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Intrusive Polynomial Chaos Methods for Forward Uncertainty Propagation

In: Handbook of Uncertainty Quantification

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  • Bert Debusschere

    (Sandia National Laboratories, Mechanical Engineering
    Sandia National Laboratories, Reacting Flow Research Department)

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.

Suggested Citation

  • Bert Debusschere, 2017. "Intrusive Polynomial Chaos Methods for Forward Uncertainty Propagation," Springer Books, in: Roger Ghanem & David Higdon & Houman Owhadi (ed.), Handbook of Uncertainty Quantification, chapter 17, pages 617-636, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12385-1_19
    DOI: 10.1007/978-3-319-12385-1_19
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