Adaptive model hierarchies for solving parametrized optimal control problems in multi-query scenarios

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Abstract

In this talk we introduce different reduced order models and machine learning surrogates to solve parametrized optimal control problems. These reduced models can further be integrated in an adaptive model hierarchy which is particularly suitable when used in many-query scenarios. The model hierarchy unites different models - such as, for instance, a full order model, reduced models and machine learning surrogates - in order to allow for a fast evaluation of the hierarchy while providing results of desired accuracy. The involved models are built and extended in an adaptive manner. Further, the evaluation of the hierarchy is performed in such a way that the cheapest possible model is used which is able to return a sufficiently accurate result. At the same time, the cheapest model is usually the least accurate one. However, the hierarchy is structured in such a way that it is possible to fall back to a more accurate model (which is typically slower) in case the prescribed criterion is not met by the cheap model. The cheaper models are trained using data from the more costly ones, thus benefiting from calls to slower and more accurate models.

Speakers from the University of Münster

Kleikamp, Hendrik

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

Publications referred to in the talk

Application of an adaptive model hierarchy to parametrized optimal control problems Kleikamp, Hendrik (2024) In: P. Frolkovič, K. Mikula and D. Ševčovič (eds.), Proceedings of the Conference Algoritmy 2024, 66-75. Bratislava:  / Jednota slovenských matematikov a fyzikov. Research article in edited proceedings (conference) | Peer reviewed | Published