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AIRSEA - 2025

2025Activity​​ reportProject-TeamAIRSEA

RNSR:​​​‌ 201521159N
  • Research center Inria‌ Centre at Université Grenoble‌​‌ Alpes
  • In partnership with:​​Université de Grenoble Alpes,​​​‌ CNRS
  • Team name: Mathematics‌ and computing applied to‌​‌ oceanic and atmospheric flows​​
  • In collaboration with:Laboratoire​​​‌ Jean Kuntzmann (LJK)

Creation‌ of the Project-Team: 2016‌​‌ April 01

Each year,​​ Inria research teams publish​​​‌ an Activity Report presenting‌ their work and results‌​‌ over the reporting period.​​ These reports follow a​​​‌ common structure, with some‌ optional sections depending on‌​‌ the specific team. They​​ typically begin by outlining​​​‌ the overall objectives and‌ research programme, including the‌​‌ main research themes, goals,​​​‌ and methodological approaches. They​ also describe the application​‌ domains targeted by the​​ team, highlighting the scientific​​​‌ or societal contexts in​ which their work is​‌ situated.

The reports then​​ present the highlights of​​​‌ the year, covering major​ scientific achievements, software developments,​‌ or teaching contributions. When​​ relevant, they include sections​​​‌ on software, platforms, and​ open data, detailing the​‌ tools developed and how​​ they are shared. A​​​‌ substantial part is dedicated​ to new results, where​‌ scientific contributions are described​​ in detail, often with​​​‌ subsections specifying participants and​ associated keywords.

Finally, the​‌ Activity Report addresses funding,​​ contracts, partnerships, and collaborations​​​‌ at various levels, from​ industrial agreements to international​‌ cooperations. It also covers​​ dissemination and teaching activities,​​​‌ such as participation in​ scientific events, outreach, and​‌ supervision. The document concludes​​ with a presentation of​​​‌ scientific production, including major​ publications and those produced​‌ during the year.

Keywords​​

Computer Science and Digital​​​‌ Science

  • A3.1.8. Big data​ (production, storage, transfer)
  • A6.1.1.​‌ Continuous Modeling (PDE, ODE)​​
  • A6.1.2. Stochastic Modeling
  • A6.1.4.​​​‌ Multiscale modeling
  • A6.1.5. Multiphysics​ modeling
  • A6.2.1. Numerical analysis​‌ of PDE and ODE​​
  • A6.2.4. Statistical methods
  • A6.2.6.​​​‌ Optimization
  • A6.2.7. HPC for​ machine learning
  • A6.3.1. Inverse​‌ problems
  • A6.3.2. Data assimilation​​
  • A6.3.4. Model reduction
  • A6.3.5.​​​‌ Uncertainty Quantification
  • A6.4.6. Optimal​ control
  • A6.5.2. Fluid mechanics​‌
  • A6.5.4. Waves
  • A9.2.1. Supervised​​ learning
  • A9.2.2. Unsupervised learning​​​‌
  • A9.2.5. Bayesian methods
  • A9.2.6.​ Neural networks
  • A9.2.7. Kernel​‌ methods
  • A9.2.8. Deep learning​​

Other Research Topics and​​​‌ Application Domains

  • B3.2. Climate​ and meteorology
  • B3.3.2. Water:​‌ sea & ocean, lake​​ & river
  • B3.3.4. Atmosphere​​​‌
  • B3.4.1. Natural risks
  • B4.3.2.​ Hydro-energy
  • B4.3.3. Wind energy​‌
  • B9.11.1. Environmental risks

1​​ Team members, visitors, external​​​‌ collaborators

Research Scientists

  • Arthur​ Vidard [Team leader​‌, INRIA, Researcher​​, HDR]
  • Laurent​​​‌ Debreu [INRIA,​ Senior Researcher, HDR​‌]
  • Eugene Kazantsev [​​INRIA, Researcher]​​​‌
  • Florian Lemarie [INRIA​, Researcher, HDR​‌]
  • Gurvan Madec [​​UGA, Researcher,​​​‌ HDR]
  • Olivier Zahm​ [INRIA, Researcher​‌]

Faculty Members

  • Elise​​ Arnaud [UGA,​​​‌ Associate Professor]
  • Éric​ Blayo [UGA,​‌ Professor, HDR]​​
  • Clément Duhamel [UGA​​​‌, ATER, until​ Aug 2025]
  • Christine​‌ Kazantsev [UGA,​​ Associate Professor]
  • Clémentine​​​‌ Prieur [UGA,​ Professor, HDR]​‌
  • Martin Schreiber [UGA​​, Professor, HDR​​​‌]
  • Romain Verdiere [​UGA, ATER,​‌ from Sep 2025]​​

Post-Doctoral Fellows

  • Hugo Brunie​​​‌ [UGA, Post-Doctoral​ Fellow, until Oct​‌ 2025]
  • Emile Deleage​​ [UGA, Post-Doctoral​​​‌ Fellow, from Oct​ 2025]

PhD Students​‌

  • Lorenzo Calzolari [IFPEN​​]
  • Gabriel Derrida [​​​‌INRIA]
  • Mohamed Doumbouya​ [INRIA, from​‌ Oct 2025]
  • Helene​​ Henon [INRIA]​​​‌
  • Pierre Lozano [UGA​, until Sep 2025​‌]
  • Exauce Luweh Adjim​​ Ngarti [BULL,​​​‌ CIFRE]
  • Manolis Perrot​ [INRIA, until​‌ Apr 2025]
  • Katarina​​ Radisic [INRIA,​​​‌ until Mar 2025]​
  • Julien Remy [UGA​‌]
  • Angelique Saillet [​​UGA]
  • Jean Baptiste​​ Seby [CNRS,​​​‌ from Oct 2025]‌
  • Romain Verdiere [INRIA‌​‌, until Aug 2025​​]
  • Melanie Villain [​​​‌INRIA, from Nov‌ 2025]
  • Benjamin Zanger‌​‌ [INRIA, until​​ Aug 2025]

Technical​​​‌ Staff

  • Céline Acary Robert‌ [UGA, Engineer‌​‌]
  • Dominik Huber [​​UNIV TECH MUNICH ,​​​‌ Engineer, from Apr‌ 2025]

