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Long-time uncertainty propagation using generalized polynomial chaos and flow map composition
9 references·4 citing·30 second hop
Long-time uncertainty propagation using generalized polynomial chaos and flow map composition (2014)Long-time uncertainty propagation using g…On the convergence of generalized polynomial chaos expansions (2011)On the convergence of general…Time-dependent generalized polynomial chaos (2010)Time-dependent generalized po…Spectral Methods for Uncertainty Quantification (2010)Spectral Methods for Uncertai…Fast Numerical Methods for Stochastic Computations: A Review (2009)Fast Numerical Methods for St…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…Uncertainty propagation in CFD using polynomial chaos decomposition (2006)Uncertainty propagation in CF…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…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…Stochastic analysis of a crash box under impact loading by an adaptive POD-PCE model (2022)Stochastic analysis of a cras…Uncertainty Quantification of Stochastic Impact Dynamic Oscillator Using a Proper Orthogonal Decomposition-Polynomial Chaos Expansion Technique (2020)Uncertainty Quantification of…A Kriging–NARX Model for Uncertainty Quantification of Nonlinear Stochastic Dynamical Systems in Time Domain (2020)A Kriging–NARX Model for Unce…Surrogate modelling for stochastic dynamical systems by combining NARX models and polynomial chaos expansions (2016)Surrogate modelling for stoch…A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems (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)Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model (2012)Metamodeling of dynamic nonlinear structural systems through polynomial chaos NARX models (2015)Polynomial Chaos Expansion for Parametric Problems in Engineering Systems: A Review (2020)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)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters (2015)POLYNOMIAL-CHAOS-BASED KRIGING (2015)Method for Random Vibration of Hysteretic Systems (1976)Design and Analysis of Computer Experiments (1989)Uncertainty quantification and reliability analysis by an adaptive sparse Bayesian inference based PCE model (2021)rLSTM-AE for dimension reduction and its application to active learning-based dynamic reliability analysis (2024)Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011)An Introduction to Computational Stochastic PDEs (2014)Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey (2020)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)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)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)
this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2010Spectral Methods for Uncertainty Quantification953 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2009Fast Numerical Methods for Stochastic Computations: A Review608 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2006Uncertainty propagation in CFD using polynomial chaos decomposition254 cited
  • 2010Time-dependent generalized polynomial chaos173 cited

Cited by

  • 2020A Kriging–NARX Model for Uncertainty Quantification of Nonlinear Stochastic Dynamical Systems in Time Domain40 cited
  • 2020Uncertainty Quantification of Stochastic Impact Dynamic Oscillator Using a Proper Orthogonal Decomposition-Polynomial Chaos Expansion Technique20 cited
  • 2016Surrogate modelling for stochastic dynamical systems by combining NARX models and polynomial chaos expansions10 cited
  • 2022Stochastic analysis of a crash box under impact loading by an adaptive POD-PCE model7 cited

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