The Library
Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap
Tools
Xing, Wei, Shah, Akeel A. and Nair, P. B. (2014) Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 471 (2174). 20140697. doi:10.1098/rspa.2014.0697 ISSN 1364-5021.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1098/rspa.2014.0697
Abstract
In this paper, Isomap and kernel Isomap are used to dramatically reduce the dimensionality of the output space to efficiently construct a Gaussian process emulator of parametrized partial differential equations. The output space consists of spatial or spatio-temporal fields that are functions of multiple input variables. For such problems, standard multi-output Gaussian process emulation strategies are computationally impractical and/or make restrictive assumptions regarding the correlation structure. The method we develop can be applied without modification to any problem involving vector-valued targets and vector-valued inputs. It also extends a method based on linear dimensionality reduction to response surfaces that cannot be described accurately by a linear subspace of the high dimensional output space. Comparisons to the linear method are made through examples that clearly demonstrate the advantages of nonlinear dimensionality reduction.
Item Type: | Journal Article | ||||||
---|---|---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||
Journal or Publication Title: | Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences | ||||||
Publisher: | Royal Society Publishing | ||||||
ISSN: | 1364-5021 | ||||||
Official Date: | 2014 | ||||||
Dates: |
|
||||||
Volume: | 471 | ||||||
Number: | 2174 | ||||||
Article Number: | 20140697 | ||||||
DOI: | 10.1098/rspa.2014.0697 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |