Adaptive sequential space-filling design for geostatistical simulations

Proper uncertainty quantification requires the construction of a large set of alternative Earth models. To overcome computational time, distance-based techniques have been recently used in the context of uncertainty quantification. However, they rely on the construction of hundreds of models, prior to the study. One difficulty is that there is no information a priori on the number of models that needs to be generated for accurate uncertainty quantification. This number will depend on the complexity of the test case and the response studied. In this paper, we present a new workflow for uncertainty quantification which aims at constructing models in an adaptive, intelligent manner. Starting with a few initial models, the method defines locations where new models should be constructed, in order to sample efficiently the space of uncertainty. The procedure is iterated until the uncertainty is stabilized, thus implicitly determining the required number of models. Preliminary results are presented on two different test cases, one of them having uncertainty in the input parameters. Results show that the proposed method results in a more accurate uncertainty quantification than the random generation of a set of models of similar size.