Multi-output local Gaussian process regression: Applications to uncertainty quantification

We develop an efficient, Bayesian Uncertainty Quantification framework using a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Exper...

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Bibliographic Details
Published in:Journal of computational physics 2012-07, Vol.231 (17), p.5718-5746
Main Authors: Bilionis, Ilias, Zabaras, Nicholas
Format: Article
Language:English
Subjects:
Adaptivity
Bayesian
Bayesian analysis
Computational techniques
Construction
Discontinuity
Exact sciences and technology
Gaussian
Gaussian process
Mathematical methods in physics
Mathematical models
Multi-element
Multi-output
Physics
Statistics
Stochastic partial differential equations
Trees
Uncertainty
Uncertainty quantification
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Summary:We develop an efficient, Bayesian Uncertainty Quantification framework using a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Experimental Design techniques in order to learn a multi-output Gaussian process. The constructed surrogate can provide analytical point estimates, as well as error bars, for the statistics of interest. We numerically demonstrate the effectiveness of the suggested framework in identifying discontinuities, local features and unimportant dimensions in the solution of stochastic differential equations.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2012.04.047