An iterative stochastic ensemble method for parameter estimation of subsurface flow models

Ahmed H Elsheikh, Mary F. Wheeler, Ibrahim Hoteit

    Research output: Contribution to journalArticle

    22 Citations (Scopus)

    Abstract

    Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. 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 Inc. All rights reserved.

    Original languageEnglish
    Pages (from-to)696-714
    Number of pages19
    JournalJournal of Computational Physics
    Volume242
    DOIs
    Publication statusPublished - 1 Jun 2013

    Keywords

    • Parameter estimation
    • Subsurface flow models
    • Iterative stochastic ensemble method
    • Regularization
    • MONTE-CARLO METHODS
    • KALMAN FILTER
    • DATA ASSIMILATION
    • L-CURVE
    • UNCERTAINTY QUANTIFICATION
    • RIDGE REGRESSION
    • INVERSE PROBLEM
    • POSED PROBLEMS
    • PRESSURE DATA
    • ALGORITHMS

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