Improvements to Multifidelity Functional Surrogates Construction for Fast Uncertainty Quantification in Reservoir Simulation

In this work we propose a novel procedure for covariance identification, based on the cross-validation of the correlation between primary and secondary responses within the context of multi-fidelity functional surrogate for uncertainty quantification. The method is validated on a synthetic reservoir model of realistic size and complexity. The outputs are obtained by simulating two different levels of fidelity, referred to as FINE level (or high-fidelity) and COARSE level (or low-fidelity). These outputs are considered as the realizations of a stochastic process and are used for the surrogate construction, by means of the Universal Trace-Cokriging approach. This method incorporates the information embedded in both the primary (FINE) and the secondary (COARSE) data. We show that the surrogate accurately predicts outputs at unknown points of the uncertainty space, but its construction requires a consistently reduced computational effort with respect to the single-fidelity Trace Kriging predictor. As a further contribution we introduce two possible transformation strategies for the analysis of simulator outputs characterized by complex functional shapes.