Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

@article{Hampton2015CompressiveSO,
title={Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies},
author={Jerrad Hampton and Alireza Doostan},
journal={J. Comput. Phys.},
year={2015},
volume={280},
pages={363-386}
}
• Published 18 August 2014
• Computer Science, Mathematics
• J. Comput. Phys.
167 Citations

Figures and Tables from this paper

Sparse polynomial chaos expansions - Benchmark of compressive sensing solvers and experimental design techniques
• Computer Science
• 2019
This work proposes a general modular framework for adaptive sparse PCE computations, in which most of the methods put forward in the literature can be fit, and collects and explains the available methods and analyse their behavior on various analytical and numerical examples.
A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions
• Computer Science
SIAM J. Sci. Comput.
• 2017
An algorithm for recovering sparse orthogonal polynomial expansions via collocation that solves a preconditioned $\ell^1$-minimization problem and presents theoretical analysis and numerical results that show the method is superior to standard Monte Carlo methods in many situations of interest.
Sparse polynomial chaos expansions via compressed sensing and D-optimal design
• Computer Science
Computer Methods in Applied Mechanics and Engineering
• 2018
Polynomial chaos expansions for dependent random variables
• Computer Science
Computer Methods in Applied Mechanics and Engineering
• 2019
Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
• Computer Science
SIAM/ASA J. Uncertain. Quantification
• 2021
It is found that the choice of sparse regression solver and sampling scheme for the computation of a sparse PCE surrogate can make a significant difference, of up to several orders of magnitude in the resulting mean-square error.
Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach
• Computer Science
Communications in Mathematical Research
• 2020
The capacity of the proposed induced sampling algorithm via sparse representation with limited data on test functions, and on a Kirchoff plating bending problem with random Young's modulus, is demonstrated.

References

SHOWING 1-10 OF 58 REFERENCES
Sparse Legendre expansions via l1-minimization
• Mathematics, Computer Science
J. Approx. Theory
• 2012
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and
DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING
• Computer Science
• 2014
This work implements a PC-based surrogate model construction that “learns” and retains only the most relevant basis terms of the PC expansion, using sparse Bayesian learning, which dramatically reduces the dimensionality of the problem, making it more amenable to further analysis such as sensitivity or calibration studies.
Numerical Methods for Stochastic Computations: A Spectral Method Approach
This book describes the class of numerical methods based on generalized polynomial chaos (gPC), an extension of the classical spectral methods of high-dimensional random spaces designed to simulate complex systems subject to random inputs.
Postmaneuver Collision Probability Estimation Using Sparse Polynomial Chaos Expansions
• Computer Science
• 2015
Results demonstrate that these polynomial chaos-based methods provide a Monte Carlo-like estimate of the collision probability, including a potential collision with debris in low Earth orbit.
STOCHASTIC COLLOCATION ALGORITHMS USING 𝓁 1 -MINIMIZATION
• Computer Science
• 2012
The analysis suggests that using the Chebyshev measure to precondition the ‘1-minimization, which has been shown to be numerically advantageous in one dimension in the literature, may in fact become less efficient in high dimensions.