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Data-driven polynomial chaos expansions: A weighted least-square approximation
16 references·2 citing·23 second hop
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2012Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion451 cited
  • 2011A non-adapted sparse approximation of PDEs with stochastic inputs436 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2010A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data400 cited
  • 2009Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design371 cited
  • 2006Modeling Arbitrary Uncertainties Using Gram-Schmidt Polynomial Chaos146 cited
  • 2007Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos139 cited

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2011
A concept for data-driven uncertainty quantification and its application to carbon dioxide storage in geological formations
106 cited
  • 2016SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos100 cited
  • 2015Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs72 cited
  • Cited by

    • 2020A data-driven polynomial chaos method considering correlated random variables10 cited
    • 2023A data-driven B-spline-enhanced Kriging method for uncertainty quantification based on Bayesian compressive sensing8 cited