A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

Picheny, Victor; Ginsbourger, David (2013). A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations. SIAM/ASA Journal on Uncertainty Quantification, 1(1), pp. 57-78. Society for Industrial and Applied Mathematics 10.1137/120882834

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In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ginsbourger, David

Subjects:

500 Science > 510 Mathematics

ISSN:

2166-2525

Publisher:

Society for Industrial and Applied Mathematics

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

12 Mar 2014 08:57

Last Modified:

10 Feb 2016 02:03

Publisher DOI:

10.1137/120882834

BORIS DOI:

10.7892/boris.41519

URI:

https://boris.unibe.ch/id/eprint/41519

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