An efficient sampling method for stochastic inverse problems |
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Authors: | Pierre Ngnepieba M Y Hussaini |
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Institution: | (1) Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, USA;(2) School of Computational Science, Florida State University, Tallahassee, FL 32306-4120, USA |
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Abstract: | A general framework is developed to treat inverse problems with parameters that are random fields. It involves a sampling
method that exploits the sensitivity derivatives of the control variable with respect to the random parameters. As the sensitivity
derivatives are computed only at the mean values of the relevant parameters, the related extra cost of the present method
is a fraction of the total cost of the Monte Carlo method. The effectiveness of the method is demonstrated on an example problem
governed by the Burgers equation with random viscosity. It is specifically shown that this method is two orders of magnitude
more efficient compared to the conventional Monte Carlo method. In other words, for a given number of samples, the present
method yields two orders of magnitude higher accuracy than its conventional counterpart. |
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Keywords: | Monte Carlo method Data assimilation Error covariance matrix Sensitivity derivatives Burgers equation |
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