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On polynomial chaos expansion via gradient-enhanced ℓ1-minimization
16 references·16 citing·24 second hopsampled
On polynomial chaos expansion via gradient-enhanced ℓ1-minimization (2016)On polynomial chaos expansion via gradien…Enhancing ℓ1 -minimization estimates of polynomial chaos expansions using basis selection (2015)Enhancing ℓ1 -minimization es…Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression (2015)Coherence motivated sampling …Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies (2014)Compressive sampling of polyn…Reweighted minimization method for stochastic elliptic differential equations (2013)Reweighted minimization metho…Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces (2013)Approximation of Quantities o…A non-adapted sparse approximation of PDEs with stochastic inputs (2011)A non-adapted sparse approxim…Spectral methods for uncertainty quantification : with applications to computational fluid dynamics (2010)Spectral methods for uncertai…Polynomial Regression Approaches Using Derivative Information for Uncertainty Quantification (2010)Polynomial Regression Approac…Numerical Methods for Stochastic Computations: A Spectral Method Approach (2010)Numerical Methods for Stochas…A Non-Intrusive Polynomial Chaos Method For Uncertainty Propagation in CFD Simulations (2006)A Non-Intrusive Polynomial Ch…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection (2003)Uncertainty quantification in…A Stochastic Collocation Algorithm for Uncertainty Analysis (2003)A Stochastic Collocation Algo…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Design Sensitivity Analysis of Structural Systems (1986)Design Sensitivity Analysis o…Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification (2023)Sensitivity-enhanced generali…Global sensitivity analysis using polynomial chaos expansion enhanced Gaussian process regression method (2023)Global sensitivity analysis u…Pygpc: A sensitivity and uncertainty analysis toolbox for Python (2020)Pygpc: A sensitivity and unce…Global sensitivity analysis: A Bayesian learning based polynomial chaos approach (2020)Global sensitivity analysis: …Multi-level multi-fidelity sparse polynomial chaos expansion based on Gaussian process regression (2019)Multi-level multi-fidelity sp…An expanded sparse Bayesian learning method for polynomial chaos expansion (2019)An expanded sparse Bayesian l…An efficient and robust adaptive sampling method for polynomial chaos expansion in sparse Bayesian learning framework (2019)An efficient and robust adapt…An efficient adaptive forward–backward selection method for sparse polynomial chaos expansion (2019)An efficient adaptive forward…Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method (2018)Statistical moment analysis o…Review of Robust Aerodynamic Design Optimization for Air Vehicles (2018)Review of Robust Aerodynamic …On the flow field and performance of a centrifugal pump under operational and geometrical uncertainties (2018)On the flow field and perform…M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions (2018)M-PCM-OFFD: An effective outp…Efficient uncertainty quantification of stochastic heat transfer problems by combination of proper orthogonal decomposition and sparse polynomial chaos expansion (2018)Efficient uncertainty quantif…Basis adaptive sample efficient polynomial chaos (BASE-PC) (2018)Basis adaptive sample efficie…Enhancing sparsity of Hermite polynomial expansions by iterative rotations (2015)Enhancing sparsity of Hermite…Compressive Sampling Methods for Sparse Polynomial Chaos Expansions (2015)Compressive Sampling Methods …Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Least squares polynomial chaos expansion: A review of sampling strategies (2017)Surrogate-assisted global sensitivity analysis: an overview (2020)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)A Stochastic Projection Method for Fluid Flow (2002)Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics (2010)The method of uncertainty quantification and minimization using polynomial chaos expansions (2011)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables (2007)Sensitivity Analysis of Discrete Structural Systems (1986)Reliability-based optimization in structural engineering (1994)A nonparametric model of random uncertainties for reduced matrix models in structural dynamics (2000)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (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)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry (2015)POLYNOMIAL-CHAOS-BASED KRIGING (2015)Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark (2021)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1986Design Sensitivity Analysis of Structural Systems1,625 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2010Numerical Methods for Stochastic Computations: A Spectral Method Approach1,107 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2011A non-adapted sparse approximation of PDEs with stochastic inputs436 cited
  • 2006A Non-Intrusive Polynomial Chaos Method For Uncertainty Propagation in CFD Simulations335 cited
  • 2003Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection333 cited
  • 2014Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies212 cited
  • 2015Enhancing ℓ1 -minimization estimates of polynomial chaos expansions using basis selection174 cited
  • 2003A Stochastic Collocation Algorithm for Uncertainty Analysis148 cited
  • 2015Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression134 cited
  • 2013Reweighted minimization method for stochastic elliptic differential equations

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108 cited
  • 2010Polynomial Regression Approaches Using Derivative Information for Uncertainty Quantification88 cited
  • 2013Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces81 cited
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    • 2020Pygpc: A sensitivity and uncertainty analysis toolbox for Python27 cited
    • 2019An efficient adaptive forward–backward selection method for sparse polynomial chaos expansion26 cited
    • 2019An expanded sparse Bayesian learning method for polynomial chaos expansion23 cited
    • 2018Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method19 cited
    • 2020Global sensitivity analysis: A Bayesian learning based polynomial chaos approach18 cited
    • 2015Compressive Sampling Methods for Sparse Polynomial Chaos Expansions17 cited
    • 2023Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification15 cited
    • 2023Global sensitivity analysis using polynomial chaos expansion enhanced Gaussian process regression method12 cited
    • 2018M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions12 cited