Error Estimation for Reduced Order Models of Dynamical Systems

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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 small sample statistical condition estimation and error estimation using the adjoint method. Most importantly, the proposed approach allows the assessment of regions of validity for reduced models, i.e., ranges of perturbations in the original system over which the ... continued below

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Homescu, C.; Petzold, L. & Serban, R. January 22, 2004.

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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 small sample statistical condition estimation and error estimation using the adjoint method. Most importantly, the proposed approach allows the assessment of regions of validity for reduced models, i.e., ranges of perturbations in the original system over which the reduced model is still appropriate. 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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PDF-file: 26 pages; size: 0.6 Mbytes

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  • Journal Name: SIAM Journal on Numerical Analysis; Journal Volume: 43; Journal Issue: 4

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  • Report No.: UCRL-JRNL-201982
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 862382
  • Archival Resource Key: ark:/67531/metadc792684

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  • January 22, 2004

Added to The UNT Digital Library

  • Dec. 19, 2015, 7:14 p.m.

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  • Nov. 28, 2016, 12:58 p.m.

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Homescu, C.; Petzold, L. & Serban, R. Error Estimation for Reduced Order Models of Dynamical Systems, article, January 22, 2004; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc792684/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.