A sensitivity matrix based methodology for inverse problem formulation
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Abstract
We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.
© de Gruyter 2009
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Artikel in diesem Heft
- Identification of a source for parabolic and hyperbolic equations with a parameter
- A sensitivity matrix based methodology for inverse problem formulation
- Well-posedness of an inverse problem of Navier–Stokes equations with the final overdetermination
- Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
- A variational approach to the Cauchy problem for nonlinear elliptic differential equations
- A new robust algorithm for solution of pressure/rate deconvolution problem
- International Conference and Young Scientists School Theory and Computational Methods for Inverse and Ill-posed Problems
- 5th International Conference Inverse Problems: Modeling and Simulation
