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Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing
16 references·16 citing·32 second hopsampled
Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing (2014)Adaptive-sparse polynomial dimensional de…Adaptive ANOVA decomposition of stochastic incompressible and compressible flows (2011)Adaptive ANOVA decomposition …An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations (2010)An adaptive high-dimensional …Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions (2009)Extended Polynomial Dimension…Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach (2008)Sparse polynomial chaos expan…A polynomial dimensional decomposition for stochastic computing (2008)A polynomial dimensional deco…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…Decomposition methods for structural reliability analysis (2005)Decomposition methods for str…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004)A generalized dimension‐reduc…Theorems and examples on high dimensional model representation (2003)Theorems and examples on high…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates (2001)Global sensitivity indices fo…General foundations of high‐dimensional model representations (1999)General foundations of high‐d…Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration (1998)Adaptive polynomial chaos exp…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…SS-MASVM: An advanced technique for assessing failure probability of high-dimensional complex systems using the multi-class adaptive support vector machine (2023)SS-MASVM: An advanced techniq…Efficient reliability analysis with a CDA-based dimension-reduction model and polynomial chaos expansion (2020)Efficient reliability analysi…Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition (2018)Uncertainty quantification un…Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method (2018)Statistical moment analysis o…Mathematical Properties of Polynomial Dimensional Decomposition (2018)Mathematical Properties of Po…Extreme value oriented random field discretization based on an hybrid polynomial chaos expansion — Kriging approach (2018)Extreme value oriented random…Towards ‘h-p adaptive’ generalized ANOVA (2017)Towards ‘h-p adaptive’ genera…Statistical Framework for Sensitivity Analysis of Structural Dynamic Characteristics (2017)Statistical Framework for Sen…An efficient algorithm for building locally refined hp – adaptive H-PCFE: Application to uncertainty quantification (2017)An efficient algorithm for bu…A new non-intrusive polynomial chaos using higher order sensitivities (2017)A new non-intrusive polynomia…An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions (2016)An efficient metamodeling app…Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation (2016)Adaptive surrogate modeling b…Reliability-based design optimization by adaptive-sparse polynomial dimensional decomposition (2015)Reliability-based design opti…Global response sensitivity analysis of uncertain structures (2015)Global response sensitivity a…Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty (2014)Stochastic finite elements of…A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures (2014)A Generalized ANOVA Dimension…Sensitivity measures,anova-like Techniques and the use of bootstrap (1997)Efficient input—output model representations (1999)Estimating the approximation error when fixing unessential factors in global sensitivity analysis (2006)Efficient computation of global sensitivity indices using sparse polynomial chaos expansions (2010)Sensitivity analysis for volcanic source modeling quality assessment and model selection (2012)The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. (1987)Uncertainty propagation using Wiener–Haar expansions (2004)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Stochastic finite element methods for partial differential equations with random input data (2014)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)Rare Event Estimation Using Polynomial-Chaos Kriging (2016)Adaptive approaches in metamodel-based reliability analysis: A review (2020)Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark (2021)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)Importance measures in global sensitivity analysis of nonlinear models (1996)Sensitivity Analysis for Chemical Models (2005)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A new uncertainty importance measure (2006)Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index (2009)SALib: An open-source Python library for Sensitivity Analysis (2017)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)
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References

  • 2001Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates6,377 cited
  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1999General foundations of high‐dimensional model representations905 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2003Theorems and examples on high dimensional model representation450 cited
  • 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics441 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2008Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach270 cited
  • 2010An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations205 cited
  • 2005Decomposition methods for structural reliability analysis159 cited
  • 2008A polynomial dimensional decomposition for stochastic computing140 cited
  • 2011Adaptive ANOVA decomposition of stochastic incompressible and compressible flows

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127 cited
  • 1998Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration106 cited
  • 2009Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions72 cited
  • Cited by

    • 2016Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation44 cited
    • 2016An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions39 cited
    • 2020Efficient reliability analysis with a CDA-based dimension-reduction model and polynomial chaos expansion39 cited
    • 2014A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures37 cited
    • 2017A new non-intrusive polynomial chaos using higher order sensitivities35 cited
    • 2015Reliability-based design optimization by adaptive-sparse polynomial dimensional decomposition33 cited
    • 2017Towards ‘h-p adaptive’ generalized ANOVA29 cited
    • 2023SS-MASVM: An advanced technique for assessing failure probability of high-dimensional complex systems using the multi-class adaptive support vector machine28 cited
    • 2018Mathematical Properties of Polynomial Dimensional Decomposition26 cited
    • 2018Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition25 cited
    • 2018Extreme value oriented random field discretization based on an hybrid polynomial chaos expansion — Kriging approach24 cited
    • 2015Global response sensitivity analysis of uncertain structures24 cited
    • 2017An efficient algorithm for building locally refined hp – adaptive H-PCFE: Application to uncertainty quantification22 cited
    • 2014Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty20 cited
    • 2017Statistical Framework for Sensitivity Analysis of Structural Dynamic Characteristics19 cited
    • 2018Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method19 cited