Interns and‌​‌ Apprentices

  • Ulysse Chabot [​​INRIA, Intern,​​​‌ from Jun 2025 until‌ Jul 2025]
  • Kaidiliya‌​‌ Dilixiati [INRIA,​​ until Jun 2025]​​​‌
  • Lucas Maillet [UGA‌, from Apr 2025‌​‌ until Jun 2025]​​
  • Vincent Meduski [INRIA​​​‌, Intern, from‌ Mar 2025 until Aug‌​‌ 2025]
  • Quentin Meyer​​ [INRIA, Intern​​​‌, from Sep 2025‌]
  • Celian Ranguis [‌​‌INRIA, Intern,​​ from Jun 2025 until​​​‌ Jul 2025]
  • Shubha‌ Sanket Samantaray [UGA‌​‌, Intern, from​​ May 2025 until Jul​​​‌ 2025]
  • Younes Trichine‌ [UGA, Intern‌​‌, from Feb 2025​​ until Aug 2025]​​​‌
  • Melanie Villain [INRIA‌, Intern, from‌​‌ Mar 2025 until Aug​​ 2025]

Administrative Assistant​​​‌

  • Luce Coelho [INRIA‌]

Visiting Scientist

  • Martin‌​‌ Alvarez Iker [UNIV​​ JAUME I ESPAGNE,​​​‌ until Apr 2025]‌

2 Overall objectives

The‌​‌ general scope of the​​ AIRSEA project-team is to​​​‌ develop mathematical and computational‌ methods for the modeling‌​‌ of oceanic and atmospheric​​ flows. The mathematical​​​‌ tools used involve both‌ deterministic and statistical approaches‌​‌. The main research​​ topics cover a) modeling​​​‌ and coupling b) model‌ reduction for sensitivity analysis,‌​‌ coupling and multiscale optimizations​​ c) sensitivity analysis, parameter​​​‌ estimation and risk assessment‌ d) algorithms for high‌​‌ performance computing. The range​​ of application is from​​​‌ climate modeling to the‌ prediction of extreme events.‌​‌

3 Research program

Recent​​ events have raised questions​​​‌ regarding the social and‌ economic implications of anthropic‌​‌ alterations of the Earth​​ system, i.e. climate change​​​‌ and the associated risks‌ of increasing extreme events.‌​‌ Ocean and atmosphere, coupled​​ with other components (continent​​​‌ and ice) are the‌ building blocks of the‌​‌ Earth system. A better​​ understanding of the ocean​​​‌ atmosphere system is a‌ key ingredient for improving‌​‌ prediction of such events.​​ Numerical models are essential​​​‌ tools to understand processes,‌ and simulate and forecast‌​‌ events at various space​​ and time scales. Geophysical​​​‌ flows generally have a‌ number of characteristics that‌​‌ make it difficult to​​ model them. This justifies​​​‌ the development of specifically‌ adapted mathematical methods:

  • Geophysical‌​‌ flows are strongly non-linear.​​ Therefore, they exhibit interactions​​​‌ between different scales, and‌ unresolved small scales (smaller‌​‌ than mesh size) of​​ the flows have to​​​‌ be parameterized in the‌ equations.
  • Geophysical fluids are‌​‌ non closed systems. They​​ are open-ended in their​​​‌ scope for including and‌ dynamically coupling different physical‌​‌ processes (e.g., atmosphere, ocean,​​ continental water, etc). Coupling​​​‌ algorithms are thus of‌ primary importance to account‌​‌ for potentially significant feedback.​​
  • Numerical models contain parameters​​​‌ which cannot be estimated‌ accurately either because they‌​‌ are difficult to measure​​​‌ or because they represent​ some poorly known subgrid​‌ phenomena. There is thus​​ a need for dealing​​​‌ with uncertainties. This​ is further complicated by​‌ the turbulent nature of​​ geophysical fluids.
  • The computational​​​‌ cost of geophysical flow​ simulations is huge, thus​‌ requiring the use of​​ reduced models, multiscale methods​​​‌ and the design of​ algorithms ready for high​‌ performance computing platforms.

Our​​ scientific objectives are divided​​​‌ into four major points.​ The first objective focuses​‌ on developing advanced mathematical​​ methods for both the​​​‌ ocean and atmosphere, and​ the coupling of these​‌ two components. The second​​ objective is to investigate​​​‌ the derivation and use​ of model reduction to​‌ face problems associated with​​ the numerical cost of​​​‌ our applications. The third​ objective is directed toward​‌ the management of uncertainty​​ in numerical simulations. The​​​‌ last objective deals with​ efficient numerical algorithms for​‌ new computing platforms. As​​ mentioned above, the targeted​​​‌ applications cover oceanic and​ atmospheric modeling and related​‌ extreme events using a​​ hierarchy of models of​​​‌ increasing complexity.

3.1 Modeling​ for oceanic and atmospheric​‌ flows

Current numerical oceanic​​ and atmospheric models suffer​​​‌ from a number of​ well-identified problems. These problems​‌ are mainly related to​​ lack of horizontal and​​​‌ vertical resolution, thus requiring​ the parameterization of unresolved​‌ (subgrid scale) processes and​​ control of discretization errors​​​‌ in order to fulfill​ criteria related to the​‌ particular underlying physics of​​ rotating and strongly stratified​​​‌ flows. Oceanic and atmospheric​ coupled models are increasingly​‌ used in a wide​​ range of applications from​​​‌ global to regional scales.​ Assessment of the reliability​‌ of those coupled models​​ is an emerging topic​​​‌ as the spread among​ the solutions of existing​‌ models (e.g., for climate​​ change predictions) has not​​​‌ been reduced with the​ new generation models when​‌ compared to the older​​ ones.

Advanced methods for​​​‌ modeling 3D rotating and​ stratified flows The continuous​‌ increase of computational power​​ and the resulting finer​​​‌ grid resolutions have triggered​ a recent regain of​‌ interest in numerical methods​​ and their relation to​​​‌ physical processes. Going beyond​ present knowledge requires a​‌ better understanding of numerical​​ dispersion/dissipation ranges and their​​​‌ connection to model fine​ scales. Removing the leading​‌ order truncation error of​​ numerical schemes is thus​​​‌ an active topic of​ research and each mathematical​‌ tool has to adapt​​ to the characteristics of​​​‌ three dimensional stratified and​ rotating flows. Studying the​‌ link between discretization errors​​ and subgrid scale parameterizations​​​‌ is also arguably one​ of the main challenges.​‌

Complexity of the geometry,​​ boundary layers, strong stratification​​​‌ and lack of resolution​ are the main sources​‌ of discretization errors in​​ the numerical simulation of​​​‌ geophysical flows. This emphasizes​ the importance of the​‌ definition of the computational​​ grids (and coordinate systems)​​​‌ both in horizontal and​ vertical directions, and the​‌ necessity of truly multi​​ resolution approaches. At the​​​‌ same time, the role​ of the small scale​‌ dynamics on large scale​​ circulation has to be​​​‌ taken into account. Such​ parameterizations may be of​‌ deterministic as well as​​ stochastic nature and both​​ approaches are taken by​​​‌ the AIRSEA team. The‌ design of numerical schemes‌​‌ consistent with the parameterizations​​ is also arguably one​​​‌ of the main challenges‌ for the coming years.‌​‌ This work is complementary​​ and linked to that​​​‌ on parameters estimation described‌ in 3.3.

