Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems

Basic data for this talk

Type of talkscientific talk
Name der VortragendenKleikamp, Hendrik
Date of talk05/03/2025
Talk languageEnglish
URL of slideshttps://www.uni-muenster.de/AMM/num/ohlberger/kleikamp/talks/siamcse2025.pdf

Information about the event

Name of the eventSIAM CSE (SIAM Conference on Computational Science and Engineering)
Event period03/03/2025 - 07/03/2025
Event locationFort Worth
Event websitehttps://www.siam.org/conferences-events/siam-conferences/cse25/
Organised bySIAM (Society for Industrial and Applied Mathematics)

Abstract

In this talk we present an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the system dynamics and of the manifold of optimal final time adjoint states to achieve a computational complexity independent of the original state space. Such a combination is particularly beneficial in the case where a deviation in a low-dimensional output is penalized. We propose different strategies for building the involved reduced order models, for instance by separate reduction of the dynamical systems and the final time adjoint states or via greedy procedures yielding a combined and fully reduced model. These algorithms are evaluated and compared for a two-dimensional heat equation problem. The numerical results show the desired accuracy of the reduced models and highlight the speedup obtained by the newly combined reduced order model in comparison to an exact computation of the optimal control or other reduction approaches.
Keywordsmodel order reduction; machine learning; model hierarchies; parametrized optimal control problems; reduced basis methods

Speakers from the University of Münster

Kleikamp, Hendrik
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)