Distance-based kriging relying on proxy simulations for inverse conditioning

David Ginsbourger, Bastien Rosspopoff, Guillaume Pirot, Nicolas Durrande, Philippe Renard

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


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. (C) 2012 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)275-291
Number of pages17
JournalAdvances in Water Resources
Publication statusPublished - Feb 2013
Externally publishedYes


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