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

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Hauger_2-kvj0jeiy0v66.pdf(2.9 MB)
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2021
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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.
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510 Mathematik
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ISO 690HAUGER, 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}
}
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Konstanz, Universität Konstanz, Masterarbeit/Diplomarbeit, 2021
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