We consider the problem of rapidly identifying, among a large set of candidate parameter fields, a subset of candidates whose responses computed by accurate forward flow and transport simulation match a reference response curve. In order to keep the number of calls to the flow simulator computationally tractable, a recent distance-based approach relying on fast proxy simulations is revisited, and turned into a non-stationary Kriging method. The covariance kernel is obtained by combining a classical kernel with the proxy function, hence generalizing the idea of random field deformation to high-dimensional Computer Experiments. Once the accurate simulator has been run for an initial subset of models and a Kriging metamodel has been inferred, the predictive distributions of misfits for the remaining geological models can be used as a guide to solve the inverse problem in a sequential way. The proposed algorithm, Proxy-based Kriging for Sequential Inversion (PROKSI), relies indeed on a variant of the Expected Improvement, a popular criterion for Kriging-based global optimization. A statistical benchmark of ProKSI's performances finally illustrates the efficiency and the robustness of the approach when using different kinds of proxies.
