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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

文献类型：期刊论文

作者Liao, Yulei1,2; Ming, Pingbing1,2
刊名COMMUNICATIONS IN COMPUTATIONAL PHYSICS
出版日期2021-05-01
卷号29期号:5页码:1365-1384
关键词Deep Nitsche Method Deep Ritz Method neural network approximation mixed boundary conditions curse of dimensionality
ISSN号1815-2406
DOI10.4208/cicp.OA-2020-0219
英文摘要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.
资助项目National Natural Science Foundation of China[11971467] ; Beijing Academy of Artificial Intelligence (BAAI)
WOS研究方向Physics
语种英语
WOS记录号WOS:000633053700003
出版者GLOBAL SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58405]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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