Article2018

Gradient-Informed Basis Adaptation for Legendre Chaos Expansions

8 citations0/0 files storedJournal of Verification Validation and Uncertainty Quantification

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Probabilistic and Robust Engineering Design Model Reduction and Neural Networks Gaussian Processes and Bayesian Inference

Abstract

Abstract The recently introduced basis adaptation method for homogeneous (Wiener) chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace (AS) where the random input exhibits most of its variability. In the case where a One-dimensional (1D) AS exists, the methodology can be applicable to generalized polynomial chaos expansions (PCE), thus enabling the projection of a high-dimensional input to a single input variable and the efficient estimation of a univariate chaos expansion. Attractive features of this approach, such as the significant computational savings and the high accuracy in computing statistics of interest are investigated.

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References

2007Global Sensitivity Analysis. The Primer 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2007Global sensitivity analysis using polynomial chaos expansions 1992Multivariate stochastic approximation using a simultaneous perturbation gradient approximation 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2012INTRODUCTION TO STOCHASTIC SEARCH AND OPTIMIZATION: ESTIMATION, SIMULATION, AND CONTROL 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics

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