Application of an adaptive model hierarchy to parametrized optimal control problems

TL;DR

An adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, is applied to parametrized linear-quadratic optimal control problems.

Abstract

In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved reduced order models are constructed adaptively and are called in such a way that the model hierarchy returns an approximate solution of given accuracy for every parameter value. At the same time, the fastest model of the hierarchy is evaluated whenever possible and slower models are only queried if the faster ones are not sufficiently accurate. The performance of the model hierarchy is studied for a parametrized heat equation example with boundary value control.

Figures (3)

• Figure 1: Visualization of the adaptive model hierarchy applied to the parametrized optimal control setting.
• Figure 2: Performance of the adaptive model hierarchy in terms of the required times for error estimation and evaluation of the involved models when applied to a parametrized heat equation problem.
• Figure 3: Error estimation of the RB-ROM and the ML-ROM in the adaptive model hierarchy when applied to a parametrized heat equation problem.