Ocean‌​‌ Atmosphere interactions and formulation​​ of coupled models State-of-the-art​​​‌ climate models (CMs) are‌ complex systems under continuous‌​‌ development. A fundamental aspect​​ of climate modeling is​​​‌ the representation of air-sea‌ interactions. This covers a‌​‌ large range of issues:​​ parameterizations of atmospheric and​​​‌ oceanic boundary layers, estimation‌ of air-sea fluxes, time-space‌​‌ numerical schemes, non conforming​​ grids, coupling algorithms ...Many​​​‌ developments related to these‌ different aspects were performed‌​‌ over the last 10-15​​ years, but were in​​​‌ general conducted independently of‌ each other.

The aim‌​‌ of our work is​​ to revisit and enrich​​​‌ several aspects of the‌ representation of air-sea interactions‌​‌ in CMs, paying special​​ attention to their overall​​​‌ consistency with appropriate mathematical‌ tools. We intend to‌​‌ work consistently on the​​ physics and numerics. Using​​​‌ the theoretical framework of‌ global-in-time Schwarz methods, our‌​‌ aim is to analyze​​ the mathematical formulation of​​​‌ the parameterizations in a‌ coupling perspective. From this‌​‌ study, we expect improved​​ predictability in coupled models​​​‌ (this aspect will be‌ studied using techniques described‌​‌ in 3.3). Complementary​​ work on space-time nonconformities​​​‌ and acceleration of convergence‌ of Schwarz-like iterative methods‌​‌ (see 8.1.2) are​​ also conducted.

3.2 Model​​​‌ reduction / multiscale algorithms‌

The high computational cost‌​‌ of the applications is​​ a common and major​​​‌ concern to have in‌ mind when deriving new‌​‌ methodological approaches. This cost​​ increases dramatically with the​​​‌ use of sensitivity analysis‌ or parameter estimation methods,‌​‌ and more generally with​​ methods that require a​​​‌ potentially large number of‌ model integrations.

A dimension‌​‌ reduction, using either stochastic​​ or deterministic methods, is​​​‌ a way to reduce‌ significantly the number of‌​‌ degrees of freedom, and​​ therefore the calculation time,​​​‌ of a numerical model.‌

Model reduction Reduction methods‌​‌ can be deterministic (proper​​ orthogonal decomposition, other reduced​​​‌ bases) or stochastic (polynomial‌ chaos, Gaussian processes, kriging),‌​‌ and both fields of​​ research are very active.​​​‌ Choosing one method over‌ another strongly depends on‌​‌ the targeted application, which​​ can be as varied​​​‌ as real-time computation, sensitivity‌ analysis (see e.g., Section‌​‌ 8.3.1) or optimisation​​ for parameter estimation (see​​​‌ below).

Our goals are‌ multiple, but they share‌​‌ a common need for​​ certified error bounds on​​​‌ the output. Our team‌ has a 4-year history‌​‌ of working on certified​​ reduction methods and has​​​‌ a unique positioning at‌ the interface between deterministic‌​‌ and stochastic approaches. Thus,​​ it seems interesting to​​​‌ conduct a thorough comparison‌ of the two alternatives‌​‌ in the context of​​ sensitivity analysis. Efforts will​​​‌ also be directed toward‌ the development of efficient‌​‌ greedy algorithms for the​​ reduction, and the derivation​​​‌ of goal-oriented sharp error‌ bounds for non linear‌​‌ models and/or non linear​​ outputs of interest. This​​​‌ will be complementary to‌ our work on the‌​‌ deterministic reduction of parametrized​​​‌ viscous Burgers and Shallow​ Water equations where the​‌ objective is to obtain​​ sharp error bounds to​​​‌ provide confidence intervals for​ the estimation of sensitivity​‌ indices.

Reduced models for​​ coupling applications Global and​​​‌ regional high-resolution oceanic models​ are either coupled to​‌ an atmospheric model or​​ forced at the air-sea​​​‌ interface by fluxes computed​ empirically preventing proper physical​‌ feedback between the two​​ media. Thanks to high-resolution​​​‌ observational studies, the existence​ of air-sea interactions at​‌ oceanic mesoscales (i.e., at​​ 𝒪(1k​​​‌m) scales) have​ been unambiguously shown. Those​‌ interactions can be represented​​ in coupled models only​​​‌ if the oceanic and​ atmospheric models are run​‌ on the same high-resolution​​ computational grid, and are​​​‌ absent in a forced​ mode. Fully coupled models​‌ at high-resolution are seldom​​ used because of their​​​‌ prohibitive computational cost. The​ derivation of a reduced​‌ model as an alternative​​ between a forced mode​​​‌ and the use of​ a full atmospheric model​‌ is an open problem.​​

Multiphysics coupling often requires​​​‌ iterative methods to obtain​ a mathematically correct numerical​‌ solution. To mitigate the​​ cost of the iterations,​​​‌ we will investigate the​ possibility of using reduced-order​‌ models for the iterative​​ process. We will consider​​​‌ different ways of deriving​ a reduced model: coarsening​‌ of the resolution, degradation​​ of the physics and/or​​​‌ numerical schemes, or simplification​ of the governing equations.​‌ At a mathematical level,​​ we will strive to​​​‌ study the well-posedness and​ the convergence properties when​‌ reduced models are used.​​ Indeed, running an atmospheric​​​‌ model at the same​ resolution as the ocean​‌ model is generally too​​ expensive to be manageable,​​​‌ even for moderate resolution​ applications. To account for​‌ important fine-scale interactions in​​ the computation of the​​​‌ air-sea boundary condition, the​ objective is to derive​‌ a simplified boundary layer​​ model that is able​​​‌ to represent important 3D​ turbulent features in the​‌ marine atmospheric boundary layer.​​

Reduced models for multiscale​​​‌ optimization The field of​ multigrid methods for optimisation​‌ has known a tremendous​​ development over the past​​​‌ few decades. However, it​ has not been applied​‌ to oceanic and atmospheric​​ problems apart from some​​​‌ crude (non-converging) approximations or​ applications to simplified and​‌ low dimensional models. This​​ is mainly due to​​​‌ the high complexity of​ such models and to​‌ the difficulty in handling​​ several grids at the​​​‌ same time. Moreover, due​ to complex boundaries and​‌ physical phenomena, the grid​​ interactions and transfer operators​​​‌ are not trivial to​ define.

