Post-Doctoral Research Visit F/M Ocean dynamics emulation with Koopman operator

The Inria Centre at Rennes University is one of Inria's eight centres and has more than thirty research teams. The Inria Centre is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative PMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute, etc.

The Odyssey team is offering  a 18 month  postdoc position on ocean modelling funded by a national initative on machine learning for ocean dynamics. Odyssey (Ocean DYnamicS obSErvation analYsis) is a joint research team between  CNRS, Inria (Rennes, France), University. Rennes, Ifremer (Brest), IMT Atlantique (Brest) and Univ. Western Britanny (Brest).

Inria is one of the leading research institute in Computer Sciences in France, and Odyssey is also affiliated to the mathematics research institute of the Rennes University (IRMAR).

The team expertise encompasses mathematical (stochastic) and numerical modelling of ocean flows, observational and physical oceanography, data assimilation and machine learning.

Gathering this large panel of skills, the team aims at improving our understanding, reconstruction and forecasting of ocean dynamics, and more specifically to bridge model-driven and observation-driven paradigms to develop and learn novel representations of the coupled ocean-atmosphere dynamics ocean models.

Research project description:

This project aims to emulate complex dynamical systems, such as ocean currents simulated in GLORYS12, by leveraging recent approaches based on the Koopman operator and reproducing kernel Hilbert spaces (RKHS). Unlike classical machine learning methods that require long time series, the proposed approach learns the system's dynamics locally from an ensemble of realizations, making it better suited to high-dimensional chaotic systems.

The project builds on recent work (Dufée et al. 2024) showing that system dynamics can be captured by linear operators in RKHS, enabling better physical interpretability, temporal scale separation, and the estimation of Lyapunov exponents. The approach also incorporates ensemble and temporal techniques to reconstruct a pseudo-ensemble of trajectories around the available time series.

The expected outcomes include a robust emulation of the system’s dynamics, improved forecasting of recurring events, and the incorporation of the continuous spectrum of the Koopman operator, all while aligning with the practical constraints of the DC1 challenge (https://github.com/ppr-ocean-ia/data-challenges-info). The project will be conducted at Inria Rennes, within the Odyssey team, in close collaboration with Ifremer and IMT Atlantique.

Dufée, Benjamin, Bérenger Hug, Étienne Mémin, et Gilles Tissot. 2024. « Ensemble forecasts in reproducing kernel Hilbert space family ». Physica D: Nonlinear Phenomena 459 (mars):134044. https://doi.org/10.1016/j.physd.2023.134044.

The candidate should have a solid background in applied mathematics related to dynamical systems and/or in fluid mechanics and/or in geophysical dynamics. She/he must have a good knowledge of Fortran, C/C+/ Python, Pytorch

• 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

Monthly gross salary from 2 788 euros.