Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimiza-tion method (EnOpt), the simplex gradient method (SG), and the stochastic simplex approximate gradient method (StoSAG), approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increas-ingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator, but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control vari-ables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save the comp…