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A Compressed Sensing Approach for Partial Differential Equations with Random Input Data
14 references·16 citing·20 second hop
A Compressed Sensing Approach for Partial Differential Equations with Random Input Data (2012)A Compressed Sensing Approach for Partial…An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An Anisotropic Sparse Grid St…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Stochastic Approaches to Uncertainty Quantification in CFD Simulations (2005)Stochastic Approaches to Unce…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Uncertainty propagation using Wiener–Haar expansions (2004)Uncertainty propagation using…Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2004)Physical Systems with Random …Multi-resolution analysis of Wiener-type uncertainty propagation schemes (2004)Multi-resolution analysis of …Finite elements for elliptic problems with stochastic coefficients (2004)Finite elements for elliptic …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 …Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Efficient uncertainty quantification of turbine blade leading edge film cooling using bi-fidelity combination of compressed sensing and Kriging (2020)Efficient uncertainty quantif…Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error (2020)Active learning polynomial ch…Basis adaptive sample efficient polynomial chaos (BASE-PC) (2018)Basis adaptive sample efficie…An efficient multifidelity ℓ1 -minimization method for sparse polynomial chaos (2018)An efficient multifidelity ℓ1…Time‐dependent global sensitivity analysis with active subspaces for a lithium ion battery model (2017)Time‐dependent global sensiti…Surrogate Models for Uncertainty Propagation and Sensitivity Analysis (2017)Surrogate Models for Uncertai…Stochastic Collocation Methods: A Survey (2017)Stochastic Collocation Method…Efficient uncertainty quantification of stochastic CFD problems using sparse polynomial chaos and compressed sensing (2017)Efficient uncertainty quantif…Sparse polynomial surrogates for aerodynamic computations with random inputs (2016)Sparse polynomial surrogates …不确定性量化的高精度数值方法和理论 (2015)不确定性量化的高精度数值方法和理论Surrogate Models for Uncertainty Propagation and Sensitivity Analysis (2015)Surrogate Models for Uncertai…Stochastic Collocation Methods: A Survey (2015)Stochastic Collocation Method…Stochastic Collocation Algorithms Using $l_1$-Minimization for Bayesian Solution of Inverse Problems (2015)Stochastic Collocation Algori…Compressive Sampling Methods for Sparse Polynomial Chaos Expansions (2015)Compressive Sampling Methods …SPARSE MULTIRESOLUTION REGRESSION FOR UNCERTAINTY PROPAGATION (2014)SPARSE MULTIRESOLUTION REGRES…Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection (2011)Multiscale Stochastic Precond…Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (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)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. (1987)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)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)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)Efficient Collocational Approach for Parametric Uncertainty Analysis (2007)Fast Numerical Methods for Stochastic Computations: A Review (2009)On the convergence of generalized polynomial chaos expansions (2011)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)
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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
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2004Finite elements for elliptic problems with stochastic coefficients364 cited
  • 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
  • 2005Stochastic Approaches to Uncertainty Quantification in CFD Simulations

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281 cited

Cited by

  • 2017Time‐dependent global sensitivity analysis with active subspaces for a lithium ion battery model46 cited
  • 2018An efficient multifidelity ℓ1 -minimization method for sparse polynomial chaos46 cited
  • 2017Efficient uncertainty quantification of stochastic CFD problems using sparse polynomial chaos and compressed sensing43 cited
  • 2018Basis adaptive sample efficient polynomial chaos (BASE-PC)42 cited
  • 2015Stochastic Collocation Algorithms Using $l_1$-Minimization for Bayesian Solution of Inverse Problems32 cited
  • 2011Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection31 cited
  • 2017Surrogate Models for Uncertainty Propagation and Sensitivity Analysis28 cited
  • 2017Stochastic Collocation Methods: A Survey27 cited
  • 2015不确定性量化的高精度数值方法和理论27 cited
  • 2020Efficient uncertainty quantification of turbine blade leading edge film cooling using bi-fidelity combination of compressed sensing and Kriging22 cited
  • 2014SPARSE MULTIRESOLUTION REGRESSION FOR UNCERTAINTY PROPAGATION20 cited
  • 2020Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error20 cited
  • 2015Compressive Sampling Methods for Sparse Polynomial Chaos Expansions17 cited
  • 2015Surrogate Models for Uncertainty Propagation and Sensitivity Analysis16 cited
  • 2016Sparse polynomial surrogates for aerodynamic computations with random inputs14 cited
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