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General Introduction to Polynomial Chaos and Collocation Methods
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General Introduction to Polynomial Chaos and Collocation Methods (2018)General Introduction to Polynomial Chaos …Numerical Methods for Stochastic Computations: A Spectral Method Approach (2010)Numerical Methods for Stochas…Fast Numerical Methods for Stochastic Computations: A Review (2009)Fast Numerical Methods for St…Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification (2009)Comparison of Non-Intrusive P…An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)An adaptive hierarchical spar…A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)A Sparse Grid Stochastic Coll…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…Global sensitivity analysis using polynomial chaos expansions (2007)Global sensitivity analysis u…Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables (2007)Efficient Sampling for Non-In…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Stochastic finite element: a non intrusive approach by regression (2006)Stochastic finite element: a …High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Uncertainty propagation using Wiener–Haar expansions (2004)Uncertainty propagation using…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …A Stochastic Projection Method for Fluid Flow (2002)A Stochastic Projection Metho…Stochastic Finite Elements: A Spectral Approach (1991)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output (1999)UQLab: A Framework for Uncertainty Quantification in Matlab (2014)Sensitivity analysis of environmental models: A systematic review with practical workflow (2016)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)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)Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles (2011)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)An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual. (2010)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters (2015)POLYNOMIAL-CHAOS-BASED KRIGING (2015)
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 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
  • 2009Fast Numerical Methods for Stochastic Computations: A Review608 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2006Stochastic finite element: a non intrusive approach by regression427 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited

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  • 2009Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification348 cited
  • 2007Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables347 cited
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