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

Ahmed H Elsheikh, Reza Tavakoli, Mary F Wheeler, Ibrahim Hoteit

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    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-Loeve 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 l(2) Boosting algorithm. l(2) 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 l(2) 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. (C) 2013 Elsevier B.V. All rights reserved.

    Original languageEnglish
    Pages (from-to)10-23
    Number of pages14
    JournalComputer Methods in Applied Mechanics and Engineering
    Volume259
    DOIs
    Publication statusPublished - 1 Jun 2013

    Keywords

    • Parameter estimation
    • Subsurface flow models
    • Boosting
    • Iterative stochastic ensemble method
    • Gaussian process regression
    • Karhunen-Loeve expansion
    • RIDGE-REGRESSION
    • MONTE-CARLO
    • L-CURVE
    • UNCERTAINTY QUANTIFICATION
    • NONORTHOGONAL PROBLEMS
    • INFORMATION CRITERION
    • DATA ASSIMILATION
    • INVERSE PROBLEM
    • POSED PROBLEMS
    • KALMAN FILTER

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