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 language | English |
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Pages (from-to) | 14-26 |
Number of pages | 13 |
Journal | Advances in Water Resources |
Volume | 56 |
DOIs | |
Publication status | Published - 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