HiDeNN-TD: Reduced-order hierarchical deep learning neural networks

doi:10.1016/j.cma.2021.114414

IMECH-IR > 非线性力学国家重点实验室

	HiDeNN-TD: Reduced-order hierarchical deep learning neural networks
	Zhang L(张磊)1,2,3,4; Lu, Ye 3; Tang, Shaoqiang 1,2; Liu, Wing Kam 3
通讯作者	Tang, Shaoqiang(maotang@pku.edu.cn) ; Liu, Wing Kam(w-liu@northwestern.edu)
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
	2022-02-01
卷号	389 页码:33
ISSN	0045-7825
摘要	This paper presents a tensor decomposition (TD) based reduced-order model of the hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-TD method keeps advantages of both HiDeNN and TD methods. The automatic mesh adaptivity makes the HiDeNN-TD more accurate than the finite element method (FEM) and conventional proper generalized decomposition (PGD) and TD, using a fraction of the FEM degrees of freedom. This work focuses on the theoretical foundation of the method. Hence, the accuracy and convergence of the method have been studied theoretically and numerically, with a comparison to different methods, including FEM, PGD, TD, HiDeNN and Deep Neural Networks. In addition, we have theoretically shown that the PGD/TD converges to FEM at increasing modes, and the PGD/TD solution error is a summation of the mesh discretization error and the mode reduction error. The proposed HiDeNN-TD shows a high accuracy with orders of magnitude fewer degrees of freedom than FEM, and hence a high potential to achieve fast computations with a high level of accuracy for large-size engineering and scientific problems. As a trade-off between accuracy and efficiency, we propose a highly efficient solution strategy called HiDeNN-PGD. Although the solution is less accurate than HiDeNN-TD, HiDeNN-PGD still provides a higher accuracy than PGD/TD and FEM with only a small amount of additional cost to PGD. (c) 2021 Elsevier B.V. All rights reserved.
关键词	Hierarchical deep-learning neural networks Proper generalized decomposition Canonical tensor decomposition Reduced order finite element method Convergence study and error bound
DOI	10.1016/j.cma.2021.114414
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:000740320100004
关键词[WOS]	PARTIAL-DIFFERENTIAL-EQUATIONS ; COMPUTATIONAL-VADEMECUM ; DATA-DRIVEN ; ALGORITHM ; HOPGD
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
资助项目	National Natural Science Foundation of China[11890681] ; National Natural Science Foundation of China[11832001] ; National Natural Science Foundation of China[11521202] ; National Natural Science Foundation of China[11988102] ; National Science Foundation, USA[CMMI-1934367] ; National Science Foundation, USA[CMMI-1762035]
项目资助者	National Natural Science Foundation of China ; National Science Foundation, USA
论文分区	一类
力学所作者排名	1
RpAuthor	Tang, Shaoqiang ; Liu, Wing Kam
引用统计	被引频次：16[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/88276
专题	非线性力学国家重点实验室
作者单位	1.Peking Univ, Coll Engn, HEDPS, Beijing 100871, Peoples R China; 2.Peking Univ, Coll Engn, LTCS, Beijing 100871, Peoples R China; 3.Northwestern Univ, Dept Mech Engn, Evanston, IL 60208 USA; 4.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang L,Lu, Ye,Tang, Shaoqiang,et al. HiDeNN-TD: Reduced-order hierarchical deep learning neural networks[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2022,389:33.
APA	张磊,Lu, Ye,Tang, Shaoqiang,&Liu, Wing Kam.(2022).HiDeNN-TD: Reduced-order hierarchical deep learning neural networks.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,389,33.
MLA	张磊,et al."HiDeNN-TD: Reduced-order hierarchical deep learning neural networks".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 389(2022):33.

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