Numerical Testing of Parameterization Schemes for Solving Parameter Estimation Problems
Abstract
We present the numerical performance of two parameterization schemes, Singular Value Decomposition (SVD) and wavelets, for solving automated parameter estimation problems using the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The two schemes are tested on a suit of two large scale two-phase flow problems that illustrate potential for addressing large-scale EQM inverse problems using high-performance computing (HPC). In this paper we present the numerical performance of three parameterization approaches, SVD, wavelets, and the combination of wavelet-SVD for solving automated parameter estimation problems based on the SPSA described in previous reports of this project. In brief terms, the parameterization methods are based on the principle of projecting the original parameter space onto a lower-dimensional space. In most cases, these projections are computed in terms of SVD (for nonsymmetric and rectangular operators), Krylov subspace methods, fast Fourier and wavelet transforms, to name a few alternatives. We conducted the numerical experiments comparing SPSA by using the aforementioned parameterization schemes. It will be shown that the SVD using 50% of the singular values and wavelet level 3 performed extremely well on two test cases of 128x128 gridblocks: channelized (structured) and random (non-structured) permeability fields. We now demonstrate its capabilities for performing parameter estimation using a HPC platform.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 2008
- Accession Number
- ADA503641
Entities
People
- C. Quintero
- H. Klie
- L. Velazquez
- M. Argaez
- M. F. Wheeler
Organizations
- University of Texas at El Paso