Optimal design for kernel interpolation: Applications to uncertainty quantification
Narayan, Akil1,2; Yan, Liang3,4; Zhou, Tao5
AbstractThe 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.
KeywordKernel interpolation Fekete points Cholesky decomposition with pivoting Hermite interpolation Uncertainty quantification
Indexed BySCI
Funding ProjectNSF[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 Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000624309300008
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Document Type期刊论文
Corresponding AuthorYan, Liang
Affiliation1.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
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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.
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