Master Internship - Fixed Point Algorithms For Inverse Wave Problems H/F - INRIA

A propos d'Inria

Inria est l'institut national de recherche dédié aux sciences et technologies du numérique. Il emploie 2600 personnes. Ses 215 équipes-projets agiles, en général communes avec des partenaires académiques, impliquent plus de 3900 scientifiques pour relever les défis du numérique, souvent à l'interface d'autres disciplines. L'institut fait appel à de nombreux talents dans plus d'une quarantaine de métiers différents. 900 personnels d'appui à la recherche et à l'innovation contribuent à faire émerger et grandir des projets scientifiques ou entrepreneuriaux qui impactent le monde. Inria travaille avec de nombreuses entreprises et a accompagné la création de plus de 200 start-up. L'institut s'eorce ainsi de répondre aux enjeux de la transformation numérique de la science, de la société et de l'économie.Master Internship - Fixed Point Algorithms for Inverse Wave Problems
Le descriptif de l'offre ci-dessous est en Anglais
Type de contrat : Stage

Niveau de diplôme exigé : Bac +5 ou équivalent

Fonction : Stagiaire de la recherche

Niveau d'expérience souhaité : Jeune diplômé

A propos du centre ou de la direction fonctionnelle

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 , 32 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.

Contexte et atouts du poste

In the context of a collaboration between OPIS and IDEFIX Inria teams, the aim of this internship is to investigatethe design and convergence analysis of fixed-point algorithms for the resolution of inverse problems involving PDEs.

Subject:
Inverse problems are central to many applications like medical imaging, geophysical inspection, and non-destructive testing, where the goal is to identify some parameters (suchas physical properties or defect geometries) from given measurements. Unlike forwardproblems, which involve solving linear PDEs with a unique solution, inverse problems areoften nonlinear and ill-posed. Commonly used inversion algorithms in engineering oftenrely on the linearization of the inverse problem, leading for example to methods like migration or time reversal for inverse wave problems. While these methods are fast and donot require iterative procedures, they suffer from biases due to linearization and can failin complex environments. A more conventional/traditional approach involves formulatingthe inverse problem as a minimization of a cost functional that measures data fidelity bycomparing it with the PDE solution for a given parameter. However, solving this is oftenmore computationally expensive than solving the PDE itself, making it impractical forreal-time applications or large-scale problems. While efforts have been made to enhancethe performance of these methods, they often treat forward iterative
solvers independently of inversion algorithms, or incorporate the forward map into the costfunctional leading to suboptimal solutions for the forward problem.

Preliminary results have been obtained, showing the suitability of proximal fixed point techniques to address the problem. The goal of the internship is to explore consensus-based formulation and implementation of the methods.

Mission confiée

Missions: The recruited student will firstperform a bibliographical study on the topic. Then, in a second step, the student will propose a mathematical formulation of the problem, and a suitable distributed fixed-point algorithm to solve it. Third, the convergence of the approach will be established.

Environment: The intern will be supervised by Emilie Chouzenoux (Head of OPIS team, Inria Saclay). The intern student will join the Inria Saclay team OPIS (https://opis-inria.eu/). He/she will be located in the Centre de la Vision Numérique, in CentraleSupélec campus, Saclay, France. He/she will enjoy an international and creative environment where research seminars and reading groups take place very often. Informatic material expenses will be covered within the limits of the scale in force. The student willparticipate to monthly collaborative meetingsresearchers from OPIS team (Emilie Chouzenoux, Jean-Christophe Pesquet), and IDEFIX team (Lorenzo Audibert, Houssem Haddar).

Organization: The proposed offer is dedicated to internship of Master 2 / Engineering students. The starting/end datesare flexible, with a minimum duration of 5 months.

Principales activités

Main activities:

Bibliographical study

Optimization problem formulation and resolution

Convergence Analysis

Scientific meetings

Writing of scientific reports

Compétences

Languages : The candidate must be fluent in english and/or french languages.

Avantages

- 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 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

Rémunération

Gratification