We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the optimal design theory that the quality of sample-based approximations is affected by the distribution of the samples. We therefore evaluate six different sampling strategies to optimization of a high-dimensional analytical benchmark optimization problem, and, in a second example, to optimization of oil reservoir management strategies with and without geological uncertainty. The effectiveness of the sampling strategies is analyzed based on the quality of the estimated gradient, the final objective function value, the rate of the convergence, and the robustness of the gradient estimate. Based on the results, an improved version of the stochastic simplex approximate gradient method is proposed based on UE(s²) sampling designs for supersaturated cases that outperforms all alternative approaches. We additionally introduce two new strategies that outperform the UE(s²) designs previously suggested in the literature. ... Read more

Estimation of physical parameters in dynamical systems driven by linear partial differential equations is an important problem. In this paper, we introduce the least costly experiment design framework for these systems. It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment. We show how to adapt the classical framework for these systems and take into account scaling and stability issues. We also introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations. Our methodology is then applied to a relevant problem in heat transfer studies: estimation of conductivity and diffusivity parameters in front-face experiments. We find good correspondence between numerical and theoretical results. ... Read more

Closed-loop reservoir management (CLRM) is a combination of life-cycle optimization and computerassisted history matching. The application of the CLRM framework to real field cases can be computationally demanding. An even higher computational load results from procedures to assess the value of information (VOI) in CLRM. Such procedures, which are performed prior to field operation, i.e. during the field development planning (FDP) phase, require extreme amounts of simulations. Therefore, we look for alternatives to reduce this computational cost. In particular we compare various clustering techniques to select a limited number of representative members from an ensemble of reservoir models. Using K-means clustering, multi-dimensional scaling and tensor decomposition techniques, we test the effectiveness of different dissimilarity measures such as distance in parameter space, distance in terms of flow patterns and distance in optimal sets of controls. As a first step towards large-scale application we apply several of these measures to a VOI-CLRM exercise using a simple 2D reservoir model which results in a reduction of the necessary number of forward reservoir simulations from millions to thousands ... Read more