An Ensemble Based Nonlinear Orthogonal Matching Pursuit Algorithm for Sparse History Matching of Reservoir Models

Ahmed H Elsheikh, Mary F Wheeler, Ibrahim Hoteit

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of reservoir models is presented. 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 at each iteration the most correlated components of the basis functions with the residual. The discovered basis (aka support) is augmented across the nonlinear iterations. Once the basis functions are selected from the dictionary, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on approximate gradient estimation using an iterative stochastic ensemble method (ISEM). ISEM utilizes an ensemble of directional derivatives to efficiently approximate gradients. In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm.
Original languageEnglish
Title of host publicationSPE Reservoir Simulation Symposium, 18-20 February, The Woodlands, Texas, USA
PublisherSociety of Petroleum Engineers
Number of pages12
ISBN (Print)978-1-61399-233-3
DOIs
Publication statusPublished - 18 Feb 2013
EventSPE Reservoir Simulation Symposium 2013 - The Woodlands, Texas, United States
Duration: 18 Feb 201320 Feb 2013

Conference

ConferenceSPE Reservoir Simulation Symposium 2013
CountryUnited States
CityThe Woodlands, Texas
Period18/02/1320/02/13

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    Elsheikh, A. H., Wheeler, M. F., & Hoteit, I. (2013). An Ensemble Based Nonlinear Orthogonal Matching Pursuit Algorithm for Sparse History Matching of Reservoir Models. In SPE Reservoir Simulation Symposium, 18-20 February, The Woodlands, Texas, USA [SPE-163582-MS] Society of Petroleum Engineers. https://doi.org/10.2118/163582-MS