Missions

The overall mission is to conduct research aimed at designing partial differential equation solvers based on neural operators adapted for the simulation of geophysical flows. The selected candidate will contribute to the FastClim project.

Activités

The selected candidate will conduct research on the time discretization of PDEs using neural operators. So far, geophysical applications of neural operators as an alternative to spectral methods have primarily relied on fixed time-stepping (which implicitly mimics an explicit Euler time discretization scheme). However, it is well established that the stability and long-term statistical behavior of numerical simulators and emulators depend critically on the time discretization scheme. This project proposes to explore how neural operators can be formulated as time-independent operators, which can be integrated into classical time-stepping schemes for solving PDEs.

Compétences

The selected candidate must hold a PhD in one of the following fields: Geosciences, Applied Machine Learning, Data Assimilation, Applied Mathematics.

Selection will be based on the following scientific and technical criteria:
● Research experience in machine learning techniques applied to dynamical systems and geoscientific models
● Proficiency in Python and major machine learning libraries (PyTorch, Jax, TensorFlow)
● Knowledge of oceanic processes and their representation in ocean circulation models
● Proven experience in writing and communicating scientific results
● Experience with collaborative software development tools and best practices
● Experience in an international, interdisciplinary research setting
● Demonstrated ability to work in a team and in a multicultural environment

Contexte de travail

Work Environment
The selected candidate will work at the Institute of Environmental Geosciences (IGE) in Grenoble, located in the French Alps. IGE is a public research institute affiliated with CNRS, IRD, Université Grenoble Alpes, Grenoble-INP, and INRAE. It hosts approximately 250 people, including 150 permanent members (researchers, faculty members, engineers) and about 100 contract employees (PhD students, postdocs, engineers, and technicians). The institute also welcomes dozens of interns and visiting scientists each year. IGE is spread across three sites on the Grenoble university campus, all within a five-minute walk of each other. It is one of the key institutes of the Observatory of Sciences of the Universe of Grenoble (OSUG), a federative structure under INSU. The selected candidate will join the MEOM group, which focuses on ocean/sea ice modeling and forecasting (see [MEOM Group](https://meom-group.github.io)) and will be jointly supervised by Julien Le Sommer (IGE). The research will be conducted in Grenoble in collaboration with Patrick Galinari (ISIR) and Freddy Bouchet (LMD) as part of the FastClim project.

Scientific Context
Numerical models used to describe ocean circulation in climate projection models are primarily based on partial differential equations (PDEs) derived from fundamental physical laws. A key challenge is the development of efficient and accurate numerical solvers for these equations. Neural networks have gained interest in this context due to their ability to approximate complex functions, leading to their application in representing fields as neural networks. This approach, known as implicit neural representations (or neural fields), is now being applied to the development of PDE solvers. A major advantage of neural fields is their mesh-free, inherently multi-scale representations, which allow for a decoupling of spatial resolution and computational cost. However, these methods are still highly experimental, requiring further research to fully exploit the potential of neural operators as key components of the next generation of hybrid differentiable weather and climate models.

Contraintes et risques

NTR