PhD Position F/M Generalized Wasserstein barycenters and applications

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Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 40 project teams , 27 of which operate jointly with Paris-Saclay University and the Institut Polytechnique de Paris; Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

Context

This projet will take place within the PARMA team at INRIA Saclay, the "Laboratoire de Mathématiques d'Orsay'' and the  "École Doctorale Mathématique Hadamard". It will be funded by the ANR JCJC project BARYFLOW (ANR-25-CE40-3242-01) coordinated by Andrea Natale.

Assignment

Context and background

Wasserstein distances are a powerful tool to compare data in a geometrically meaningful way that does not rely on a specific vector representation. While significant progress has been made in using these distances for data interpolation, many applications – such as statistical analysis of measured valued data, reduced order modeling, or the construction of numerical methods for physics simulations – require not only interpolation but also extrapolation of data. However, there is currently only a partial understanding of how to define such extrapolations consistently with the Wasserstein geometry. One promising direction is based on the notion of Wasserstein barycenter with signed weights, which has been recently investigated in [1] in a simplified setting.

Objectives

The main objective of this thesis is to expand our understanding of Wasserstein barycenters, focussing in particular on the case with signed weights. In particular, we aim to produce a computationally tractable characterization of such objects and provide efficient numerical algorithms for their computation. We will also invesitigate different applications of the developed tools, including:

  • the discretization of Wasserstein gradient flows, developing the ideas of [2];
  • the discretization of fluid models such as the pressureless and isentropic Euler equations;
  • the development of accelerated schemes for optimization on the space of measures.

[1] Thomas O. Gallouët, Andrea Natale, and Gabriele Todeschi. Metric extrapolation in the wasserstein space, 2025. Calculus of Variations and Partial Differential Equations

[2]  Thomas O. Gallouët, Andrea Natale, and Gabriele Todeschi. From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows. Mathematics of Computation, 93:2769–2810, 2024.

 

Main activities

  • Literature review
  • Participation to local seminars and workshops as well as international conferences
  • Writing of research articles and thesis manuscript

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Remuneration

Monthly gross salary : 2.300 Euros