Program

School : A NUMERICAL INTRODUCTION TO OPTIMAL TRANS- PORT

Sponsors : ERC NORIA, CEA/EDF/INRIA, ROMSOC ITN

Organization : Jean-David Benamou , Derya Gok, Simon Legrand  (INRIA, Paris) Gabriel Peyré, Zaina Elmir (ENS, ULM), Regis Vizet (CEA DAM)

Location : INRIA Paris 75012.

Dates: 13-17 May 2019.

Targeted Audience : Engineers, PhD Students, Researchers.

Synopsis : The monday afternoon will be devoted to the presentation of different formulations and mathematical results which form the starting point of the modern Optimal Transport theory. The rest of the week will be split between the four class of numerical methods which are now the state of the art in the community. The morning lecture will give the theoretical background : the OT formulation, geometrical and regularity restrictions of the method. They will be applied to selected applications during numerical tutorials.

Prerequisite : No prior knowledge of OT needed – Basic notions of Optimization/Calculus of Variations/EDPs needed.

Hardware requirements for the tutorials : Bring you own laptop. 

Software requirements for the tutorials : Numerical tutorials will be based on python Jupyter notebooks.  The easiest way to install is through Anaconda. Choose the Python 3 version.

——————————–

LOCATION : 

All Lectures in Room JL Lions on the first floor of building C INRIA Paris.

———————————-

Schedule and Lecturers  (1 Break of 30mn by session) 

Monday 13:30-17:00 : Filippo Santambrogio (U. Lyon 1).

Afternoon – Introduction on Basic OT formulations and their analysis : Monge Problem, Kantorovich relaxation, Wasserstein Distance. Multi-marginal Formulations.

Monday 17:30-19:00 (optional)  :   Get together – Installing/Using Jupyter Notebooks.

Monday 19:30   :  Diner at  http://www.jodhpurpalace.com/

————————–

Tuesday :  FX Vialard (U. Marne la Vallée) and Lenaic Chizat (U. Paris Sud)

9:30 -13:00 – Entropic regularization of Kantorovich relaxation, Sinkhorn iterative method.

Lunch (5th floor building C) 

14:30-18:00 – Numerical Tutorial

NOTEBOOK DOWNLOAD  tuto_sinkhorn

————————–

Wenesday :  FX Vialard (U. Marne la Vallée) and Theo Golvet (U. Paris Dauphine)

9:30 -13:00 – The CFD formulation and Proximal Splitting methods.

Lunch (5th floor building C) 

14:30-18:00– Numerical Tutorial

NOTEBOOK DOWNLOAD tutoPROX

Thursday : Jean-Marie Mirebeau and Guillaume Bonnet (U. Paris Sud)

9:30-18:00 –  Second Boundary value problem for the Monge-Ampère equation/ Finite  Difference  methods  for  the Monge-Ampère  equation  and Optimal  Transport  Boundary conditions. and numerical tutorial.

All files at

https://github.com/Mirebeau/AdaptiveGridDiscretizations

Lunch (5th floor building C)  13:00-14:30– 

Friday :  Quentin Mérigot and Hugo Leclerc (U. Paris Sud)

9:30-13:00  – Semi-Discrete Optimal Transport and Computational geometry.

Lunch (5th floor building C) 

14:30-18:00 – Numerical Tutorial : Will need the following packages

from pysdot import PowerDiagram
import numpy as np
pd = PowerDiagram(np.random.rand(11, 2))
pd.display_jupyter()