Research Internship in optimization, machine learning, and inverse problems

Research Internship in optimization, machine learning, and inverse problems Download job offer in PDF format Contract type : Internship agreement Level of qualifications required : Master's or equivalent Fonction : Internship Research About the research centre or Inria department 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. Assignment 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 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. Skills 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. Benefits package • 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 • Leaves Remuneration Gratification : 4,50 euro gross / hour Apply for this position Share • Facebook • Linkedin • Twitter • Email General Information • Theme/Domain : Optimization, machine learning and statistical methods Statistics (Big data) (BAP E) • Town/city : Lyon • Inria Center : Centre Inria de Lyon • Starting date : 2027-03-01 • Duration of contract : 5 months • Deadline to apply : 2026-11-16 Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed. Instruction to apply Applications must be submitted online via the Inria website. Processing of applications submitted via other channels is not guaranteed. Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment. Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities. Contacts • Inria Team : OCKHAM • Recruiter : Martin Segolene / segolene.martin@inria.fr About Inria Inria, the French national institute for research in digital science and technology, supports the French government in national research and innovation strategies in the digital field, acting as Digital Programs Agency. Inria leads over 300 research and innovation projects with its 3,500 scientists, engineers, and support staff, in partnership with universities and the digital ecosystem (businesses, entrepreneurs, and public stakeholders). Together, we explore strategic fields such as artificial intelligence, cybersecurity, quantum computing, cloud technologies, digital transformation in healthcare, digital twins, and digital technologies for defence. We develop practical solutions such as software, tech startups, partnerships with national companies, and cutting-edge training programmes. Our goal is to drive scientific, technological, and industrial excellence to ensure France’s digital sovereignty.