Multigrid solvers (or​‌ multigrid preconditioners) are efficient​​ methods for the solution​​​‌ of variational data assimilation​ problems. We would like​‌ to take advantage of​​ these methods to tackle​​​‌ the optimization problem in​ high dimensional space. High​‌ dimensional control space is​​ obtained when dealing with​​​‌ parameter fields estimation, or​ with control of the​‌ full 4D (space time)​​ trajectory. It is important​​​‌ since it enables us​ to take into account​‌ model errors. In that​​ case, multigrid methods can​​​‌ be used to solve​ the large scales of​‌ the problem at a​​ lower cost, this being​​ potentially coupled with a​​​‌ scale decomposition of the‌ variables themselves.

3.3 Dealing‌​‌ with uncertainties

There are​​ many sources of uncertainties​​​‌ in numerical models. They‌ are due to imperfect‌​‌ external forcing, poorly known​​ parameters, missing physics and​​​‌ discretization errors. Studying these‌ uncertainties and their impact‌​‌ on the simulations is​​ a challenge, mostly because​​​‌ of the high dimensionality‌ and non-linear nature of‌​‌ the systems. To deal​​ with these uncertainties we​​​‌ work on three axes‌ of research, which are‌​‌ linked: sensitivity analysis, parameter​​ estimation and risk assessment.​​​‌ They are based on‌ either stochastic or deterministic‌​‌ methods.

Sensitivity analysis Sensitivity​​ analysis (SA), which links​​​‌ uncertainty in the model‌ inputs to uncertainty in‌​‌ the model outputs, is​​ a powerful tool for​​​‌ model design and validation.‌ First, it can be‌​‌ a pre-stage for parameter​​ estimation (see 3.3),​​​‌ allowing for the selection‌ of the more significant‌​‌ parameters. Second, SA permits​​ understanding and quantifying (possibly​​​‌ non-linear) interactions induced by‌ the different processes defining‌​‌ e.g., realistic ocean atmosphere​​ models. Finally SA allows​​​‌ for validation of models,‌ checking that the estimated‌​‌ sensitivities are consistent with​​ what is expected by​​​‌ the theory. On ocean,‌ atmosphere and coupled systems,‌​‌ only first order deterministic​​ SA are performed, neglecting​​​‌ the initialization process (data‌ assimilation). AIRSEA members and‌​‌ collaborators proposed to use​​ second order information to​​​‌ provide consistent sensitivity measures,‌ but so far it‌​‌ has only been applied​​ to simple academic systems.​​​‌ Metamodels are now commonly‌ used, due to the‌​‌ cost induced by each​​ evaluation of complex numerical​​​‌ models: mostly Gaussian processes,‌ whose probabilistic framework allows‌​‌ for the development of​​ specific adaptive designs, and​​​‌ polynomial chaos not only‌ in the context of‌​‌ intrusive Galerkin approaches but​​ also in a black-box​​​‌ approach. Until recently, global‌ SA was based primarily‌​‌ on a set of​​ engineering practices. New mathematical​​​‌ and methodological developments have‌ led to the numerical‌​‌ computation of Sobol' indices,​​ with confidence intervals assessing​​​‌ for both metamodel and‌ estimation errors. Approaches have‌​‌ also been extended to​​ the case of dependent​​​‌ entries, functional inputs and/or‌ output and stochastic numerical‌​‌ codes. Other types of​​ indices and generalizations of​​​‌ Sobol' indices have also‌ been introduced.

Concerning the‌​‌ stochastic approach to SA​​ we plan to work​​​‌ with parameters that show‌ spatio-temporal dependencies and to‌​‌ continue toward more realistic​​ applications where the input​​​‌ space is of huge‌ dimension with highly correlated‌​‌ components. Sensitivity analysis for​​ dependent inputs also introduces​​​‌ new challenges. In our‌ applicative context, it would‌​‌ seem prudent to carefully​​ learn the spatio-temporal dependences​​​‌ before running a global‌ SA. In the deterministic‌​‌ framework we focus on​​ second order approaches where​​​‌ the sought sensitivities are‌ related to the optimality‌​‌ system rather than to​​ the model; i.e., we​​​‌ consider the whole forecasting‌ system (model plus initialization‌​‌ through data assimilation).

All​​ these methods allow for​​​‌ computing sensitivities and more‌ importantly a posteriori error‌​‌ statistics.

Parameter estimation Advanced​​ parameter estimation methods are​​​‌ barely used in ocean,‌ atmosphere and coupled systems,‌​‌ mostly due to a​​​‌ difficulty of deriving adequate​ response functions, a lack​‌ of knowledge of these​​ methods in the ocean-atmosphere​​​‌ community, and also to​ the huge associated computing​‌ costs. In the presence​​ of strong uncertainties on​​​‌ the model but also​ on parameter values, simulation​‌ and inference are closely​​ associated. Filtering for data​​​‌ assimilation and Approximate Bayesian​ Computation (ABC) are two​‌ examples of such association.​​

The stochastic approach can​​​‌ be compared with the​ deterministic approach, which allows​‌ to determine the sensitivity​​ of the flow to​​​‌ parameters and optimize their​ values relying on data​‌ assimilation. This approach is​​ already shown to be​​​‌ capable of selecting a​ reduced space of the​‌ most influent parameters in​​ the local parameter space​​​‌ and to adapt their​ values in view of​‌ correcting errors committed by​​ the numerical approximation. This​​​‌ approach assumes the use​ of automatic differentiation of​‌ the source code with​​ respect to the model​​​‌ parameters, and optimization of​ the obtained raw code.​‌

