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

Ahmed H. Elsheikh, Reza Tavakoli, Mary Fanett Wheeler, Ibrahim Hoteit

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)10-23
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jun 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications


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