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Open AccessArticle

Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation

by 1,2,*,† and 1,2,†
1
Institute for Accelerator Science and Electromagnetic Fields (TEMF), Technische Universität Darmstadt, 64289 Darmstadt, Germany
2
Centre for Computational Engineering, Technische Universität Darmstadt, 64289 Darmstadt, Germany
*
Author to whom correspondence should be addressed.
Current address: Schlossgartenstraße 8, 64289 Darmstadt, Germany.
Algorithms 2020, 13(3), 51; https://doi.org/10.3390/a13030051
Received: 14 December 2019 / Revised: 20 February 2020 / Accepted: 22 February 2020 / Published: 26 February 2020
Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more system parameters are not normal, uniform, or closely related distributions, due to the computational issues that arise when one wishes to define interpolation nodes for general distributions. This paper examines the use of the recently introduced weighted Leja nodes for that purpose. Weighted Leja interpolation rules are presented, along with a dimension-adaptive sparse interpolation algorithm, to be employed in the case of high-dimensional input uncertainty. The performance and reliability of the suggested approach is verified by four numerical experiments, where the respective models feature extreme value and truncated normal parameter distributions. Furthermore, the suggested approach is compared with a well-established polynomial chaos method and found to be either comparable or superior in terms of approximation and statistics estimation accuracy. View Full-Text
Keywords: adaptive algorithms; arbitrary probability distributions; sparse interpolation; uncertainty quantification; weighted Leja sequences adaptive algorithms; arbitrary probability distributions; sparse interpolation; uncertainty quantification; weighted Leja sequences
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MDPI and ACS Style

Loukrezis, D.; De Gersem, H. Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation. Algorithms 2020, 13, 51. https://doi.org/10.3390/a13030051

AMA Style

Loukrezis D, De Gersem H. Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation. Algorithms. 2020; 13(3):51. https://doi.org/10.3390/a13030051

Chicago/Turabian Style

Loukrezis, Dimitrios; De Gersem, Herbert. 2020. "Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation" Algorithms 13, no. 3: 51. https://doi.org/10.3390/a13030051

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