Toward the use of Machine-Learning models to improve the initial guess of iterative time-integration schemes (Thibaut Lunet, TU Hamburg)

16.12.2024 15:15 – 16:00

The recent impressive advances in machine-learning (ML) driven applications and the wide accessibility of the associated development tools has motivated many parts of the scientific community to explore potential applications of ML in research. The one we are considering is to use a ML prediction to estimate the initial guess of a Spectral Deferred Correction time integration scheme at each time-step, that could permit a faster convergence to an accurate solution and / or better numerical stability and performance. The PDE considered is a Rayleigh-Benard convection between two plates, solved using pseudo spectral methods implemented in the Dedalus software.

We will present the challenges induced by this application, the most recent results found and problems encountered, and discuss the perspectives of such introduction of ML-based approaches in computational mathematics. Finally, we will give context to this (still) open question: can a ML-model simply replace all the numerical algorithms that have been developed over the last 100 years ...

Lieu

Bâtiment: Conseil Général 7-9

Conference room 8th floor, Séminaire d'analyse numérique
(att. unusual time and place!)

entrée libre