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Polynomial Chaos Expansion of a Multimodal Random Vector
16 references·7 citing·25 second hop
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 1996Numerical solution of spectral stochastic finite element systems294 cited
  • 2007Stochastic model reduction for chaos representations191 cited
  • 2005Maximum likelihood estimation of stochastic chaos representations from experimental data146 cited
  • 2004Generalized polynomial chaos and random oscillators129 cited
  • 2008Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices

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117 cited
  • 2010Identification of Bayesian posteriors for coefficients of chaos expansions103 cited
  • 2010Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data87 cited
  • Cited by

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    • 2022Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion24 cited
    • 2020COMPUTATION OF SOBOL INDICES IN GLOBAL SENSITIVITY ANALYSIS FROM SMALL DATA SETS BY PROBABILISTIC LEARNING ON MANIFOLDS21 cited
    • 2018Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds19 cited
    • 2015STOCHASTIC REPRESENTATIONS AND STATISTICAL INVERSE IDENTIFICATION FOR UNCERTAINTY QUANTIFICATION IN COMPUTATIONAL MECHANICS17 cited