Characterization of Uncertainties of Parameters with F-Statistic for Flows through Porous Media
by Guo-Qiang Yang.
The F-test (lack-of-fit) is applied to characterize the uncertainties in the estimation of parameters for flows through porous media. In the forward simulation, mixed finite element and second-order donor cell methods are used for the pressure-velocity equation and concentration equation respectively. The treatment of the wells are described. We show that $F$-test is flexible when handling the (ill-posed) inverse problem and gives the (exact) confidence regions for the unknown permeability field. Although the high dimensional confidence regions usually cannot be visualized, the simple evaluation of the $F$-statistic for each realization is desirable, as opposed to the usual Monte Carlo methods, which can only lead to approximate confidence levels with sufficient many samplings.
Uncertainty, Forward and Inverse Problems, Mixed Finite Element, Donor Cell, $F$-Test and Lack-of-Fit, Confidence Regions and Confidence Intervals, Singular Value Decomposition
Guo-Qiang Yang, email@example.com
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