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Victor Michel-Dansac
Numerical methods for the simulation of partial differential equations, based on nonlinear approximation spaces
21 mai 2026 - 09:00Salle de conférences IRMA
Abstract: In this talk, I'll give a gentle introduction to both traditional and neural numerical methods for the simulation of partial differential equations (PDEs). On the one hand, traditional numerical methods (finite differences, finite elements, ...) have been successfully used for the last 50 years to obtain approximate solutions to PDEs. On the other hand, new methods based on neural networks (e.g. PINNs, Physics-Informed Neural Networks) have recently been introduced for the same purpose. While they are often (mistakenly!) seen as black-box solvers, I'll show that both (traditional and neural numerical) approaches can be defined as oblique projections on suitable function spaces. This unified framework offers a better way to compare their specific strengths and weaknesses. If time permits, I will also briefly conclude with some research directions undertaken in the MACARON team.
Bio: Victor Michel-Dansac is a permanent researcher (ISFP, INRIA Starting Faculty Position) in the project-team MACARON of the Inria Strasbourg research center, located at IRMA (Institut de Recherche Mathématique Avancée), in Strasbourg. His research areas encompass several topics, including scientific computing, the development of numerical methods, and, more recently, Scientific Machine Learning, enriching numerical schemes with techniques from machine learning. -
Cédric Bastoul
TBA
18 juin 2026 - 09:00Salle de conférences IRMA
TBA