Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

Ahmed H Elsheikh, Mary F Wheeler, Ibrahim Hoteit

    Research output: Contribution to journalArticle

    Abstract

    A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. (C) 2013 Elsevier B.V. All rights reserved.

    Original languageEnglish
    Pages (from-to)40-55
    Number of pages16
    JournalJournal of Hydrology
    Volume491
    DOIs
    Publication statusPublished - 29 May 2013

    Keywords

    • Parameter estimation
    • Subsurface Flow Models
    • Regularization
    • K-means Clustering
    • Multi-modal Optimization
    • SEQUENTIAL DATA ASSIMILATION
    • KALMAN FILTER
    • MONTE-CARLO
    • PARAMETERIZATION
    • OCEANOGRAPHY
    • OPTIMIZATION
    • ALGORITHMS
    • ENKF

    Cite this

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    title = "Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models",
    abstract = "A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. (C) 2013 Elsevier B.V. All rights reserved.",
    keywords = "Parameter estimation, Subsurface Flow Models, Regularization, K-means Clustering, Multi-modal Optimization, SEQUENTIAL DATA ASSIMILATION, KALMAN FILTER, MONTE-CARLO, PARAMETERIZATION, OCEANOGRAPHY, OPTIMIZATION, ALGORITHMS, ENKF",
    author = "Elsheikh, {Ahmed H} and Wheeler, {Mary F} and Ibrahim Hoteit",
    year = "2013",
    month = "5",
    day = "29",
    doi = "10.1016/j.jhydrol.2013.03.037",
    language = "English",
    volume = "491",
    pages = "40--55",
    journal = "Journal of Hydrology",
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    }

    Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models. / Elsheikh, Ahmed H; Wheeler, Mary F; Hoteit, Ibrahim.

    In: Journal of Hydrology, Vol. 491, 29.05.2013, p. 40-55.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

    AU - Elsheikh, Ahmed H

    AU - Wheeler, Mary F

    AU - Hoteit, Ibrahim

    PY - 2013/5/29

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    N2 - A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. (C) 2013 Elsevier B.V. All rights reserved.

    AB - A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. (C) 2013 Elsevier B.V. All rights reserved.

    KW - Parameter estimation

    KW - Subsurface Flow Models

    KW - Regularization

    KW - K-means Clustering

    KW - Multi-modal Optimization

    KW - SEQUENTIAL DATA ASSIMILATION

    KW - KALMAN FILTER

    KW - MONTE-CARLO

    KW - PARAMETERIZATION

    KW - OCEANOGRAPHY

    KW - OPTIMIZATION

    KW - ALGORITHMS

    KW - ENKF

    U2 - 10.1016/j.jhydrol.2013.03.037

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