# MOKAMEETINGS 2018

## Large deviations and rare events in climate dynamic phenomena.

Abstract:
Introduction to large deviation theory (40 minutes)
This talk will start with an introduction to large deviation theory and its applications in physics, statistical mechanics, and dynamical systems. We will introduce in a pedagogical way the three main classes of large deviation principles (Donsker-Varadhan, Freidlin-Wentzell, and large deviation theory in relation with averaging for dynamical systems with two time scales).
Large deviation theory, gradient flows and optimal transport for partial differential equations (40 minutes)
As a more advanced subject we will discuss the deep relations between large deviation theory, gradient flows, and optimal transport, through kinetic theory. After a mathematical introduction, we will illustrate this relation by discussing the large deviation for the Boltzmann equation, and how it naturally leads to a gradient structure for the homogeneous Boltzmann equations, and a gradient structure for the Navier-Stokes equation.
Computing the probability of extreme heat wave using large deviation theory  (40 minutes)
Finally we will discuss the use of large deviation theory for geophysical fluid dynamics and climate. For some aspects of climate dynamics, rare dynamical events may play a key role, for instance when they have a huge impact. We will focus on the paradigmatic example of extreme heat waves. In the recent past, new numerical tools have been developed in the statistical mechanics community, in order to specifically study such rare events. Some of those approaches are based on large deviation theory for complex dynamical systems. Using such an algorithm, we study the probability of extreme heat waves in a comprehensive GCM. At a fixed numerical cost, several hundreds more heat waves are observed than in a control run. The thousands of sampled extreme heat waves open the door to their dynamical studies, precursor, and fluctuation paths, in a way that can not be foreseen using conventional tools based on direct numerical simulations. Moreover extreme events that can not be observed in a GCM at a reasonable cost can now be studied. This new tool open new perspectives for the study of climate extremes. As an example we discuss teleconnection patterns for extremes.

11 Avril :  Arnak Dalalyan.

2 Mai : Yvik Swan.

23 Mai  :  Blanche Buet.

13 Juin :  Antoine Gautier.

INRIA Paris Salle A415

#### Titre: Discrétisation d’EDPs anisotropes fondées sur la première réduction de Voronoi: le cas des équations eikonales.

Résumé:  Nous décrirons la première réduction de Voronoi, un outil initialement conçu pour décrire la géométrie des réseaux euclidiens, qui se montre particulièrement efficace pour la discrétisation d’EDPs anisotropes sur grille cartésienne.
Ayant évoqué les multiples schémas d’EDP qui s’en déduisent – allant des équations elliptiques à l’opérateur de Monge-Ampère, en passant par le contrôle stochastique – nous nous focaliserons sur le cas des équations eikonales anisotropes et non-holonomes (anisotropie dégénérée). Grâce à ces dernières, nous calculons des chemins minimisant globalement des énergies du second ordre, faisant intervenir leur courbure. Des applications en segmentation d’image et en planification de mouvement seront présentées.

7 Mars : Samer Dweik.