Loukrezis, Dimitrios ; De Gersem, Herbert (2020)
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation.
In: Algorithms, 13 (3)
doi: 10.3390/a13030051
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
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
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2020 |
| Autor(en): | Loukrezis, Dimitrios ; De Gersem, Herbert |
| Art des Eintrags: | Bibliographie |
| Titel: | Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation |
| Sprache: | Englisch |
| Publikationsjahr: | 2020 |
| Verlag: | MDPI |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Algorithms |
| Jahrgang/Volume einer Zeitschrift: | 13 |
| (Heft-)Nummer: | 3 |
| Kollation: | 20 Seiten |
| DOI: | 10.3390/a13030051 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | 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 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Teilchenbeschleunigung und Theorie Elektromagnetische Felder |
| Hinterlegungsdatum: | 02 Aug 2024 12:35 |
| Letzte Änderung: | 02 Aug 2024 12:35 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
-
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation. (deposited 28 Jul 2021 08:11)
- Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation. (deposited 02 Aug 2024 12:35) [Gegenwärtig angezeigt]
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum