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A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models
16 references·0 citing·24 second hop
A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models (2008)A seamless approach towards stochastic mo…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…Efficient Collocational Approach for Parametric Uncertainty Analysis (2007)Efficient Collocational Appro…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Stochastic analysis of transport in tubes with rough walls (2006)Stochastic analysis of transp…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…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Solving elliptic boundary val…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …A new stochastic approach to transient heat conduction modeling with uncertainty (2003)A new stochastic approach to …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos (2002)Modeling uncertainty in stead…Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Probabilistic characterization of transport in heterogeneous media (1998)Probabilistic characterizatio…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. (1987)Uncertainty propagation using Wiener–Haar expansions (2004)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)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)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)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Fast Numerical Methods for Stochastic Computations: A Review (2009)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)
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References

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  • 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
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  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation345 cited
  • 2007Efficient Collocational Approach for Parametric Uncertainty Analysis309 cited
  • 2003A new stochastic approach to transient heat conduction modeling with uncertainty216 cited
  • 1998Probabilistic characterization of transport in heterogeneous media

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166 cited
  • 2005Maximum likelihood estimation of stochastic chaos representations from experimental data146 cited
  • 2006Stochastic analysis of transport in tubes with rough walls104 cited
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