Simplex Stochastic Collocation for Piecewise Smooth Functions With Kinks

Fuchs, B.A.; Garcke, Jochen

doi:10.1615/int.j.uncertaintyquantification.2019030208

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…18 Here, we focus on the non-intrusive multi-element stochastic collocation method on hypercubes for forward and inverse UQ. Although several proposals for multi-element collocation exist, 16,17,[19][20][21][22][23] a number of challenges remain to be addressed. Most notably, computational efficiency considerations require to limit the number of collocation points, which is problematic since existing points do not necessarily fit to a collocation pattern once the subdomains in the parameter space are refined.…”

Section: Introductionmentioning

confidence: 99%

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Galetzka

Loukrezis

Georg

et al. 2023

Numerical Meth Engineering

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This article introduces an hp-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either h-or p-refinement. The collocation method is based on weighted Leja nodes. After h-refinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created sub-element in a hierarchical manner.For p-refinement, the local polynomial approximations are based on total-degree or dimension-adaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localized response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.

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Section: Introductionmentioning

confidence: 99%

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Galetzka

Loukrezis

Georg

et al. 2023

Numerical Meth Engineering

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show abstract

“…Here, we focus on the non-intrusive multi-element stochastic collocation method for forward and inverse UQ. Although several proposals for multi-element collocation exist [14][15][16][17][18][19][20] , a number of challenges remain to be addressed. Most notably, computational efficiency considerations require to limit the number of collocation points, which is problematic since existing points do not necessarily fit to a collocation pattern once the subdomains in the parameter space are refined.…”

Section: Introductionmentioning

confidence: 99%

An $hp$-adaptive multi-element stochastic collocation method for surrogate modeling with information re-use

Galetzka¹,

Loukrezis²,

Georg³

et al. 2022

Preprint

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This paper introduces an ℎ -adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either ℎ-or -refinement. The collocation method is based on weighted Leja nodes. After ℎrefinement, local interpolations are stabilized by adding Leja nodes on each newly created sub-element in a hierarchical manner. A dimension-adaptive algorithm is employed for local -refinement. The suggested multi-element stochastic collocation method is employed in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localised response surfaces. Comparisons against existing multi-element collocation schemes and other competing methods in five different test cases verify the advantages of the suggested method in terms of accuracy versus computational cost.

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State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

Fuhg¹,

Fau²,

Nackenhorst³

2020

Arch Computat Methods Eng

150

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Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox.

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Simplex Stochastic Collocation for Piecewise Smooth Functions With Kinks

Cited by 4 publications

References 19 publications

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

An $hp$-adaptive multi-element stochastic collocation method for surrogate modeling with information re-use

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

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