INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems

doi:10.1016/j.jcp.2022.111588

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	INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems
	Wu, Sidi 1,2; Lu, Benzhuo 1,2
	2022-12-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	470 页码:18
摘要	Machine learning has been successfully applied to various fields in computational science and engineering. In this paper, we propose interfaced neural networks (INNs) to solve interface problems with discontinuous coefficients as well as irregular interfaces. Unlike using a single network, which has been found to be almost unable to retain the inherent properties of interface problems, INN decomposes the computational domain into several subdomains according to the interface and leverages multiple networks, each of which is responsible for the solution on one subdomain. An extended multiple-gradient descent (MGD) method is introduced during the training phase, which utilizes multiple -gradient information to adaptively balance the interplay between different terms in the loss function. The effectiveness, accuracy and robustness of the proposed framework are demonstrated through a collection of interface problems in two and three spatial dimensions, including a moving interface case. (C) 2022 Elsevier Inc. All rights reserved.
关键词	Interface problems Multiple-gradient descent Neural network PDEs
DOI	10.1016/j.jcp.2022.111588
收录类别	SCI
语种	英语
资助项目	Nan Ji, Sheng Gui ; National Natural Science Foundation of China[11771435] ; National Natural Science Foundation of China[22073110]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000864475500012
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60857
专题	中国科学院数学与系统科学研究院
通讯作者	Lu, Benzhuo
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wu, Sidi,Lu, Benzhuo. INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,470:18.
APA	Wu, Sidi,&Lu, Benzhuo.(2022).INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems.JOURNAL OF COMPUTATIONAL PHYSICS,470,18.
MLA	Wu, Sidi,et al."INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems".JOURNAL OF COMPUTATIONAL PHYSICS 470(2022):18.