AIRSEA assembles all the​​ required expertise to tackle​​​‌ these difficulties. As mentioned​ previously, the choice of​‌ parameterization schemes and their​​ tuning has a significant​​​‌ impact on the result​ of model simulations. Our​‌ research will focus on​​ parameter estimation for parameterized​​​‌ Partial Differential Equations (PDEs)​ and also for parameterized​‌ Stochastic Differential Equations (SDEs).​​ Deterministic approaches are based​​​‌ on optimal control methods​ and are local in​‌ the parameter space (i.e.,​​ the result depends on​​​‌ the starting point of​ the estimation) but thanks​‌ to adjoint methods they​​ can cope with a​​​‌ large number of unknowns​ that can also vary​‌ in space and time.​​ Multiscale optimization techniques as​​​‌ described in 8.2 will​ be one of the​‌ tools used. This in​​ turn can be used​​​‌ either to propose a​ better (and smaller) parameter​‌ set or as a​​ criterion for discriminating parameterization​​​‌ schemes. Statistical methods are​ global in the parameter​‌ state but may suffer​​ from the curse of​​​‌ dimensionality. However, the notion​ of parameter can also​‌ be extended to functional​​ parameters. We may consider​​​‌ as parameter a functional​ entity such as a​‌ boundary condition on time,​​ or a probability density​​​‌ function in a stationary​ regime. For these purposes,​‌ non-parametric estimation will also​​ be considered as an​​​‌ alternative.

Risk assessment Risk​ assessment in the multivariate​‌ setting suffers from a​​ lack of consensus on​​​‌ the choice of indicators.​ Moreover, once the indicators​‌ are designed, it still​​ remains to develop estimation​​​‌ procedures, efficient even for​ high risk levels. Recent​‌ developments for the assessment​​ of financial risk have​​​‌ to be considered with​ caution as methods may​‌ differ pertaining to general​​ financial decisions or environmental​​​‌ risk assessment. Modeling and​ quantifying uncertainties related to​‌ extreme events is of​​ central interest in environmental​​​‌ sciences. In relation to​ our scientific targets, risk​‌ assessment is very important​​ in several areas: hydrological​​​‌ extreme events, cyclone intensity,​ storm surges...Environmental risks most​‌ of the time involve​​ several aspects which are​​​‌ often correlated. Moreover, even​ in the ideal case​‌ where the focus is​​ on a single risk​​ source, we have to​​​‌ face the temporal and‌ spatial nature of environmental‌​‌ extreme events. The study​​ of extremes within a​​​‌ spatio-temporal framework remains an‌ emerging field where the‌​‌ development of adapted statistical​​ methods could lead to​​​‌ major progress in terms‌ of geophysical understanding and‌​‌ risk assessment thus coupling​​ data and model information​​​‌ for risk assessment.

Based‌ on the above considerations‌​‌ we aim to answer​​ the following scientific questions:​​​‌ how to measure risk‌ in a multivariate/spatial framework?‌​‌ How to estimate risk​​ in a non stationary​​​‌ context? How to reduce‌ dimension (see 3.2)‌​‌ for a better estimation​​ of spatial risk?

Extreme​​​‌ events are rare, which‌ means there is little‌​‌ data available to make​​ inferences of risk measures.​​​‌ Risk assessment based on‌ observation therefore relies on‌​‌ multivariate extreme value theory.​​ Interacting particle systems for​​​‌ the analysis of rare‌ events is commonly used‌​‌ in the community of​​ computer experiments. An open​​​‌ question is the pertinence‌ of such tools for‌​‌ the evaluation of environmental​​ risk.

Most numerical models​​​‌ are unable to accurately‌ reproduce extreme events. There‌​‌ is therefore a real​​ need to develop efficient​​​‌ assimilation methods for the‌ coupling of numerical models‌​‌ and extreme data.

3.4​​ High performance computing

Methods​​​‌ for sensitivity analysis, parameter‌ estimation and risk assessment‌​‌ are extremely costly due​​ to the necessary number​​​‌ of model evaluations. This‌ number of simulations require‌​‌ considerable computational resources, depends​​ on the complexity of​​​‌ the application, the number‌ of input variables and‌​‌ desired quality of approximations.​​ To this aim, the​​​‌ AIRSEA team is an‌ intensive user of HPC‌​‌ computing platforms, particularly grid​​ computing platforms. The associated​​​‌ grid deployment has to‌ take into account the‌​‌ scheduling of a huge​​ number of computational requests​​​‌ and the links with‌ data-management between these requests,‌​‌ all of these as​​ automatically as possible. In​​​‌ addition, there is an‌ increasing need to propose‌​‌ efficient numerical algorithms specifically​​ designed for new (or​​​‌ future) computing architectures and‌ this is part of‌​‌ our scientific objectives. According​​ to the computational cost​​​‌ of our applications, the‌ evolution of high performance‌​‌ computing platforms has to​​ be taken into account​​​‌ for several reasons. While‌ our applications are able‌​‌ to exploit space parallelism​​ to its full extent​​​‌ (oceanic and atmospheric models‌ are traditionally based on‌​‌ a spatial domain decomposition​​ method), the spatial discretization​​​‌ step size limits the‌ efficiency of traditional parallel‌​‌ methods. Thus the inherent​​ parallelism is modest, particularly​​​‌ for the case of‌ relative coarse resolution but‌​‌ with very long integration​​ time (e.g., climate modeling).​​​‌ Paths toward new programming‌ paradigms are thus needed.‌​‌ As a step in​​ that direction, we plan​​​‌ to focus our research‌ on parallel in time‌​‌ methods.

New numerical algorithms​​ for high performance computing​​​‌ Parallel in time methods‌ can be classified into‌​‌ three main groups. In​​ the first group, we​​​‌ find methods using parallelism‌ across the method, such‌​‌ as parallel integrators for​​ ordinary differential equations. The​​​‌ second group considers parallelism‌ across the problem. Falling‌​‌ into this category are​​​‌ methods such as waveform​ relaxation where the space-time​‌ system is decomposed into​​ a set of subsystems​​​‌ which can then be​ solved independently using some​‌ form of relaxation techniques​​ or multigrid reduction in​​​‌ time. The third group​ of methods focuses on​‌ parallelism across the steps.​​ One of the best​​​‌ known algorithms in this​ family is parareal. Other​‌ methods combining the strengths​​ of those listed above​​​‌ (e.g., PFASST) are currently​ under investigation in the​‌ community.

