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

by A. El-Sheikh, M. Wheeler, I. Hoteit


A iterative stochastic ensemble method for parameter estimation of subsurface flow models
A. El-Sheikh, M. Wheeler, and I. Hoteit
Journal of Computational Physics, 242, 696-714, 2013


​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.

DOI: 10.1016/j.jcp.2013.01.047


Iterative Stochastic Ensemble Method Parameter Estimation Regularization Subsurface Flow Models

"KAUST shall be a beacon for peace, hope and reconciliation, and shall serve the people of the Kingdom and the world."

King Abdullah bin Abdulaziz Al Saud, 1924 – 2015

Contact Us

  • 4700 King Abdullah University of Science and Technology

    Thuwal 23955-6900, Kingdom of Saudi Arabia

    Al-Khwarizmi Building (1)

© King Abdullah University of Science and Technology. All rights reserved