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

doi:10.1016/j.jcp.2022.111202

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	Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models
	Guo, Ling 1; Wu, Hao 2; Zhou, Tao 3
	2022-07-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	461 页码:18
摘要	We 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.
关键词	Data -driven modeling Normalizing flows Uncertainty quantification Random fields
DOI	10.1016/j.jcp.2022.111202
收录类别	SCI
语种	英语
资助项目	NSF 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研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000802129600002
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61518
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.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
推荐引用方式 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.