Article2010

The estimation of functional uncertainty using polynomial chaos and adjoint equations

Aleksey K. Alekseev · Ionel Michael Navon · M. E. Zelentsov

27 citations0/0 files storedInternational Journal for Numerical Methods in Fluids

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

Abstract

Abstract The combined use of nonintrusive polynomial chaos (PC) and adjoint equations (yielding the gradient) is addressed aimed at the estimation of uncertainty of a valuable functional subject to large errors in the input data. Random variables providing maximum impact on the result (leading values) may be found using the gradient information that allows reduction of the problem dimension. The gradient may be also used for the calculation of PC coefficients, thus enabling further acceleration of the computations. Copyright © 2010 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics 2009Fast Numerical Methods for Stochastic Computations: A Review 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes 2009Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification

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