Some greedy algorithms for sparse polynomial chaos expansions

Baptista, Ricardo; Stolbunov, Valentin; Nair, Prasanth B.

doi:10.1016/j.jcp.2019.01.035

Cited by 27 publications

(6 citation statements)

References 38 publications

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“…At present, the commonly used methods for selecting the basis function include the convex relaxation algorithm (CR) [ 26 ] and orthogonal matching pursuit (OMP), etc. [ 12 , 30 ]. Among them, OMP determines the position of the nonzero item by verifying the orthogonality between the residual and the expansion item, and then the approximate solution of the L0 norm minimization problem is directly obtained by the least square method.…”

Section: Methodsmentioning

confidence: 99%

Global sensitivity analysis of parameters based on sPCE: The case study of a concrete face rockfill dam in northwest China

Ran,

Yang,

et al. 2023

PLoS ONE

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To effectively identify the key material parameters of different zones of concrete face rockfill dams and improve the efficiency of parameter optimization, a global sensitivity analysis method of parameters based on sparse polynomial chaotic expansion (sPCE) is proposed in this paper. The latin hypercube sampling method is used to select multiple groups of material parameters, and then finite element method is used to calculate the displacement of dam characteristic nodes in dam body. On this basis, the displacement is expanded by sPCE, and the polynomial basis function is reconstructed by orthogonal matching pursuit to improve the construction and analysis efficiency of the proxy model. According to the chaos coefficients, Sobol’ indices are calculated to evaluate the influence of the material parameters and their interaction on different displacements of the dam. The results show that the sPCE model can accurately simulate dam displacement and its statistical characteristics with a relatively small sample size. The sensitivity of the same parameter has spatial variability, and under the influence of parameter levels and spatial distribution of different materials, the parameter sensitivity ranking of different zones has certain differences. The proposed method provides a new reference to sensitivity analysis and uncertainty analysis for practical engineering.

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Section: Methodsmentioning

confidence: 99%

Global sensitivity analysis of parameters based on sPCE: The case study of a concrete face rockfill dam in northwest China

Ran,

Yang,

et al. 2023

PLoS ONE

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show abstract

“…Orthogonal matching pursuit (OMP) (Tropp and Gilbert, 2007;Doostan and Owhadi, 2011;Marelli and Sudret, 2019) is a classical forward selection algorithm in which orthonormalized regressors are added to the model one-by-one according to their correlation with the residual, and the coefficients are computed by least-squares. Baptista et al (2019) suggest extensions to OMP such as parallelization, randomization and a modified regressor selection procedure. Subspace pursuit (SP) (Dai and Milenkovic, 2009;Diaz et al, 2018;Diaz, 2018) is an iterative algorithm that repeatedly uses least squares on a subset of regressors.…”

Section: Solution Of the Minimization Problemmentioning

confidence: 99%

Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark

Lüthen,

Marelli,

Sudret

2020

Preprint

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Sparse polynomial chaos expansions are a popular surrogate modelling method that takes advantage of the properties of polynomial chaos expansions (PCE), the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with many input parameters, relying on only few model evaluations. Within the last decade, a large number of algorithms for the computation of sparse PCE have been published in the applied math and engineering literature. We present an extensive review of the existing methods and develop a framework to classify the algorithms. Furthermore, we conduct a benchmark on a selection of methods to identify which methods work best in practical applications.Comparing their accuracy on several benchmark models of varying dimension and complexity, we find 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. Different methods seem to be superior in different regimes of model dimensionality and experimental design size.

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“…In this paper, an enhanced version of the algorithm proposed in [17] is adopted. In [17], a greedy algorithm [45] and a (dense) grid obtained as the Cartesian product of Gaussian Points of Legendre polynomials were adopted for the construction of the reduced order model, incurring in the curse of dimensionality problem. In this work, a random-based method for the construction of the reduced order model is used instead, thus avoiding the problem of the curse of dimensionality and significantly accelerating the algorithm without loosing accuracy, as shown in section IV.…”

Section: A Parametric Model Order Reductionmentioning

confidence: 99%

Fast Uncertainty Quantification in Low Frequency Electromagnetic Problems by an Integral Equation Method Based on Hierarchical Matrix Compression

et al. 2019

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A parametric model order reduction method combined with a polynomial spectral approximation is applied for the first time to a Volume Integral Equation method accelerated by a low-rank matrix compression technique. Such an approach allows for drastically reducing the computational cost required by uncertainty quantifications in electromagnetic problems. Moreover, the proposed numerical tool can be adopted for computing stochastic information (e.g. mean, variance, probability density function) of any electromagnetic quantity of interest, in order to test the reliability of industrial devices with uncertainties on the material parameters. Conductive, dielectric, and magnetic media which exhibit uncorrelated and correlated random material parameters are considered by the proposed method.

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Some greedy algorithms for sparse polynomial chaos expansions

Cited by 27 publications

References 38 publications

Global sensitivity analysis of parameters based on sPCE: The case study of a concrete face rockfill dam in northwest China

Global sensitivity analysis of parameters based on sPCE: The case study of a concrete face rockfill dam in northwest China

Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark

Fast Uncertainty Quantification in Low Frequency Electromagnetic Problems by an Integral Equation Method Based on Hierarchical Matrix Compression

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