An adaptive sparse-grid iterative ensemble Kalman filter approach for parameter field estimation

Abstract

A new sparse-grid (SG) iterative ensemble Kalman filter (IEnKF) approach is proposed for estimating spatially varying parameters. The adaptive high-order hierarchical sparse-grid (aHHSG) method is adopted to discretize the unknown parameter field. An IEnKF is used to explore the parameter space and estimate the surpluses of the aHHSG interpolant at each SG level. Moreover, the estimated aHHSG interpolant on coarser levels is employed to provide a good initial guess of the IEnKF solver for the approximation on the finer levels. The method is demonstrated in estimating permeability field in flows through porous media.

Keywords:

• sparse grids
• ensemble Kalman filter
• mesh refinement
• parameter estimation
• random data
• uncertainty quantification

2010 AMS Subject Classifications::

• 65N30
• 65N35
• 65N12
• 65N15
• 65C20

Acknowledgements

The first author was supported by the US Air Force Office of Scientific Research (AFOSR) under grant number 1854-V521-12. The first author was also supported by the Laboratory Directed Research and Development (LDRD) Programme at the Oak Ridge National Laboratory (ORNL). The second author was supported by the US AFOSR under grant number 1854-V521-12. The second author was also supported by the Advanced Simulation Computing Research (ASCR), Department of Energy, through the Householder Fellowship at ORNL. The third author was supported by the US AFOSR under grant number FA9550-11-1-0149.

The Oak Ridge National Laboratory is operated by UT-Battelle, LLC, for the United States Department of Energy under contract DE-AC05-00OR22725.