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Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
15 references·16 citing·31 second hop
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The Primer (2007)Uncertainty quantification in multiscale simulation of woven fiber composites (2018)Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey (2020)Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review (2023)Stochastic Finite Elements: A Spectral Approach (1991)Structural reliability under combined random load sequences (1978)Estimation of small failure probabilities in high dimensions by subset simulation (2001)A new learning function for Kriging and its applications to solve reliability problems in engineering (2015)Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation (2016)LIF: A new Kriging based learning function and its application to structural reliability analysis (2016)A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output (1999)Sensitivity analysis of environmental models: A systematic review with practical workflow (2016)Structural Reliability under Incomplete Probability Information (1986)Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements (1997)Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes (2001)The PHI2 method: a way to compute time-variant reliability (2003)Structural Reliability Methods (1996)Reliability-based design optimization using kriging surrogates and subset simulation (2011)Multi-Factor Experimental Designs for Exploring Response Surfaces (1957)Experiments with Mixtures (1958)Optimum Experimental Designs (1959)General Equivalence Theory for Optimum Designs (Approximate Theory) (1974)Optimum Experimental Designs (1992)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)UQLab: A Framework for Uncertainty Quantification in Matlab (2014)Stochastic finite element methods for partial differential equations with random input data (2014)A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry (2015)
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2007Global sensitivity analysis using polynomial chaos expansions2,547 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2010Adaptive sparse polynomial chaos expansion based on least angle regression1,507 cited
  • 2009An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis834 cited
  • 1959Optimum Designs in Regression Problems796 cited
  • 1993Optimal Discretization of Random Fields728 cited
  • 2012A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models692 cited
  • 2015The generalization of Latin hypercube sampling656 cited
  • 2011A non-adapted sparse approximation of PDEs with stochastic inputs436 cited
  • 2006Stochastic finite element: a non intrusive approach by regression427 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2015POLYNOMIAL-CHAOS-BASED KRIGING398 cited
  • 2010Efficient computation of global sensitivity indices using sparse polynomial chaos expansions383 cited
  • 2008

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Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach
270 cited

Cited by

  • 2020Adaptive approaches in metamodel-based reliability analysis: A review280 cited
  • 2024A Review of Recent Advances in Surrogate Models for Uncertainty Quantification of High-Dimensional Engineering Applications81 cited
  • 2022Enhancing the explainability of regression-based polynomial chaos expansion by Shapley additive explanations75 cited
  • 2021Variance-based adaptive sequential sampling for Polynomial Chaos Expansion53 cited
  • 2022On distribution-based global sensitivity analysis by polynomial chaos expansion46 cited
  • 2022Efficient reliability analysis using prediction-oriented active sparse polynomial chaos expansion42 cited
  • 2022STOCHASTIC POLYNOMIAL CHAOS EXPANSIONS TO EMULATE STOCHASTIC SIMULATORS40 cited
  • 2023An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials38 cited
  • 2022An active-learning reliability method based on support vector regression and cross validation36 cited
  • 2023A spectral surrogate model for stochastic simulators computed from trajectory samples33 cited
  • 2021AUTOMATIC SELECTION OF BASIS-ADAPTIVE SPARSE POLYNOMIAL CHAOS EXPANSIONS FOR ENGINEERING APPLICATIONS33 cited
  • 2022A new method for stochastic analysis of structures under limited observations33 cited
  • 2024Active Learning of Ensemble Polynomial Chaos Expansion Method for Global Sensitivity Analysis32 cited
  • 2021Buckling Sensitivity of Tow-Steered Plates Subjected to Multiscale Defects by High-Order Finite Elements and Polynomial Chaos Expansion32 cited
  • 2021Structural reliability analysis by a Bayesian sparse polynomial chaos expansion31 cited
  • 2023Partial least squares-based polynomial chaos Kriging for high-dimensional reliability analysis29 cited