Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

Ahmed H Elsheikh, Mary F Wheeler, Ibrahim Hoteit

    Research output: Contribution to journalArticle

    22 Citations (Scopus)

    Abstract

    We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers a teach iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. (c) 2013 Elsevier Ltd. All rights reserved.

    Original languageEnglish
    Pages (from-to)14-26
    Number of pages13
    JournalAdvances in Water Resources
    Volume56
    DOIs
    Publication statusPublished - Jun 2013

    Keywords

    • Parameter estimation
    • Subsurface flow models
    • Sparse regularization
    • Orthogonal matching pursuit
    • Iterative stochastic ensemble method
    • MONTE-CARLO
    • L-CURVE
    • SIGNAL RECOVERY
    • INVERSE PROBLEM
    • POSED PROBLEMS
    • KALMAN FILTER
    • PRESSURE DATA
    • APPROXIMATION
    • DICTIONARIES
    • UNCERTAINTY

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