Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty
- 주제(키워드) stochastic gradient , ensemble optimization , simplex gradient , stochastic simplex approximate gradient , hybrid simplex gradient , active pressure management
- 주제(기타) Geosciences, Multidisciplinary
- 설명문(일반) [Jeong, Hoonyoung] Seoul Natl Univ, Dept Energy Resources Engn, Seoul, South Korea; [Jeong, Hoonyoung] Seoul Natl Univ, Res Inst Energy & Resources, Seoul, South Korea; [Jeong, Hoonyoung] Seoul Natl Univ, Inst Engn Res, Seoul, South Korea; [Sun, Alexander Y.] Univ Texas Austin, Bur Econ Geol, Jackson Sch Geosci, Austin, TX USA; [Jeon, Jonghyeon] Univ Texas Austin, Dept Petr & Geosyst Engn, Cockrell Sch Engn, Austin, TX 78712 USA; [Min, Baehyun] Ewha Womans Univ, Dept Climate & Energy Syst Engn, Seoul, South Korea; [Jeong, Daein] Schlumberger Software Integrated Solut, Tokyo, Japan
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted, gold
- 발행기관 FRONTIERS MEDIA SA
- 발행년도 2020
- URI http://www.dcollection.net/handler/ewha/000000168678
- 본문언어 영어
- Published As https://dx.doi.org/10.3389/feart.2020.00108
초록/요약
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.
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