Introduction à la théorie des PINNs Room: TBA

Tutoriel : un PINNs en JAX en partant de zéro

• Rémi Imbach
• Victor Michel-Dansac

Room: TBA After a short introduction to the JAX library (https://github.com/jax-ml/jax), we will continue with a tutorial. In this tutorial, we will illustrate the Physics-Informed Neural Network (PINN, Raissy et al, 2019) approach to approximate the solution of a physical problem modeled by a Partial Differential Equation (PDE). We will: - build a Neural Network (NN) to serve as a parameterized function uθuθ​, - use the autodiff engine to evaluate the residual of the PDE for the candidate solution uθuθ​, - train the NN (i.e. tune parameters θθ to minimize the residual of the PDE) so that uθuθ​ approximates the solution u∗u∗ of the PDE.

Présentation et tutoriel pour la bibliothèque jinns

• Nicolas Jouvin (INRAE)
• Hugo Gangloff (MIA Paris Saclay, INRAE)

Room: TBA https://gitlab.com/mia_jinns/jinns

Présentation et tutoriel pour la bibliothèque Scimba

• Victor Michel-Dansac
• Rémi Imbach

Room: TBA After introducing the Scimba library (https://www.scimba.org/), we will continue with two tutorials. In the first tutorial, we will solve a 2D Poisson PDE on an annulus with mixed boundary conditions using a Scimba PINNs. The second tutorial covers the use of some time-discrete schemes available in Scimba for solving the rotating transport problem.