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

	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
刊名	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
	2022-10-01
卷号	400 页码:17
关键词	Physics -informed neural networks Fractional Laplacian Nonlocal operators Uncertainty quantification
ISSN号	0045-7825
DOI	10.1016/j.cma.2022.115523
英文摘要	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.
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
语种	英语
出版者	ELSEVIER SCIENCE SA
WOS记录号	WOS:000860353800002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60944]
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.