南方科技大学知识苑(SUSTech KC): A Local Deep Learning Method for Solving High Order Partial Differential Equations

题名	A Local Deep Learning Method for Solving High Order Partial Differential Equations
作者	Jiang Yang; Quanhui Zhu
发表日期	2021-09
DOI	10.4208/nmtma.OA-2021-0035
发表期刊	Numerical Mathematics-Theory Methods and Applications 影响因子和分区
ISSN	1004-8979
EISSN	2079-7338
摘要	At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly, and high order derivatives lack robustness for training purposes. We propose a novel approach to solving PDEs with high order derivatives by simultaneously ap proximating the function value and derivatives. We introduce intermediate variables to rewrite the PDEs into a system of low order differential equations as what is done in the local discontinuous Galerkin method. The intermediate variables and the so lutions to the PDEs are simultaneously approximated by a multi-output deep neural network. By taking the residual of the system as a loss function, we can optimize the network parameters to approximate the solution. The whole process relies on low order derivatives. Numerous numerical examples are carried out to demon strate that our local deep learning is effificient, robust, flflexible, and is particularly well-suited for high-dimensional PDEs with high order derivatives.
关键词	Deep Learning Deep Neural Network High Order Pdes Reduction Of Order Deep Galerkin Method
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	第一
资助项目	National Natural Science Foundation of China/Hong Kong RRC Joint Research Scheme[NSFC/RGC 11961160718] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001] ; National Science Foundation of China[NSFC-11871264] ; Guangdong Basic and Applied Basic Research Foundation[2018A0303130123]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000723826100001
出版者	GLOBAL SCIENCE PRESS
来源库	人工提交
引用统计	被引频次[WOS]：10
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/256943
专题	南方科技大学理学院_数学系
作者单位	Southern University of Science and Technology
第一作者单位	南方科技大学
第一作者的第一单位	南方科技大学
推荐引用方式 GB/T 7714	Jiang Yang,Quanhui Zhu. A Local Deep Learning Method for Solving High Order Partial Differential Equations[J]. Numerical Mathematics-Theory Methods and Applications,2021.
APA	Jiang Yang,&Quanhui Zhu.(2021).A Local Deep Learning Method for Solving High Order Partial Differential Equations.Numerical Mathematics-Theory Methods and Applications.
MLA	Jiang Yang,et al."A Local Deep Learning Method for Solving High Order Partial Differential Equations".Numerical Mathematics-Theory Methods and Applications (2021).

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