TY - JOUR
T1 - Distance-based kriging relying on proxy simulations for inverse conditioning
AU - Ginsbourger, David
AU - Rosspopoff, Bastien
AU - Pirot, Guillaume
AU - Durrande, Nicolas
AU - Renard, Philippe
PY - 2013/2
Y1 - 2013/2
N2 - 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.
AB - 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.
KW - Design of numerical experiments
KW - Inverse problem
KW - Proxy-based distances
KW - Kriging
KW - Metamodels
KW - Optimization
KW - FLUVIOGLACIAL AQUIFER ANALOG
KW - BAYESIAN CALIBRATION
KW - OPTIMIZATION
KW - ALGORITHM
KW - FIELD
U2 - 10.1016/j.advwatres.2012.11.019
DO - 10.1016/j.advwatres.2012.11.019
M3 - Article
SN - 0309-1708
VL - 52
SP - 275
EP - 291
JO - Advances in Water Resources
JF - Advances in Water Resources
ER -