 2023 Elsevier Inc. All rights reserved.
Keywords
URL[Source Record]
Indexed By
Language
English
SUSTech Authorship
Corresponding
Funding Project
Shenzhen Sci-Tech Fund[17300318] ; Hong Kong RGC["17307921","11901282"] ; null[RCBS20200714114941241] ; null[12171406]
WOS Research Area
Computer Science ; Physics
WOS Subject
Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS Accession No
WOS:000990548800001
Publisher
ESI Research Field
PHYSICS
Data Source
Web of Science
Citation statistics
Cited Times [WOS]:0
Document TypeJournal Article
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/534752
DepartmentDepartment of Mathematics
Affiliation
1.Univ Chicago, Dept Stat, Chicago, IL 60637 USA
2.Univ Chicago, CCAM, Chicago, IL 60637 USA
3.Southern Univ Sci & Technol SUSTech, Dept Math, 1088 Xueyuan Blvd, Shenzhen, Guangdong, Peoples R China
4.Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Peoples R China
Corresponding Author AffilicationDepartment of Mathematics
Recommended Citation
GB/T 7714
Wang, Zhongjian,Zhang, Wenlong,Zhang, Zhiwen. A data-driven model reduction method for parabolic inverse source problems and its convergence analysis[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2023,487.
APA
Wang, Zhongjian,Zhang, Wenlong,&Zhang, Zhiwen.(2023).A data-driven model reduction method for parabolic inverse source problems and its convergence analysis.JOURNAL OF COMPUTATIONAL PHYSICS,487.
MLA
Wang, Zhongjian,et al."A data-driven model reduction method for parabolic inverse source problems and its convergence analysis".JOURNAL OF COMPUTATIONAL PHYSICS 487(2023).
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