Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models

Handle URI:
http://hdl.handle.net/10754/562784
Title:
Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models
Authors:
Elsheikh, Ahmed H.; Tavakoli, Reza; Wheeler, Mary Fanett; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.
KAUST Department:
Earth Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Fluid Modeling and Prediction Group
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Jun-2013
DOI:
10.1016/j.cma.2013.02.012
Type:
Article
ISSN:
00457825
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorElsheikh, Ahmed H.en
dc.contributor.authorTavakoli, Rezaen
dc.contributor.authorWheeler, Mary Fanetten
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2015-08-03T11:05:36Zen
dc.date.available2015-08-03T11:05:36Zen
dc.date.issued2013-06en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2013.02.012en
dc.identifier.urihttp://hdl.handle.net/10754/562784en
dc.description.abstractA novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.en
dc.publisherElsevier BVen
dc.subjectBoostingen
dc.subjectGaussian process regressionen
dc.subjectIterative stochastic ensemble methoden
dc.subjectKarhunen-Loève expansionen
dc.subjectParameter estimationen
dc.subjectSubsurface flow modelsen
dc.titleBoosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow modelsen
dc.typeArticleen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentEarth Fluid Modeling and Prediction Groupen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionCenter for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX, United Statesen
kaust.authorHoteit, Ibrahimen
kaust.authorElsheikh, Ahmed H.en
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