Research Internship in optimization, machine learning, and inverse problems

Inria; Lyon; Hybrid; EUR 8,900 - 11,000; Full time

Benefits offered by this job

Partial reimbursement of public TRANSP

Professional equipment available

Telework possible from 2 months

Social, cultural and sports events

Job summary

Inria Lyon invites a talented student to undertake a research internship focused on optimization, inverse problems, and flow-based image restoration. Under the supervision of senior researchers, you will implement multilevel plug-and-play algorithms and perform numerical experiments to study convergence and performance.

You will collaborate with researchers in optimization, inverse problems, and generative modeling, and report progress in regular meetings.

Qualifications

• Strong background in applied mathematics, optimization and machine learning.
• Good Python programming skills (PyTorch).
• Knowledge of inverse problems is appreciated.

Responsibilities

• Implement and evaluate the proposed algorithms.
• Analyze numerical results and contribute to the theoretical study.
• Take initiatives in exploring algorithmic improvements.

Skills

Strong background in applied maths

Optimization

Machine learning

Python programming

Analytical thinking

Tools

PyTorch

Job description

Research Internship in optimization, machine learning, and inverse problems

The Inria research centre in Lyon is the 9th Inria research centre, formally created in January 2022. It brings together approximately 410 people in 20 research teams and research support services.

Its staff are distributed in Villeurbanne, Lyon Gerland, and Saint-Etienne.

The Lyon centre is active in the fields of software, distributed and high-performance computing, embedded systems, quantum computing and privacy in the digital world, but also in digital health and computational biology.

Assignments

Under the supervision of Nelly Pustelnik, Elisa Riccietti and Ségolène Martin the recruited intern will develop and study multilevel plug-and-play algorithms based on flow matching for large-scale image restoration. The work will involve algorithm design, numerical experiments, and the investigation of convergence properties. For more details see the descriptions here .

For a better knowledge of the proposed research subject

The following publications provide background on the proposed research topic:

N. Laurent, J. Tachella, E. Riccietti, and N. Pustelnik. Multilevel Plug-and-Play Image Restoration. IEEE Transactions on Computational Imaging, 12, 445–456, 2026.

S. Martin, A. Gagneux, P. Hagemann, and G. Steidl. PnP-Flow: Plug-and-Play Image Restoration with Flow Matching. International Conference on Learning Representations, 2025.

G. Lauga, E. Riccietti, N. Pustelnik, and P. Gonçalves. IML FISTA: A Multilevel Framework for Inexact and Inertial Forward-Backward. Application to Image Restoration. SIAM Journal on Imaging Sciences, 17(3), 1347–1376, 2024.

Collaboration

The intern will work closely with the supervisors and interact with researchers in optimization, inverse problems, and generative modeling at ENS de Lyon.

Responsibilities

The intern will be responsible for implementing and evaluating the proposed algorithms, analyzing numerical results, and contributing to the theoretical study. They will be encouraged to take initiatives in exploring algorithmic improvements.

Steering/Management

The intern will organize and report on their research progress through regular meetings with the supervisors. No management responsibilities are expected.

Main activities (5 maximum)

Review the literature on plug-and-play methods, flow matching, and multilevel optimization algorithms.

Develop and implement multilevel plug-and-play algorithms incorporating flow-matching-based denoisers, and study it numerically.

Conduct numerical experiments on image restoration tasks and compare the proposed methods with existing approaches.

Technical skills and level required

Strong background in applied mathematics, optimization, and machine learning. Good Python programming skills (PyTorch). Knowledge of inverse problems is appreciated.

Languages

English or French

Relational skills

Autonomy, scientific curiosity, teamwork, and analytical thinking.

Other valued skills

Interest in generative models, numerical experiments, and theoretical analysis.

Avantages

• Partial reimbursement of public transport costs


• Professional equipment available (videoconferencing, loan of computer equipment, etc.)


• Telework possible from 2 months of internship


• Social, cultural and sports events and activities