Parallel in time​​ methods are iterative methods​​​‌ that may require a​ large number of iteration​‌ before convergence. Our first​​ focus will be on​​​‌ the convergence analysis of​ parallel in time (Parareal​‌ / Schwarz) methods for​​ the equation systems of​​​‌ oceanic and atmospheric models.​ Our second objective will​‌ be on the construction​​ of fast (approximate) integrators​​​‌ for these systems. This​ part is naturally linked​‌ to the model reduction​​ methods of Section 8.2.1​​​‌. Fast approximate integrators​ are required both in​‌ the Schwarz algorithm (where​​ a first guess of​​​‌ the boundary conditions is​ required) and in the​‌ Parareal algorithm (where the​​ fast integrator is used​​​‌ to connect the different​ time windows). Our main​‌ application of these methods​​ will be on climate​​​‌ (i.e., very long time)​ simulations. Our second application​‌ of parallel in time​​ methods will be in​​​‌ the context of optimization​ methods. In fact, one​‌ of the major drawbacks​​ of the optimal control​​​‌ techniques used in 3.3​ is a lack of​‌ intrinsic parallelism in comparison​​ with ensemble methods. Here,​​​‌ parallel in time methods​ also offer ways to​‌ better efficiency. The mathematical​​ key point is centered​​​‌ on how to efficiently​ couple two iterative methods​‌ (i.e., parallel in time​​ and optimization methods).

4​​​‌ Application domains

The Ocean-Atmosphere​ System

The evolution of​‌ natural systems, in the​​ short, mid, or long​​​‌ term, has extremely important​ consequences for both the​‌ global Earth system and​​ humanity. Forecasting this evolution​​​‌ is thus a major​ challenge from the scientific,​‌ economic, and human viewpoints.​​

Humanity has to face​​​‌ the problem of global​ warming, brought on​‌ by the emission of​​ greenhouse gases from human​​​‌ activities. This warming will​ probably cause huge changes​‌ at global and regional​​ scales, in terms of​​​‌ climate, vegetation and biodiversity,​ with major consequences for​‌ local populations. Research has​​ therefore been conducted over​​​‌ the past 15 to​ 20 years in an​‌ effort to model the​​ Earth's climate and forecast​​​‌ its evolution in the​ 21st century in response​‌ to anthropic action.

With​​ regard to short-term forecasts,​​​‌ the best and oldest​ example is of course​‌ weather forecasting. Meteorological​​ services have been providing​​​‌ daily short-term forecasts for​ several decades which are​‌ of crucial importance for​​ numerous human activities.

Numerous​​​‌ other problems can also​ be mentioned, like seasonal​‌ weather forecasting (to enable​​ powerful phenomena like an​​​‌ El Nin˜​o event or a​‌ drought period to be​​ anticipated a few months​​​‌ in advance), operational oceanography​ (short-term forecasts of the​‌ evolution of the ocean​​ system to provide services​​ for the fishing industry,​​​‌ ship routing, defense, or‌ the fight against marine‌​‌ pollution) or the prediction​​ of floods.

As​​​‌ mentioned previously, mathematical and‌ numerical tools are omnipresent‌​‌ and play a fundamental​​ role in these areas​​​‌ of research. In this‌ context, the vocation of‌​‌ AIRSEA is not to​​ carry out numerical prediction,​​​‌ but to address mathematical‌ issues raised by the‌​‌ development of prediction systems​​ for these application fields,​​​‌ in close collaboration with‌ geophysicists.

5 Social and‌​‌ environmental responsibility

Most of​​ the research activities of​​​‌ the AIRSEA team are‌ directed towards the improvement‌​‌ of numerical systems of​​ the ocean and the​​​‌ atmosphere. This includes the‌ development of appropriate numerical‌​‌ methods, model/parameter calibration using​​ observational data and uncertainty​​​‌ quantification for decision making.‌ The AIRSEA team members‌​‌ work in close collaboration​​ with the researchers in​​​‌ the field of geophyscial‌ fluid and are partners‌​‌ of several interdisciplinary projects.​​ They also strongly contribute​​​‌ to the development of‌ state of the art‌​‌ numerical systems, like NEMO​​ and CROCO in the​​​‌ ocean community.

6 Highlights‌ of the year

  • Clémentine‌​‌ Prieur was a Kirk​​ Distinguished Visiting Fellow in​​​‌ the Isaac Newton Institute‌ for Mathematical Sciences, Cambridge.‌​‌ She participated in the​​ Programme "Representing, calibrating &​​​‌ leveraging prediction uncertainty, from‌ statistics to machine learning"‌​‌ and delivered a lecture​​ titled "On feasible set​​​‌ estimation with Bayesian active‌ learning" www.newton.ac.uk.
  • E.‌​‌ Blayo and A. Vidard​​ have produced a series​​​‌ of pedagogical videos on‌ numerical ocean modeling, in‌​‌ collaboration with L’Esprit Sorcier​​ TV, available here).​​​‌

7 Latest software developments,‌ platforms, open data

7.1‌​‌ Latest software developments

7.1.1​​ AGRIF

  • Name:
    Adaptive Grid​​​‌ Refinement In Fortran
  • Keyword:‌
    Mesh refinement
  • Scientific Description:‌​‌
    AGRIF is a Fortran​​ 90 package for the​​​‌ integration of full adaptive‌ mesh refinement (AMR) features‌​‌ within a multidimensional finite​​ difference model written in​​​‌ Fortran. Its main objective‌ is to simplify the‌​‌ integration of AMR potentialities​​ within an existing model​​​‌ with minimal changes. Capabilities‌ of this package include‌​‌ the management of an​​ arbitrary number of grids,​​​‌ horizontal and/or vertical refinements,‌ dynamic regridding, parallelization of‌​‌ the grids interactions on​​ distributed memory computers. AGRIF​​​‌ requires the model to‌ be discretized on a‌​‌ structured grid, like it​​ is typically done in​​​‌ ocean or atmosphere modelling.‌
  • Functional Description:
    AGRIF is‌​‌ a Fortran 90 package​​ for the integration of​​​‌ full adaptive mesh refinement‌ (AMR) features within a‌​‌ multidimensional finite difference model​​ written in Fortran. Its​​​‌ main objective is to‌ simplify the integration of‌​‌ AMR potentialities within an​​ existing model with minimal​​​‌ changes. Capabilities of this‌ package include the management‌​‌ of an arbitrary number​​ of grids, horizontal and/or​​​‌ vertical refinements, dynamic regridding,‌ parallelization of the grids‌​‌ interactions on distributed memory​​ computers. AGRIF requires the​​​‌ model to be discretized‌ on a structured grid,‌​‌ like it is typically​​ done in ocean or​​​‌ atmosphere modelling.
  • News of‌ the Year:
    Within the‌​‌ framework of a European​​ Copernicus contract, improvements have​​​‌ been made to the‌ management of parallelization (‌​‌ assignment of processors to​​​‌ computational grids).
  • URL:
  • Publications:
  • Contact:
    Laurent Debreu
  • Participant:​​
    Laurent Debreu

