D3M: A Deep Domain Decomposition Method for Partial Differential Equations

doi:10.1109/ACCESS.2019.2957200

	D3M: A Deep Domain Decomposition Method for Partial Differential Equations
	Ke Li1,2,3 ; Kejun Tang1,2,3 ; Tianfan Wu 4; Qifeng Liao1
	2020
发表期刊	IEEE ACCESS (IF:3.4[JCR-2023],3.7[5-Year])
ISSN	2169-3536
卷号	8
发表状态	已发表
DOI	10.1109/ACCESS.2019.2957200
摘要	A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems. Our analysis shows that the D3M approximation solution converges to the exact solution of the underlying PDEs. The accuracy and the efficiency of D3M are validated and demonstrated with numerical experiments.
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收录类别	SCI ; SCIE ; EI
来源库	IEEE
引用统计	被引频次：80[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/104514
专题	信息科学与技术学院_硕士生信息科学与技术学院_PI研究组_廖奇峰组信息科学与技术学院_博士生
作者单位	1.School of Information Science and Technology, ShanghaiTech University, Shanghai, China 2.Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China 3.University of Chinese Academy of Sciences, Beijing, China 4.Viterbi School of Engineering, University of Southern California, Los Angeles, USA
第一作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Ke Li,Kejun Tang,Tianfan Wu,et al. D3M: A Deep Domain Decomposition Method for Partial Differential Equations[J]. IEEE ACCESS,2020,8.
APA	Ke Li,Kejun Tang,Tianfan Wu,&Qifeng Liao.(2020).D3M: A Deep Domain Decomposition Method for Partial Differential Equations.IEEE ACCESS,8.
MLA	Ke Li,et al."D3M: A Deep Domain Decomposition Method for Partial Differential Equations".IEEE ACCESS 8(2020).