High-order averaging and machine learning (Léopold Trémant, Université de Strasbourg)

31.10.2023 14:00

Highly-oscillatory phenomena combine the well-known numerical challenges of stiff equations and geometric problems, such as order reduction and energy preservation. These problems involve both fast oscillatory dynamics and slow drift dynamics, which interact to create complex dynamics. High-order averaging allows to asymptotically decouple these dynamics using formal calculations, which generates modified problems that can be solved with better numerical accuracy.

In this talk, I will introduce high-order averaging using a (somewhat recent) closed form approach, and exhibit the improvement in numerical accuracy it allows. I will then present the geometric properties of the method, notably regarding the preservation of a Hamiltonian structure. The talk will end with some preliminary results regarding geometric neural networks, which can replace the offline symbolic computations of averaging with an offline training procedure.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre