Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations

doi:10.1016/j.cma.2022.115523

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	Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations
	Guo, Ling 1; Wu, Hao 2,3,4; Yu, Xiaochen 4; Zhou, Tao 5
	2022-10-01
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	400 页码:17
摘要	We introduce a sampling-based machine learning approach, Monte Carlo fractional physics-informed neural networks (MC-fPINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of the physics-informed neural networks (PINNs), MC-fPINNs utilize a Monte Carlo approximation strategy to compute the fractional derivatives of the DNN outputs, and construct an unbiased estimation of the physical soft constraints in the loss function. Our sampling approach can yield lower overall computational cost compared to fPINNs proposed in Pang et al.(2019), hence it can solve high dimensional FPDEs at reasonable cost. We validate the performance of MC-fPINNs via several examples, including high dimensional integral fractional Laplacian equations, parametric identification of time-space fractional PDEs, and fractional diffusion equation with random inputs. The results show that MC-fPINNs are flexible and quite effective in tackling high dimensional FPDEs.(c) 2022 Elsevier B.V. All rights reserved.
关键词	Physics -informed neural networks Fractional Laplacian Nonlocal operators Uncertainty quantification
DOI	10.1016/j.cma.2022.115523
收录类别	SCI
语种	英语
资助项目	NSF of China[12071301] ; NSF of China[11671265] ; NSF of China[12171367] ; NSF of China[21JC1403700] ; NSF of China[2021SHZDZX0100] ; Shanghai Municipal Science and Technology Commission[11822111] ; Shanghai Municipal Science and Technology Commission[11688101] ; Shanghai Municipal Science and Technology Commission[20JC1412500] ; Shanghai Municipal Science and Technology Commission[20JC1413500] ; National Key R&D Program of China[2020YFA0712000] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA25010404]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000860353800002
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60945
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Hao
作者单位	1.Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China 2.Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai, Peoples R China 3.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China 4.Tongji Univ, Sch Math Sci, Shanghai, Peoples R China 5.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Guo, Ling,Wu, Hao,Yu, Xiaochen,et al. Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2022,400:17.
APA	Guo, Ling,Wu, Hao,Yu, Xiaochen,&Zhou, Tao.(2022).Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,400,17.
MLA	Guo, Ling,et al."Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 400(2022):17.