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Handbook of Uncertainty Quantification pp 617–636Cite as

Intrusive Polynomial Chaos Methods for Forward Uncertainty Propagation

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Abstract

Polynomial chaos (PC)-based intrusive methods for uncertainty quantification reformulate the original deterministic model equations to obtain a system of equations for the PC coefficients of the model outputs. This system of equations is larger than the original model equations, but solving it once yields the uncertainty information for all quantities in the model. This chapter gives an overview of the literature on intrusive methods, outlines the approach on a general level, and then applies it to a system of three ordinary differential equations that model a surface reaction system. Common challenges and opportunities for intrusive methods are also highlighted.

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Author information

Authors and Affiliations

  1. Mechanical Engineering, Sandia National Laboratories, Livermore, CA, USA

    Bert Debusschere

  2. Reacting Flow Research Department, Sandia National Laboratories, Livermore, CA, USA

    Bert Debusschere

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  1. Bert Debusschere
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Correspondence to Bert Debusschere .

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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA

    Roger Ghanem

  2. Social and Decision Analytics Laboratory, Virginia Bioinformatics Institute, Virginia Tech University, Arlington, Virginia, USA

    David Higdon

  3. Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California, USA

    Houman Owhadi

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Debusschere, B. (2017). Intrusive Polynomial Chaos Methods for Forward Uncertainty Propagation. In: Ghanem, R., Higdon, D., Owhadi, H. (eds) Handbook of Uncertainty Quantification. Springer, Cham. https://doi.org/10.1007/978-3-319-12385-1_19

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