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Adaptive approximations for high-dimensional uncertainty quantification in stochastic parametric electromagnetic field simulations

Loukrezis, Dimitrios (2019):
Adaptive approximations for high-dimensional uncertainty quantification in stochastic parametric electromagnetic field simulations.
Darmstadt, Technische Universität, [Online-Edition: https://tuprints.ulb.tu-darmstadt.de/8485],
[Ph.D. Thesis]

Abstract

The present work addresses the problems of high-dimensional approximation and uncertainty quantification in the context of electromagnetic field simulations. In the presence of many parameters, one faces the so-called curse of dimensionality. The focus of this work lies on adaptive methods that mitigate the effect of the curse of dimensionality, and therefore enable otherwise intractable uncertainty quantification studies. Its application scope includes electromagnetic field models suffering from moderately high-dimensional input uncertainty. However, the presented methods can be used in a black-box fashion and are therefore applicable to other types of problems as well.

Item Type: Ph.D. Thesis
Erschienen: 2019
Creators: Loukrezis, Dimitrios
Title: Adaptive approximations for high-dimensional uncertainty quantification in stochastic parametric electromagnetic field simulations
Language: English
Abstract:

The present work addresses the problems of high-dimensional approximation and uncertainty quantification in the context of electromagnetic field simulations. In the presence of many parameters, one faces the so-called curse of dimensionality. The focus of this work lies on adaptive methods that mitigate the effect of the curse of dimensionality, and therefore enable otherwise intractable uncertainty quantification studies. Its application scope includes electromagnetic field models suffering from moderately high-dimensional input uncertainty. However, the presented methods can be used in a black-box fashion and are therefore applicable to other types of problems as well.

Place of Publication: Darmstadt
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields > Electromagnetic Field Theory (until 31.12.2018 Computational Electromagnetics Laboratory)
18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 10 Mar 2019 20:55
Official URL: https://tuprints.ulb.tu-darmstadt.de/8485
URN: urn:nbn:de:tuda-tuprints-84854
Referees: De Gersem, Prof. Dr. Herbert and Römer, Prof. Dr. Ulrich
Refereed / Verteidigung / mdl. Prüfung: 4 February 2019
Alternative Abstract:
Alternative abstract Language
Die vorliegende Arbeit beschäftigt sich mit den Problemen der hochdimensionalen Approximation und der Quantifizierung der Unsicherheit im Zusammenhang mit elektromagnetischen Feldsimulationen. In Anwesenheit vieler Parameter steht man dem sogenannten Fluch der Dimensionalität gegenüber. Der Fokus dieser Arbeit liegt auf adaptiven Methoden, die die Auswirkung des Fluches der Dimensionalität abschwächen und daher ansonsten unlösbare Quantifizierungsstudien zur Unsicherheit ermöglichen. Sein Anwendungsbereich umfasst elektromagnetische Feldmodelle, die unter mäßig hochdimensionaler Eingangsunsicherheit leiden. Die vorgestellten Verfahren können jedoch in einer Black-Box-Art verwendet werden und sind daher auch auf andere Arten von Problemen anwendbar.German
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