Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity

doi:10.1016/j.cma.2023.116356

IMECH-IR > 非线性力学国家重点实验室

	Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity
	Zhang, Lei 1,2; Park, Chanwook 3; Lu, Ye 4; Li, Hengyang 3; Mojumder, Satyajit 5; Saha, Sourav 5; Guo, Jiachen 5; Li, Yangfan 3; Abbott, Trevor 3; Wagner, Gregory J.3; Tang, Shaoqiang 6; Liu, Wing Kam 3
通讯作者	Liu, Wing Kam(w-liu@northwestern.edu)
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
	2023-12-15
卷号	417 页码:46
ISSN	0045-7825
摘要	We are witnessing a rapid transition from Software 1.0 to 2.0. Software 1.0 focuses on manually designed algorithms, while Software 2.0 leverages data and machine learning algorithms (or artificial intelligence) for optimized, fast, and accurate solutions. For the past few years, we have been developing Convolution Hierarchical Deep-learning Neural Network Artificial Intelligence (C-HiDeNN-AI), which enables the realization of Engineering Software 2.0 by opening the next-generation neural network-based computational tools that can simultaneously train data and solve mechanistic equations. This paper focuses on solving partial differential equations with C-HiDeNN. Still, the same neural network can be used for training and calibration with experimental data, which will be discussed in a separate paper. This paper presents a computational framework combining the C-HiDeNN theory with isogeometric analysis (IGA), called Convolution IGA (C-IGA). C-IGA has five key features that advance IGA: (1) arbitrarily high-order smoothness and convergence rates without increasing degrees of freedom; (2) a Kronecker delta property that enables direct imposition of Dirichlet boundary conditions; (3) automatic and flexible global/local mesh-adaptivity with built-in length scale control and adjustable radial basis functions; (4) ability to handle irregular meshes and triangular/tetrahedral elements; and (5) GPU implementation that speeds up the program as fast as finite element method (FEM). Mathematically, we prove that both IGA and C-IGA mappings are equivalent, and by taking a special design and modified anchors as nodes, C-IGA degenerates to IGA. We demonstrate the accuracy, convergence rates, mesh-adaptivity, and performance of C-IGA with several 1D, 2D, and 3D numerical examples. The future applications of C-IGA from topology optimization to product manufacturing with multi-GPU programming are discussed.(c) 2023 Elsevier B.V. All rights reserved.
关键词	Convolution isogeometric analysis (C-IGA) Convolution hierarchical deep-learning neural network (C-hiDeNN) Software 2.0 r-h-p-s-a adaptive finite element method (FEM) High-order smoothness and convergence
DOI	10.1016/j.cma.2023.116356
收录类别	SCI
语种	英语
WOS记录号	WOS:001114199100001
关键词[WOS]	ELEMENT-METHOD ; VOLUME PARAMETERIZATION ; NURBS
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
引用统计
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/93632
专题	非线性力学国家重点实验室
通讯作者	Liu, Wing Kam
作者单位	1.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China 3.Northwestern Univ, Dept Mech Engn, Evanston, IL 60208 USA 4.Univ Maryland Baltimore Cty, Dept Mech Engn, Baltimore, MD 21250 USA 5.Northwestern Univ, Theoret & Appl Mech Program, Evanston, IL USA 6.Peking Univ, Coll Engn, HEDPS & LTCS, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Lei,Park, Chanwook,Lu, Ye,et al. Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2023,417:46.
APA	Zhang, Lei.,Park, Chanwook.,Lu, Ye.,Li, Hengyang.,Mojumder, Satyajit.,...&Liu, Wing Kam.(2023).Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,417,46.
MLA	Zhang, Lei,et al."Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 417(2023):46.

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