Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems
Grunddaten zum Vortrag
Art des Vortrags: wissenschaftlicher Vortrag
Name der Vortragenden: Kleikamp, Hendrik
Datum des Vortrags: 19.03.2024
Vortragssprache: Englisch
URL zu den Präsentationsfolien: https://www.uni-muenster.de/AMM/num/ohlberger/kleikamp/talks/algoritmy2024.pdf
Informationen zur Veranstaltung
Name der Veranstaltung: Minisymposium on "New Trends in Model Order Reduction and Learning" at ALGORITMY 2024, Central-European Conference on Scientific Computing
Zeitraum der Veranstaltung: 15.03.2024 - 20.03.2024
Ort der Veranstaltung: Podbanske
Webseite der Veranstaltung: https://www.math.sk/alg2024/
Veranstaltet von: Slovak University of Technology in Bratislava, Comenius University in Bratislava, Algoritmy:SK s.r.o. and Union of the Slovak Mathematicians and Physicists
Zusammenfassung
We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control algorithm, which builds a reduced basis for the manifold of optimal final time adjoint states, to the setting where the objective functional consists of a penalty term measuring the deviation from a desired state and a term describing the control energy. Afterwards, we apply machine learning surrogates to accelerate the online evaluation of the reduced model. The error estimates proven for the greedy procedure are further transferred to the machine learning models and thus allow for efficient a posteriori error certification. Numerical examples highlight the potential of the proposed methodology.Stichwörter: Parametrized optimal control; Model order reduction; Machine learning; Model hierarchy; Adaptivity
Vortragende der Universität Münster
| Kleikamp, Hendrik | Professur für Angewandte Mathematik, insbesondere Numerik (Prof. Ohlberger) |