École Thématique sur les Incertitudes en Calcul Scientifique (ETICS)

• Prof. Marianne Clausel (Université de Lorraine, France): Causality and explainable artificial intelligence - TBA
• Prof. Jérôme Darbon (Brown University, USA): Adversarial optimal control in high dimension and multiobjective optimization - TBA
• Prof. Olivier Roustant (INSA Toulouse, France): Physics-informed Gaussian process - Gaussian processes (GP) are widely used in machine learning to build fast approximations of complex physical phenomena even in data-scarce settings. They deliver both predictions and uncertainty quantification. When the underlying physics is described by partial differential equations (PDE), these approximations can be made more realistic. Furthermore, the physical information can be used for inversion, enabling the revovery of the solution of the PDE and the estimation of unknown scalar or functional parameters. The course will cover this material, supported by hands-on computer labs. The outline is as follows :

   Part 0. General introduction or the benefits of using GPs for PDEs
   Part 1. Generalities on GPs. Function approximation (GP regression). Lab : GPs and GP regression.
   Part 2: GPs subject to linear constraints. Application to linear PDEs. Lab GPs under linear constraints.
   Part 3: RKHS, function approximation and GP regression. Lab : GPs regression with derivative information.
   Part 4: Solving non-linear PDEs with kernel methods. Lab : Example of the Burger’s equation.

https://uq.math.cnrs.fr/etics