Optimal design for kernel interpolation: Applications to uncertainty quantification

doi:10.1016/j.jcp.2020.110094

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	Optimal design for kernel interpolation: Applications to uncertainty quantification
	Narayan, Akil 1,2; Yan, Liang 3,4; Zhou, Tao 5
	2021-04-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	430 页码:19
摘要	The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we propose a type of quasi-optimal interpolation points, searching from a large set of candidate points, using a procedure similar to designing Fekete points or power function maximizing points that use pivot from a Cholesky decomposition. The proposed quasi-optimal points results in smaller condition number, and thus mitigates the instability of the interpolation procedure when the number of points becomes large. Applications to parametric uncertainty quantification are presented, and it is shown that the proposed interpolation method can outperform sparse grid methods in many interesting cases. We also demonstrate the new procedure can be applied to constructing gradient-enhanced Gaussian process emulators. (C) 2021 Elsevier Inc. All rights reserved.
关键词	Kernel interpolation Fekete points Cholesky decomposition with pivoting Hermite interpolation Uncertainty quantification
DOI	10.1016/j.jcp.2020.110094
收录类别	SCI
语种	英语
资助项目	NSF[DMS-1848508] ; AFOSR[FA9550-20-1-0338] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[11731006] ; NSF of China[11771081] ; Southeast University Zhishan Young Scholars Program ; National Key R&D Program of China[2020YFA0712000] ; Science Challenge Project[TZ2018001] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA25000404] ; Youth Innovation Promotion Association, CAS
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000624309300008
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/58358
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Liang
作者单位	1.Univ Utah, Dept Math, Salt Lake City, UT 84112 USA 2.Univ Utah, Sci Comp & Imaging Inst, Salt Lake City, UT 84112 USA 3.Southeast Univ, Sch Math, Nanjing 210096, Peoples R China 4.Nanjing Ctr Appl Math, Nanjing 211135, Peoples R China 5.Chinese Acad Sci, Inst Computat Math, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Narayan, Akil,Yan, Liang,Zhou, Tao. Optimal design for kernel interpolation: Applications to uncertainty quantification[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2021,430:19.
APA	Narayan, Akil,Yan, Liang,&Zhou, Tao.(2021).Optimal design for kernel interpolation: Applications to uncertainty quantification.JOURNAL OF COMPUTATIONAL PHYSICS,430,19.
MLA	Narayan, Akil,et al."Optimal design for kernel interpolation: Applications to uncertainty quantification".JOURNAL OF COMPUTATIONAL PHYSICS 430(2021):19.