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Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

Guo, Ling1; Wu, Hao2; Zhou, Tao3
2022-07-15
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume461Pages:18
AbstractWe introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a Gaussian random field with the Karhunen-Loeve (KL) expansion structure and the target stochastic field, where the KL expansion coefficients and the invertible networks are trained by maximizing the sum of the log-likelihood on scattered measurements. This NFF model can be used to solve data-driven forward, inverse, and mixed forward/inverse stochastic partial differential equations in a unified framework. We demonstrate the capability of the proposed NFF model for learning non-Gaussian processes and different types of stochastic partial differential equations. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
KeywordData -driven modeling Normalizing flows Uncertainty quantification Random fields
DOI10.1016/j.jcp.2022.111202
Indexed BySCI
Language英语
Funding ProjectNSF of China[12071301] ; NSF of China[11671265] ; NSF of China[11822111] ; NSF of China[2020YFA0712000] ; NSF of China[XDA25010404] ; Shanghai Municipal Science and Technology Commission[12171367] ; 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[21JC1403700] ; Strategic Priority Research Program of Chinese Academy of Sciences[2021SHZDZX0100]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000802129600002
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61518
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWu, Hao
Affiliation1.Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China
2.Tongji Univ, Sch Math Sci, Shanghai, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Guo, Ling,Wu, Hao,Zhou, Tao.

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,461:18.
APA Guo, Ling,Wu, Hao,&Zhou, Tao.(2022).

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

.JOURNAL OF COMPUTATIONAL PHYSICS,461,18.
MLA Guo, Ling,et al."

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

".JOURNAL OF COMPUTATIONAL PHYSICS 461(2022):18.
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