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

Title
Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty
Authors
Jeong, HoonyoungSun, Alexander Y.Jeon, JonghyeonMin, BaehyunJeong, Daein
Ewha Authors
민배현
Issue Date
2020
Journal Title
FRONTIERS IN EARTH SCIENCE
ISSN
2296-6463JCR Link
Citation
FRONTIERS IN EARTH SCIENCE vol. 8
Keywords
stochastic gradientensemble optimizationsimplex gradientstochastic simplex approximate gradienthybrid simplex gradientactive pressure management
Publisher
FRONTIERS MEDIA SA
Indexed
SCIE; SCOPUS WOS
Document Type
Article
Abstract
Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly 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 variables 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 on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30-50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.
DOI
10.3389/feart.2020.00108
Appears in Collections:
엘텍공과대학 > 기후·에너지시스템공학전공 > Journal papers
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