Multi-resolution-analysis scheme for uncertainty quantification in chemical systems

O. P. Le Maître, H. N. Najm, P. P. Pébay, R. G. Ghanem, O. M. Knio

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


This paper presents a multi-resolution approach for the propagation of parametric uncertainty in chemical systems. It is motivated by previous studies where Galerkin formulations of Wiener-Hermite expansions were found to fail in the presence of steep dependences of the species concentrations with regard to the reaction rates. The multi-resolution scheme is based on representation of the uncertain concentration in terms of compact polynomial multi-wavelets, allowing for the control of the convergence in terms of polynomial order and resolution level. The resulting representation is shown to greatly improve the robustness of the Galerkin procedure in presence of steep dependences. However, this improvement comes with a higher computational cost which drastically increases with the number of uncertain reaction rates. To overcome this drawback an adaptive strategy is proposed to control locally (in the parameter space) and in time the resolution level. The efficiency of the method is demonstrated for an uncertain chemical system having eight random parameters.

Original languageEnglish (US)
Pages (from-to)864-889
Number of pages26
JournalSIAM Journal on Scientific Computing
Issue number2
StatePublished - 2007
Externally publishedYes


  • Chemical systems
  • Multi-wavelets
  • Polynomial chaos
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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