Bienvenue - Laboratoire Jacques-Louis Lions

Vendredi 18 février 2022 — 14h00
En raison de la situation sanitaire, exposé à distance retransmis par Zoom
Gianluigi Rozza (Ecole Internationale Supérieure d’Etudes Avancées, Trieste)
Reduced order modelling for parametric time-dependent non-linear optimal control problems
Résumé Parametric optimal control problems are powerful mathematical tools to make simulations more reliable and accurate, filling the gap between collected data and partial differential equations. This mathematical tool is widespread in many research fields, yet, its theoretical and computational complexity still limits its applicability, most of all in a parametric setting where many evaluations of the problem must be run to have a more comprehensive knowledge of very complex systems, such as time-dependent and non-linear ones. Reduced order methods can tackle this issue. Indeed, they describe the parametric nature of the optimality system in a low-dimensional framework accelerating the system solution but maintaining the model accuracy.
This talk focuses on well-known reduced order approaches for steady equations generalized to time-dependent non-linear ones. First of all, we will propose two different algorithms : a space-time POD algorithm validated on a non-linear environmental coastal management problem and a space-time greedy algorithm guided by a new error estimate for parabolic governing equations. Then, we will focus on the great potential of optimal control techniques in advanced applications. Indeed, we will highlight strategies to better analyse the input-output relation of the optimal control pipeline and to show the versatility of the proposed model in different scenarios such as uncertainty quantification for environmental sciences and bifurcation analysis for non-linear partial differential equations.