Date/heure
16 janvier 2024
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Mathias Dus
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
The aim of this article is to analyze numerical schemes using two-layer neural networks with infinite width for the resolution of the high-dimensional Poisson partial differential equation (PDE) with Neumann boundary condition. Using Barron’s representation of the solution with a probability measure defined on the set of parameter values, the
energy is minimized thanks to a gradient curve dynamic on the 2-Wasserstein space of the set of parameter values defining the neural network. Inspired by the work from Bach and Chizat, we prove that if the gradient curve converges, then the represented function is the solution of the elliptic equation considered. In contrast to previous works, the activation function we use here is not assumed to be homogeneous to obtain global convergence of the flow. Numerical experiments are given to show the potential of the method.