7.1.2 NEMOVAR​​​‌

  • Name:
    Variational data assimilation​ for NEMO
  • Keywords:
    Oceanography,​‌ Data assimilation, Adjoint method,​​ Optimal control
  • Functional Description:​​​‌
    NEMOVAR is a state-of-the-art​ multi-incremental variational data assimilation​‌ system with both 3D​​ and 4D var capabilities,​​​‌ and which is designed​ to work with NEMO​‌ on the native ORCA​​ grids. The background error​​​‌ covariance matrix is modelled​ using balance operators for​‌ the multivariate component and​​ a diffusion operator for​​​‌ the univariate component. It​ can also be formulated​‌ as a linear combination​​ of covariance models to​​​‌ take into account multiple​ correlation length scales associated​‌ with ocean variability on​​ different scales. NEMOVAR has​​​‌ recently been enhanced with​ the addition of ensemble​‌ data assimilation and multi-grid​​ assimilation capabilities. It is​​​‌ used operationnaly in both​ ECMWF and the Met​‌ Office (UK)
  • Contact:
    Patrick​​ Vidard
  • Partners:
    CERFACS, ECMWF,​​​‌ Met Office

7.1.3 SWEET​

  • Name:
    Shallow Water Equation​‌ Environment for Tests, Awesome!​​
  • Keywords:
    High-Performance Computing, Time​​​‌ integration methods
  • Functional Description:​

    Solver for various kinds​‌ of PDEs (not only​​ Shallow Water) in 1D,​​​‌ the bi-periodic plane or​ sphere based on using​‌ global spectral methods (Fourier​​ / spherical harmonics).

    SWEET​​​‌ supports periodic boundary conditions​ for - the bi-periodic​‌ plane (2D torus) -​​ the sphere

    Space discretization​​​‌ - PLANE: Spectral methods​ based on Fourier space​‌ - PLANE: Finite differences​​ - SPHERE: Spherical Harmonics​​​‌

    Time discretization - Explicit​ RK - Implicit RK​‌ - Crank-Nicolson - Semi-Lagrangian​​ - Parallel-in-time - Parareal​​​‌ - PFASST - Rational​ approximation of exponential Integrators​‌ (REXI) ...and many more​​ time steppers...

    Special features​​​‌ - Graphical user interface​ - Fast Helmholtz solver​‌ in spectral space -​​ Easy-to-code in C++ ...​​​‌

    There’s support for various​ applications - Shallow-water equations​‌ on plane/sphere - Advection​​ - Burgers’ ...

  • URL:​​​‌
  • Contact:
    Martin Schreiber​
  • Partners:
    University of São​‌ Paulo, Technical University of​​ Munich (TUM)

7.2 Open​​​‌ data

8 New results​

8.1 Modeling for Oceanic​‌ and Atmospheric flows

8.1.1​​ Numerical Schemes for Ocean​​​‌ Modeling

Participants: Eric Blayo​, Laurent Debreu,​‌ Gabriel Derrida, Florian​​ Lemarié, Gurvan Madec​​​‌, Pierre Lozano.​

Beyond the hydrostatic assumption​‌

Most large scale ocean​​ models are based on​​​‌ the so-called “primitive equations”,​ which use the hydrostatic​‌ and incompressibility assumptions. However,​​ with the increase of​​​‌ resolution, a systematic use​ of the hydrostatic assumption​‌ becomes less valid. The​​ French regional oceanic modeling​​​‌ system CROCO (Coastal and​ Regional Ocean COmmunity model)​‌ developed these last years​​ allows for the use​​​‌ of either the hydrostatic​ incompressible (HI) equations and​‌ the non-hydrostatic compressible (NHC)​​ equations, the latter being​​​‌ much more computationally expensive.​ A natural idea is​‌ thus to limit the​​ use of the NHC​​​‌ version to some particular​ regions of interest where​‌ the hydrostatic assumption is​​ not relevant, and to​​​‌ nest such local NHC​ zooms within a larger​‌ model using the HI​​ version. However such a​​​‌ coupling is quite delicate​ from a mathematical point​‌ of view, due to​​ the different nature of​​ hydrostatic and nonhydrostatic equations​​​‌ (where the vertical velocity‌ is either a diagnostic‌​‌ or a prognostic variable).​​ In his PhD (​​​‌20, defended in‌ December 2025), P. Lozano‌​‌ has pointed out and​​ analyzed the fundamental problems​​​‌ occurring when coupling hydrostatic‌ and nonhydrostatic models 16‌​‌. He also performed​​ numerical simulations in a​​​‌ simplified configuration to illustrate‌ their impact, and proposed‌​‌ avenues toward improved coupling​​ procedures, in particular through​​​‌ the definition of an‌ adapted transition zone.

Optimized‌​‌ vertical coordinates for ocean​​ modeling

In the PhD​​​‌ work of G. Derrida‌ (started in October 2023),‌​‌ we are investigating new​​ vertical coordinate systems for​​​‌ ocean modeling, with the‌ objective of improving the‌​‌ representation of key physical​​ processes while maintaining numerical​​​‌ accuracy and efficiency. The‌ idea is to design‌​‌ flexible vertical coordinates that​​ can adapt to the​​​‌ specific characteristics of the‌ oceanic regions being modeled,‌​‌ such as areas with​​ strong stratification or complex​​​‌ topography. The first part‌ of the work focuses‌​‌ on an improved representation​​ of the vertical normal​​​‌ modes in the ocean,‌ which are crucial for‌​‌ accurately capturing internal wave​​ dynamics. In a submitted​​​‌ papier, we show that‌ the vertical discretization can‌​‌ be improved two ways:​​ first by developing a​​​‌ new original scheme (based‌ on error compensation for‌​‌ discrete eigenvalues systems) in​​ the vertical, and second​​​‌ by optimizing the vertical‌ grid point distribution to‌​‌ better capture the structure​​ of the modes.

This​​​‌ work is carried out‌ in collaboration with Mercator‌​‌ Ocean International.

