Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 471, Issue 2174, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2014.0697
Keywords
parametrized partial differential equations; emulators; Gaussian process regression; Isomap; Kernel Isomap
Categories
Funding
- Chinese Scholarship Council
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available