Article2007

Multi‐Resolution‐Analysis Scheme for Uncertainty Quantification in Chemical Systems

Olivier P. Le Maître · Habib N. Najm · Philippe Pébaÿ · Roger Ghanem · Omar Knio

87 citations0/0 files storedSIAM Journal on Scientific Computing

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Probabilistic and Robust Engineering Design Model Reduction and Neural Networks Gaussian Processes and Bayesian Inference

Abstract

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.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2002A Stochastic Projection Method for Fluid Flow 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes 2004Uncertainty propagation using Wiener–Haar expansions 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes 2003Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection 1999The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables

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