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

文献类型：期刊论文

作者Zhang L(张磊)1,2,3,4; Lu, Ye2; Tang, Shaoqiang3,4; Liu, Wing Kam2
刊名COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
出版日期2022-02-01
卷号389页码:33
关键词Hierarchical deep-learning neural networks Proper generalized decomposition Canonical tensor decomposition Reduced order finite element method Convergence study and error bound
ISSN号0045-7825
DOI10.1016/j.cma.2021.114414
通讯作者Tang, Shaoqiang(maotang@pku.edu.cn) ; Liu, Wing Kam(w-liu@northwestern.edu)
英文摘要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.
分类号一类
WOS关键词PARTIAL-DIFFERENTIAL-EQUATIONS ; COMPUTATIONAL-VADEMECUM ; DATA-DRIVEN ; ALGORITHM ; HOPGD
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]
WOS研究方向Engineering ; Mathematics ; Mechanics
语种英语
WOS记录号WOS:000740320100004
资助机构National Natural Science Foundation of China ; National Science Foundation, USA
其他责任者Tang, Shaoqiang ; Liu, Wing Kam
源URL[http://dspace.imech.ac.cn/handle/311007/88275]  
专题力学研究所_非线性力学国家重点实验室
作者单位1.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China
2.Northwestern Univ, Dept Mech Engn, Evanston, IL 60208 USA;
3.Peking Univ, Coll Engn, LTCS, Beijing 100871, Peoples R China;
4.Peking Univ, Coll Engn, HEDPS, Beijing 100871, 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.

入库方式： OAI收割

来源：力学研究所

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