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Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs
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Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs (2018)Non-intrusive Tensor Reconstruction for H…Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format (2015)Polynomial Chaos Expansion of…Stochastic finite element methods for partial differential equations with random input data (2014)Stochastic finite element met…An Introduction to Computational Stochastic PDEs (2014)An Introduction to Computatio…Adaptive stochastic Galerkin FEM (2013)Adaptive stochastic Galerkin …Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs (2011)Sparse tensor discretizations…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A Stochastic Collocation Meth…A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)A Sparse Grid Stochastic Coll…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Karhunen–Loève approximation of random fields by generalized fast multipole methods (2006)Karhunen–Loève approximation …Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Solving elliptic boundary val…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)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)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)On the convergence of generalized polynomial chaos expansions (2011)Accelerating Monte Carlo estimation with derivatives of high-level finite element models (2017)Large deformation shape uncertainty quantification in acoustic scattering (2018)Fuzzy sets (1965)Fuzzy sets (1996)Stochastic model reduction for chaos representations (2007)The Logic of Scientific Discovery (2013)Finite elements for elliptic problems with stochastic coefficients (2004)Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010)Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2015)Multilevel Estimation of Rare Events (2015)Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients (2017)Structural Reliability Analysis and Prediction (2017)Stochastic Integration and Differential Equations (2005)Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk (2016)Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems (2020)Digital simulation of random processes and its applications (1972)A Fast Polynomial Chaos Expansion for Uncertainty Quantification in Stochastic Electromagnetic Problems (2019)Analysis of Boundary Effects on PDE-Based Sampling of Whittle--Matérn Random Fields (2019)The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions (2020)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations (2010)Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual. (2010)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2014An Introduction to Computational Stochastic PDEs544 cited
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  • 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation345 cited
  • 2011Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs260 cited
  • 2014Stochastic finite element methods for partial differential equations with random input data218 cited
  • 2013Adaptive stochastic Galerkin FEM111 cited
  • 2015Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format63 cited

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