Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems
Basic data for this talk
Type of talk: scientific talk
Name der Vortragenden: Kleikamp, Hendrik
Date of talk: 19/03/2024
Talk language: English
Information about the event
Name of the event: Minisymposium on "New Trends in Model Order Reduction and Learning" at ALGORITMY 2024, Central-European Conference on Scientific Computing
Event period: 15/03/2024 - 20/03/2024
Event location: Podbanske
Event website: https://www.math.sk/alg2024/
Organised by: Slovak University of Technology in Bratislava, Comenius University in Bratislava, Algoritmy:SK s.r.o. and Union of the Slovak Mathematicians and Physicists
Abstract
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.Keywords: Parametrized optimal control; Model order reduction; Machine learning; Model hierarchy; Adaptivity
Speakers from the University of Münster
| Kleikamp, Hendrik | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) |