Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models

Oleg Roderick, Mihai Anitescu, Yulia Peet

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We investigate uncertainty propagation in the context of high-end complex simulation codes, whose runtime on one configuration is on the order of the total limit of computational resources. To this end, we study the use of lower-fidelity data generated by proper orthogonal decomposition-based model reduction. A Gaussian process approach is used to model the difference between the higher-fidelity and the lower-fidelity data. The approach circumvents the extensive sampling of model outputs - impossible in our context - by substituting abundant, lower-fidelity data in place of high-fidelity data. This enables uncertainty analysis while accounting for the reduction in information caused by the model reduction. We test the approach on Navier-Stokes flow models: first on a simplified code and then using the scalable high-fidelity fluid mechanics solver Nek5000. We demonstrate that the approach can give reasonably accurate while conservative error estimates of important statistics including high quantiles of the drag coefficient.

Original languageEnglish (US)
Pages (from-to)748-769
Number of pages22
JournalInternational Journal of Computer Mathematics
Issue number4
StatePublished - Apr 2014


  • Gaussian processes
  • kriging
  • model reduction
  • proper orthogonal decomposition
  • uncertainty quantification

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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