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

文献类型：期刊论文

作者Guo, Ling1; Wu, Hao2,3,4; Yu, Xiaochen4; Zhou, Tao5
刊名COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
出版日期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
DOI10.1016/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
WOS记录号WOS:000860353800002
出版者ELSEVIER SCIENCE SA
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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