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Wiener–Hermite polynomial expansion for multivariate Gaussian probability measures
9 references·7 citing·37 second hop
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this work references cited by second hop

References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2007Simulation and the Monte Carlo Method2,454 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics441 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics194 cited
  • 2004On the accuracy of the polynomial chaos approximation140 cited
  • 2013Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities70 cited

Cited by

  • 2018Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition25 cited
  • 2020Global sensitivity analysis: A Bayesian learning based polynomial chaos approach18 cited
  • 2022Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems14 cited
  • 2022An adaptive dimension-reduction method-based sparse polynomial chaos expansion via sparse Bayesian learning and Bayesian model averaging13 cited

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  • 2020An efficient numerical method to solve 2-D interval bi-modular problems via orthogonal polynomial expansion9 cited
  • 2023Intrusive and non-intrusive uncertainty quantification methodologies for pyrolysis modeling6 cited
  • 2019An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non‐Gaussian randomness6 cited