Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method |
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| Institution: | 1. Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX, USA;2. Dept. of Earth Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia;3. Dept. of Applied Mathematics and Computational Sciences, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia;1. Department of Materials and Environmental Technology, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia;2. crystalsol OÜ, Akadeemia tee 15a, 12618, Tallinn, Estonia;1. Instituto de Telecomunicações, Instituto Superior Técnico, 1049-001, Lisboa, Portugal;2. College of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, China;1. School of Automation Science and Electrical Engineering, Beihang University, China;2. School of Computer Science and Technology, Harbin Institute of Technology at Weihai, Weihai 264209, China;3. School of Automation, Southeast University, Nanjing 210096, China |
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| 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 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. |
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