A Stochastic Simplex Approximate Gradient (StoSAG) for optimization under uncertainty
Summary We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlyi...
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| Vydané v: | International journal for numerical methods in engineering Ročník 109; číslo 13; s. 1756 - 1776 |
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Bognor Regis
Wiley Subscription Services, Inc
30.03.2017
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | Summary
We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one‐to‐one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd. |
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| AbstractList | We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen
et al
. (2009), it has been suggested that a straightforward one‐to‐one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca
et al
. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt. © 2016 The Authors.
International Journal for Numerical Methods in Engineering
Published by John Wiley & Sons, Ltd. Summary We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, 'robust optimization' is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as 'modified robust EnOpt') and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd. We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, 'robust optimization' is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as 'modified robust EnOpt') and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt. Summary We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one‐to‐one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd. |
| Author | Chen, Bailian Reynolds, Albert Jansen, Jan Dirk Fonseca, Rahul Rahul‐Mark |
| Author_xml | – sequence: 1 givenname: Rahul Rahul‐Mark surname: Fonseca fullname: Fonseca, Rahul Rahul‐Mark organization: Delft University of Technology – sequence: 2 givenname: Bailian surname: Chen fullname: Chen, Bailian organization: University of Tulsa – sequence: 3 givenname: Jan Dirk surname: Jansen fullname: Jansen, Jan Dirk email: j.d.jansen@tudelft.nl organization: Delft University of Technology – sequence: 4 givenname: Albert surname: Reynolds fullname: Reynolds, Albert organization: University of Tulsa |
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We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization... We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the... Summary We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization... |
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| SubjectTerms | Algorithms Approximate gradient Ensemble optimization Geology Mathematical analysis Mathematical models Optimization Robust optimization Robustness (mathematics) Stochastic gradient Stochasticity StoSAG Uncertainty |
| Title | A Stochastic Simplex Approximate Gradient (StoSAG) for optimization under uncertainty |
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