Adaptive Sampling and Online Enrichment Strategies for RB-Based PDE-Constrained Stochastic Optimization

Hauger, Fabio

Adaptive Sampling and Online Enrichment Strategies for RB-Based PDE-Constrained Stochastic Optimization

Dateien

Hauger_2-kvj0jeiy0v66.pdfGröße: 2.9 MBDownloads: 151

Datum

2021

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Masterarbeit/Diplomarbeit

Publikationsstatus

Published

Zusammenfassung

In the thesis presented, we will analyze a PDE-constrained optimal control problem with uncertain coefficients. While solving such optimal control problems, many expensive PDE solves are required, leading to high run times. It is beneficial to use a reduced order model instead of the high-dimensional PDE solves to overcome that problem. To achieve this, reduced basis (RB) methods are used in the following. This thesis contributes to the existing literature by developing a Greedy algorithm with adaptive sampling strategies for the training set and analyzing the Greedy algorithm in conjunction with stochastic descent methods and a Trust-Region framework. In addition to the Trust-Region method, further online enrichment strategies are investigated.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

HAUGER, Fabio, 2021. Adaptive Sampling and Online Enrichment Strategies for RB-Based PDE-Constrained Stochastic Optimization [Master thesis]. Konstanz: Universität Konstanz

BibTex

@mastersthesis{Hauger2021Adapt-55763,
  year={2021},
  title={Adaptive Sampling and Online Enrichment Strategies for RB-Based PDE-Constrained Stochastic Optimization},
  address={Konstanz},
  school={Universität Konstanz},
  author={Hauger, Fabio}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/55763">
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-12-07T08:27:47Z</dcterms:available>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-12-07T08:27:47Z</dc:date>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Hauger, Fabio</dc:creator>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:contributor>Hauger, Fabio</dc:contributor>
    <dcterms:issued>2021</dcterms:issued>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/55763/3/Hauger_2-kvj0jeiy0v66.pdf"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55763"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:title>Adaptive Sampling and Online Enrichment Strategies for RB-Based PDE-Constrained Stochastic Optimization</dcterms:title>
    <dcterms:abstract xml:lang="eng">In the thesis presented, we will analyze a PDE-constrained optimal control problem with uncertain coefficients. While solving such optimal control problems, many expensive PDE solves are required, leading to high run times. It is beneficial to use a reduced order model instead of the high-dimensional PDE solves to overcome that problem. To achieve this, reduced basis (RB) methods are used in the following. This thesis contributes to the existing literature by developing a Greedy algorithm with adaptive sampling strategies for the training set and analyzing the Greedy algorithm in conjunction with stochastic descent methods and a Trust-Region framework. In addition to the Trust-Region method, further online enrichment strategies are investigated.</dcterms:abstract>
    <dc:language>eng</dc:language>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/55763/3/Hauger_2-kvj0jeiy0v66.pdf"/>
  </rdf:Description>
</rdf:RDF>

Hochschulschriftenvermerk

Konstanz, Universität Konstanz, Masterarbeit/Diplomarbeit, 2021

Universitätsbibliographie

Nein