Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

doi:10.4208/cicp.OA-2020-0219

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	Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
	Liao, Yulei 1,2; Ming, Pingbing 1,2
	2021-05-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	29 期号:5 页码:1365-1384
摘要	We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functions representing by deep neural networks are non-interpolatory, which makes the enforcement of the essential boundary conditions a nontrivial matter. Our method resorts to Nitsche?s variational formulation to deal with this difficulty, which is consistent, and does not require significant extra computational costs. We prove the error estimate in the energy norm and illustrate the method on several representative problems posed in at most 100 dimension.
关键词	Deep Nitsche Method Deep Ritz Method neural network approximation mixed boundary conditions curse of dimensionality
DOI	10.4208/cicp.OA-2020-0219
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971467] ; Beijing Academy of Artificial Intelligence (BAAI)
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000633053700003
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58406
专题	中国科学院数学与系统科学研究院
通讯作者	Ming, Pingbing
作者单位	1.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, 55 East Rd Zhong Guan Cun, 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	Liao, Yulei,Ming, Pingbing. Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2021,29(5):1365-1384.
APA	Liao, Yulei,&Ming, Pingbing.(2021).Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,29(5),1365-1384.
MLA	Liao, Yulei,et al."Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 29.5(2021):1365-1384.