Séminaire Périodique LAMSIN-MIMS-IRA
Huyên Pham (Université de Paris)
Title: Solving man-field PDEs with symmetric neural networks
Abstract: We propose numerical methods for solving non-linear partial differential equations (PDEs) in the Wasserstein space of probability measures, which arise notably in the optimal control of mean-field dynamics, and are motivated by models of large population of interacting agents. The method relies first on the approximation of the PDE in infinite dimension by a backward stochastic differential equation (BSDE) with a forward system of $N$ interacting particles. We provide the rate of convergence of this finite-dimensional probabilistic approximation for the solution to the PDE and its $L$-derivative. Next, by exploiting the symmetry of the particles system, we design a machine learning algorithm based on certain types of neural networks, named PointNet and DeepSet, for computing simultaneously the pair solution to the BSDE by backward induction through sequential minimization of loss functions. We illustrate the efficiency of the PointNet/DeepSet networks compared to classical feedforward ones, and provide some numerical results of our algorithm for the examples of a mean-field systemic risk and a mean-variance problem.
Le séminaire se fera a distance, sur la plateforme ZOOM. Le lien est disponible ci-dessous.
Time: May 5, 2021 11:30 PM Tunis
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IRA = Institute du Risque et de l'Assurance du Mans
Mohamed Mnif - Anis Matoussi - Sadok Kallel
Mohamed Mnif - Anis Matoussi