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 at each 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.
"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
Thuwal 23955-6900, Kingdom of Saudi Arabia
Al-Khwarizmi Building (1)
© King Abdullah University of Science and Technology. All rights reserved