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Kernel principal component analysis for stochastic input model generation
13 references·11 citing·21 second hop
Kernel principal component analysis for stochastic input model generation (2011)Kernel principal component analysis for s…Identification of Bayesian posteriors for coefficients of chaos expansions (2010)Identification of Bayesian po…An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations (2010)An adaptive high-dimensional …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…Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method (2007)Modeling diffusion in random …A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data (2006)On the construction and analy…Maximum likelihood estimation of stochastic chaos representations from experimental data (2005)Maximum likelihood estimation…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…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 …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Applying artificial intelligence to determination of legal age of majority from radiographic data (2023)Applying artificial intellige…Recent progress of uncertainty quantification in small-scale materials science (2020)Recent progress of uncertaint…Multivariate Control Chart Based on Kernel PCA for Monitoring Mixed Variable and Attribute Quality Characteristics (2020)Multivariate Control Chart Ba…Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models (2019)Regression-based sparse polyn…An efficient algorithm for building locally refined hp – adaptive H-PCFE: Application to uncertainty quantification (2017)An efficient algorithm for bu…Sampling, Metamodeling, and Sensitivity Analysis of Numerical Simulators with Functional Stochastic Inputs (2016)Sampling, Metamodeling, and S…DGSA: A Matlab toolbox for distance-based generalized sensitivity analysis of geoscientific computer experiments (2016)DGSA: A Matlab toolbox for di…Parametrization of Random Vectors in Polynomial Chaos Expansions via Optimal Transportation (2015)Parametrization of Random Vec…Karhunen–Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis. (2013)Karhunen–Loève expansion revi…A multiscale approach for model reduction of random microstructures (2012)A multiscale approach for mod…Investigating variability of fatigue indicator parameters of two-phase nickel-based superalloy microstructures (2011)Investigating variability of …Stochastic Differential Equations: An Introduction with Applications. (1987)Adaptive ANOVA decomposition of stochastic incompressible and compressible flows (2011)Uncertainty Quantification in Multiscale Simulation of Materials: A Prospective (2013)Surrogate-assisted global sensitivity analysis: an overview (2020)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)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)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Efficient computation of global sensitivity indices using sparse polynomial chaos expansions (2010)Stochastic finite element methods for partial differential equations with random input data (2014)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)Stochastic model reduction for chaos representations (2007)A better understanding of model updating strategies in validating engineering models (2008)A least-squares approximation of partial differential equations with high-dimensional random inputs (2009)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)Fast Numerical Methods for Stochastic Computations: A Review (2009)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 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
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2010An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations205 cited
  • 2006On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data191 cited
  • 2005Maximum likelihood estimation of stochastic chaos representations from experimental data146 cited
  • 2010Identification of Bayesian posteriors for coefficients of chaos expansions103 cited
  • 2007Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method96 cited

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Cited by

  • 2016DGSA: A Matlab toolbox for distance-based generalized sensitivity analysis of geoscientific computer experiments84 cited
  • 2020Recent progress of uncertainty quantification in small-scale materials science38 cited
  • 2013Karhunen–Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis.37 cited
  • 2023Applying artificial intelligence to determination of legal age of majority from radiographic data29 cited
  • 2019Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models26 cited
  • 2017An efficient algorithm for building locally refined hp – adaptive H-PCFE: Application to uncertainty quantification22 cited
  • 2012A multiscale approach for model reduction of random microstructures21 cited
  • 2016Sampling, Metamodeling, and Sensitivity Analysis of Numerical Simulators with Functional Stochastic Inputs21 cited
  • 2011Investigating variability of fatigue indicator parameters of two-phase nickel-based superalloy microstructures13 cited
  • 2020Multivariate Control Chart Based on Kernel PCA for Monitoring Mixed Variable and Attribute Quality Characteristics10 cited
  • 2015Parametrization of Random Vectors in Polynomial Chaos Expansions via Optimal Transportation10 cited