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Comparison of intrusive and nonintrusive polynomial chaos expansion-based approaches for high dimensional parametric uncertainty quantification and propagation
13 references·5 citing·31 second hop
Comparison of intrusive and nonintrusive polynomial chaos expansion-based approaches for high dimensional parametric uncertainty quantification and propagation (2019)Comparison of intrusive and nonintrusive …A new bivariate dimension reduction method for efficient structural reliability analysis (2018)A new bivariate dimension red…Robust optimization of chemical processes using Bayesian description of parametric uncertainty (2013)Robust optimization of chemic…Applying uncertainty quantification to multiphase flow computational fluid dynamics (2013)Applying uncertainty quantifi…Numerical Methods for Stochastic Computations: A Spectral Method Approach (2010)Numerical Methods for Stochas…Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification (2009)Comparison of Non-Intrusive P…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)A Sparse Grid Stochastic Coll…Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations (2005)Uncertainty Analysis by Dimen…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004)A generalized dimension‐reduc…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Monte Carlo Treatment of Random Fields: A Broad Perspective (1998)Monte Carlo Treatment of Rand…Kriging Methodology for Uncertainty Quantification in Computational Electromagnetics (2024)Kriging Methodology for Uncer…Propagating input uncertainties into parameter uncertainties and model prediction uncertainties—A review (2023)Propagating input uncertainti…Fast Uncertainty Quantification by Sparse Data Learning From Multiphysics Systems (2023)Fast Uncertainty Quantificati…An Efficient Polynomial Chaos Expansion Method for Uncertainty Quantification in Dynamic Systems (2021)An Efficient Polynomial Chaos…Adjoint Sensitivity Analysis for Uncertain Material Parameters in Frequency-Domain 3-D FEM (2021)Adjoint Sensitivity Analysis …Structural reliability under combined random load sequences (1978)Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation (2011)Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual (2014)First order reliability method for time-variant problems using series expansions (2014)Stochastic Finite Elements: A Spectral Approach (1991)Global sensitivity analysis using polynomial chaos expansions (2007)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)The Malliavin Calculus and Related Topics (2006)On the convergence of generalized polynomial chaos expansions (2011)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)A comparative study of uncertainty propagation methods for black-box-type problems (2008)A survey on approaches for reliability-based optimization (2010)Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method (2013)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)Exact and Invariant Second-Moment Code Format (1974)A Second-Order Reliability Method With First-Order Efficiency (2010)A new approach for reliability analysis with time-variant performance characteristics (2013)Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011)Stochastic finite element methods for partial differential equations with random input data (2014)Chaospy: An open source tool for designing methods of uncertainty quantification (2015)Dynamic response and reliability analysis of non-linear stochastic structures (2004)The probability density evolution method for dynamic response analysis of non‐linear stochastic structures (2005)The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures (2006)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual. (2010)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics (2010)A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing (2011)
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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
  • 2010Numerical Methods for Stochastic Computations: A Spectral Method Approach1,107 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics441 cited
  • 2009Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification348 cited
  • 1998Monte Carlo Treatment of Random Fields: A Broad Perspective225 cited
  • 2005Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations161 cited
  • 2018A new bivariate dimension reduction method for efficient structural reliability analysis115 cited
  • 2013Applying uncertainty quantification to multiphase flow computational fluid dynamics44 cited
  • 2013Robust optimization of chemical processes using Bayesian description of parametric uncertainty43 cited

Cited by

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  • 2023Propagating input uncertainties into parameter uncertainties and model prediction uncertainties—A review25 cited
  • 2024Kriging Methodology for Uncertainty Quantification in Computational Electromagnetics18 cited
  • 2021Adjoint Sensitivity Analysis for Uncertain Material Parameters in Frequency-Domain 3-D FEM17 cited
  • 2021An Efficient Polynomial Chaos Expansion Method for Uncertainty Quantification in Dynamic Systems14 cited
  • 2023Fast Uncertainty Quantification by Sparse Data Learning From Multiphysics Systems10 cited