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STOCHASTIC REPRESENTATIONS AND STATISTICAL INVERSE IDENTIFICATION FOR UNCERTAINTY QUANTIFICATION IN COMPUTATIONAL MECHANICS
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STOCHASTIC REPRESENTATIONS AND STATISTICAL INVERSE IDENTIFICATION FOR UNCERTAINTY QUANTIFICATION IN COMPUTATIONAL MECHANICS (2015)STOCHASTIC REPRESENTATIONS AND STATISTICA…Stochastic Models of Uncertainties in Computational Mechanics (2012)Stochastic Models of Uncertai…On the convergence of generalized polynomial chaos expansions (2011)On the convergence of general…Spectral methods for uncertainty quantification : with applications to computational fluid dynamics (2010)Spectral methods for uncertai…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices (2008)Construction of probability d…Uncertainty propagation in CFD using polynomial chaos decomposition (2006)Uncertainty propagation in CF…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators (2005)Non-Gaussian positive-definit…Maximum likelihood estimation of stochastic chaos representations from experimental data (2005)Maximum likelihood estimation…Uncertainty propagation using Wiener–Haar expansions (2004)Uncertainty propagation using…Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…Generalized polynomial chaos and random oscillators (2004)Generalized polynomial chaos …Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms (2002)Non-Gaussian simulation using…Numerical solution of spectral stochastic finite element systems (1996)Numerical solution of spectra…Probabilistic engineering mechanics (1993)Probabilistic engineering mec…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems (2010)Time-dependent generalized polynomial chaos (2010)Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression (2017)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Stochastic Differential Equations and Diffusion Processes (1983)Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances (2011)Numerical solution of stochastic differential equations (2016)Structural Reliability under Incomplete Probability Information (1986)Optimal Discretization of Random Fields (1993)Comparison of finite element reliability methods (2002)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)The Malliavin Calculus and Related Topics (2006)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)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)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies (2014)Stochastic finite element methods for partial differential equations with random input data (2014)Multi-resolution analysis of Wiener-type uncertainty propagation schemes (2004)Efficient Collocational Approach for Parametric Uncertainty Analysis (2007)Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs (2011)Adaptive Smolyak Pseudospectral Approximations (2013)Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark (2021)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 1996Numerical solution of spectral stochastic finite element systems294 cited
  • 2006Uncertainty propagation in CFD using polynomial chaos decomposition254 cited
  • 2005Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators183 cited
  • 1993Probabilistic engineering mechanics160 cited
  • 2005Maximum likelihood estimation of stochastic chaos representations from experimental data146 cited
  • 2004Generalized polynomial chaos and random oscillators129 cited
  • 2002Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms122 cited

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2008
Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices
117 cited
  • 2012Stochastic Models of Uncertainties in Computational Mechanics112 cited
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