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Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data
16 references·16 citing·24 second hopsampled
Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data (2010)Identification of high-dimension polynomi…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)Stochastic spectral methods f…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…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 …Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…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 …Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos (2002)Modeling uncertainty in stead…A Stochastic Projection Method for Fluid Flow (2002)A Stochastic Projection Metho…A state-of-the-art report on computational stochastic mechanics (1997)A state-of-the-art report on …Entropy optimization principles with applications (1993)Entropy optimization principl…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Polynomial Chaos in Stochastic Finite Elements (1990)Polynomial Chaos in Stochasti…Stochastic Finite Element Expansion for Random Media (1989)Stochastic Finite Element Exp…An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials (2023)An overview on uncertainty qu…A non-Gaussian stochastic model from limited observations using polynomial chaos and fractional moments (2022)A non-Gaussian stochastic mod…LSTM-augmented deep networks for time-variant reliability assessment of dynamic systems (2021)LSTM-augmented deep networks …Recent progress of uncertainty quantification in small-scale materials science (2020)Recent progress of uncertaint…Bayesian deep learning with hierarchical prior: Predictions from limited and noisy data (2020)Bayesian deep learning with h…Polynomial Chaos Expansion of a Multimodal Random Vector (2015)Polynomial Chaos Expansion of…A stochastic computational multiscale approach; Application to MEMS resonators (2015)A stochastic computational mu…A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates (2015)A data driven polynomial chao…Random field representations for stochastic elliptic boundary value problems and statistical inverse problems (2014)Random field representations …Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media (2013)Stochastic Model and Generato…Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations (2012)Identification of Polynomial …On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview (2011)On the Capabilities of the Po…Non‐Gaussian positive‐definite matrix‐valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries (2011)Non‐Gaussian positive‐definit…Generalized stochastic approach for constitutive equation in linear elasticity: a random matrix model (2011)Generalized stochastic approa…A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension (2011)A computational inverse metho…Computational Aspects for Constructing Realizations of Polynomial Chaos in High Dimension (2010)Computational Aspects for Con…Neumann Expansion for Stochastic Finite Element Analysis (1988)A nonparametric model of random uncertainties for reduced matrix models in structural dynamics (2000)A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)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)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles (2011)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)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)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Fast Numerical Methods for Stochastic Computations: A Review (2009)On the convergence of generalized polynomial chaos expansions (2011)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)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)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)
this work references cited by second hop· second hop is a sample of the most-cited connections

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 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
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 1989Stochastic Finite Element Expansion for Random Media512 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 1993Entropy optimization principles with applications493 cited
  • 2006Stochastic spectral methods for efficient Bayesian solution of inverse problems471 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited

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1997
A state-of-the-art report on computational stochastic mechanics
424 cited
  • 1990Polynomial Chaos in Stochastic Finite Elements416 cited
  • Cited by

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    • 2012Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations50 cited
    • 2021LSTM-augmented deep networks for time-variant reliability assessment of dynamic systems48 cited
    • 2011Generalized stochastic approach for constitutive equation in linear elasticity: a random matrix model44 cited
    • 2015A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates41 cited
    • 2023An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials38 cited
    • 2020Recent progress of uncertainty quantification in small-scale materials science38 cited
    • 2015A stochastic computational multiscale approach; Application to MEMS resonators37 cited
    • 2014Random field representations for stochastic elliptic boundary value problems and statistical inverse problems36 cited
    • 2020Bayesian deep learning with hierarchical prior: Predictions from limited and noisy data36 cited
    • 2011On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview32 cited
    • 2010Computational Aspects for Constructing Realizations of Polynomial Chaos in High Dimension32 cited
    • 2022A non-Gaussian stochastic model from limited observations using polynomial chaos and fractional moments31 cited
    • 2011Non‐Gaussian positive‐definite matrix‐valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries31 cited