Distance-based kriging relying on proxy simulations for inverse conditioning

Ginsbourger, David; Rosspopoff, Bastien; Pirot, Guillaume; Durrande, Nicolas; Renard, Philippe (2013). Distance-based kriging relying on proxy simulations for inverse conditioning. Advances in water ressources, 52, pp. 275-291. Elsevier 10.1016/j.advwatres.2012.11.019

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Let us consider a large set of candidate parameter fields, such as hydraulic conductivity maps, on which we can run an accurate forward flow and transport simulation. We address the issue of rapidly identifying a subset of candidates whose response best match a reference response curve. In order to keep the number of calls to the accurate flow simulator computationally tractable, a recent distance-based approach relying on fast proxy simulations is revisited, and turned into a non-stationary kriging method where the covariance kernel is obtained by combining a classical kernel with the proxy. Once the accurate simulator has been run for an initial subset of parameter fields and a kriging metamodel has been inferred, the predictive distributions of misfits for the remaining parameter fields can be used as a guide to select candidate parameter fields in a sequential way. The proposed algorithm, Proxy-based Kriging for Sequential Inversion (ProKSI), relies on a variant of the Expected Improvement, a popular criterion for kriging-based global optimization. A statistical benchmark of ProKSI’s performances illustrates the efficiency and the robustness of the approach when using different kinds of proxies.

Item Type:

Journal Article (Original Article)


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

UniBE Contributor:

Ginsbourger, David, Rosspopoff, Bastien


500 Science > 510 Mathematics
500 Science > 550 Earth sciences & geology








Lutz Dümbgen

Date Deposited:

01 Apr 2014 02:42

Last Modified:

05 Dec 2022 14:28

Publisher DOI:




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