Work

Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems

Year: 2024

Type: article

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. We discuss the computational costs of all considered methods in detail and show by means of two numerical examples the tremendous potential of the proposed methodology.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2024074

Authors: Hendrik Kleikamp, Martin Lazar, Cesare Molinari

Institutions: University of Münster, University of Dubrovnik, University of Genoa

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: