Error Estimation for Reduced Order Models of Dynamical systems [electronic resource]
The use of reduced order models to describe a dynamical system is pervasive in science and engineering. Often these models are used without an estimate of their error or range of validity. In this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition. We...
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| Format: | Government Document Electronic eBook |
| Language: | English |
| Published: |
Washington, D.C. : Oak Ridge, Tenn. :
United States. Department of Energy ; distributed by the Office of Scientific and Technical Information, U.S. Department of Energy,
2003.
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| Subjects: |
MARC
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| 245 | 0 | 0 | |a Error Estimation for Reduced Order Models of Dynamical systems |h [electronic resource] |
| 260 | |a Washington, D.C. : |b United States. Department of Energy ; |a Oak Ridge, Tenn. : |b distributed by the Office of Scientific and Technical Information, U.S. Department of Energy, |c 2003. | ||
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| 500 | |a Homescu, C; Petzold, L R; Serban, R. | ||
| 520 | 3 | |a The use of reduced order models to describe a dynamical system is pervasive in science and engineering. Often these models are used without an estimate of their error or range of validity. In this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition. We show how to compute estimates and bounds for these errors, by a combination of the small sample statistical condition estimation method and of error estimation using the adjoint method. More importantly, the proposed approach allows the assessment of so-called regions of validity for reduced models, i.e., ranges of perturbations in the original system over which the reduced model is still appropriate. This question is particularly important for applications in which reduced models are used not just to approximate the solution to the system that provided the data used in constructing the reduced model, but rather to approximate the solution of systems perturbed from the original one. Numerical examples validate our approach: the error norm estimates approximate well the forward error while the derived bounds are within an order of magnitude. | |
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