8.1.2 Coupling​​ Methods for Oceanic and​​​‌ Atmospheric Models and representation‌ of the Air-Sea Interface‌​‌

Participants: Eric Blayo,​​ Emile Deléage, Florian​​​‌ Lemarié.

The Airsea‌ team is involved in‌​‌ the modeling and algorithmic​​ aspects of ocean-atmosphere (OA)​​​‌ coupling. We have been‌ actively working on the‌​‌ analysis of such coupling​​ both in terms of​​​‌ continuous and numerical formulations.‌ Particular attention is paid‌​‌ to the inclusion of​​ physical parameterizations in our​​​‌ theoretical framework. Our activities‌ have led to practical‌​‌ implementations in state-of-the-art oceanic​​ and Earth system models.​​​‌ Our focus during the‌ last few years has‌​‌ been on the following​​ topics:

  1. Mathematical analysis of​​​‌ OA coupling formulation    Coupling‌ problems arising in Earth‌​‌ system modeling involve turbulent​​ boundary layers, for which​​​‌ parameterizations induce non-standard interface‌ conditions and nonlinear diffusion‌​‌ operators. The complexity of​​ these coupled models is​​​‌ increasing far more rapidly‌ than their mathematical formalization‌​‌ and theoretical analysis. Notably,​​ rigorous studies that explicitly​​​‌ incorporate boundary layer parameterizations‌ remain scarce in the‌​‌ literature. As part of​​ the postdoctoral project of​​​‌ Emile Deléage (funded by‌ the PEPR MathsVives program),‌​‌ the mathematical analysis of​​ a coupling problem between​​​‌ an air column and‌ a water column is‌​‌ being conducted, incorporating turbulent​​ boundary layer parameterizations based​​​‌ on turbulent kinetic energy‌ and an interface flux‌​‌ computation derived from Monin–Obukhov​​ similarity theory to be​​​‌ representative of the formulation‌ of realistic coupled models.‌​‌ One objective is to​​ study the well-posedness of​​​‌ strong solutions over a‌ short time interval.
  2. Impact‌​‌ of the coupling formulation​​​‌ in a realistic context​    Building on preliminary work​‌ carried out by members​​ of the airsea team,​​​‌ a Schwarz-like iterative method​ has been applied in​‌ a state-of-the-art Earth-System model​​ (IPSL-CM6) to evaluate the​​​‌ consequences of inaccuracies in​ the usual ad-hoc ocean-atmosphere​‌ coupling algorithms used in​​ realistic models 48,​​​‌ 49. Numerical results​ obtained with an iterative​‌ process show large differences​​ at sunrise and sunset​​​‌ compared to usual ad-hoc​ algorithms, thus showing that​‌ synchrony errors inherent to​​ ad-hoc coupling methods can​​​‌ be large. As part​ of V. Schüller's thesis​‌ in collaboration with Lund​​ University, a single-column version​​​‌ of the EC-Earth climate​ model has been used​‌ to further our study​​ of coupling algorithms. The​​​‌ goal was to extend​ the analysis of 48​‌ using a less complex​​ model that remains representative​​​‌ of the parameterization schemes​ employed in 3D models.​‌ This single-column model has​​ made it possible to​​​‌ focus on ocean-atmosphere coupling​ in the presence of​‌ sea ice. It was​​ identified, among other findings,​​​‌ that the convergence of​ an iterative coupling in​‌ this context was compromised​​ due to non-differentiabilities (jumps)​​​‌ in the parameterization of​ albedo. We showed that​‌ a regularized albedo parameterization​​ solved the convergence issues.​​​‌ This work is summarized​ in a publication 1​‌. An important conclusion​​ of this work is​​​‌ that global-in-time Schwarz algorithms​ provide a general framework​‌ for performing sanity checks​​ during the development of​​​‌ model physics. This approach​ is expected to offer​‌ a means to better​​ understand the interactions between​​​‌ parameterizations developed independently and​ in an uncoupled framework.​‌
  3. A simplified atmospheric boundary​​ layer model for oceanic​​​‌ purposes    Our activities within​ the ongoing ENMASSE project​‌ is dedicated to the​​ development of a simplified​​​‌ model of the marine​ atmospheric boundary layer of​‌ intermediate complexity between a​​ bulk parameterization and a​​​‌ full three-dimensional atmospheric model,​ and to its integration​‌ into the NEMO general​​ circulation model (based on​​​‌ 46). A constraint​ in the conception of​‌ such a simplified model​​ is to allow an​​​‌ apt representation of the​ main air-sea feedbacks while​‌ keeping the computational efficiency​​ and flexibility inherent to​​​‌ ocean-only modeling. The simplified​ model, called ABL3d, has​‌ been derived using multiple​​ scales asymptotic techniques to​​​‌ cast the equations in​ terms of perturbations around​‌ an ambient state given​​ by a large-scale dataset.​​​‌ Such simplified model leads​ to good results for​‌ academic semi-idealized cases 45​​. The objective is​​​‌ now to extend the​ analysis to realistic cases​‌ in the framework of​​ the ENMASSE project funded​​​‌ by the Copernicus Marine​ Environment Monitoring Service (CMEMS).​‌ Over the course of​​ 2025, the ABL3d approach​​​‌ was implemented in the​ NEMO model, and preprocessing​‌ tools were developed to​​ support the preparation of​​​‌ ambient state input datasets.​ In parallel, in the​‌ framework of the AIRSEA/Eviden​​ collaboration, an objective is​​​‌ to design a surrogate​ via learning strategies of​‌ the response of the​​ atmospheric boundary layer to​​​‌ anomalies in ocean surface​ temperatures and currents. An​‌ M2 internship was co-supervised​​ on this topic (A.​​ Ameziane, M2 Calcul Haute​​​‌ Performance, Simulation; Saclay) in‌ 2025, and will be‌​‌ followed by a CIFRE​​ PhD thesis starting in​​​‌ 2026.

These topics are‌ addressed through strong collaborations‌​‌ between the applied mathematicians​​ and the climate and​​​‌ operational community (Météo-France, Ifremer,‌ SHOM, Mercator-Ocean, LMD, and‌​‌ LOCEAN). Airsea team members​​ play a major role​​​‌ in the structuration of‌ a multi-disciplinary scientific community‌​‌ working on ocean-atmosphere coupling​​ spanning a broad range​​​‌ from mathematical theory to‌ practical implementations in climate‌​‌ and operational models.

8.1.3​​ Physics-Dynamics coupling: Consistent subgrid-scale​​​‌ modeling

Participants: Eric Blayo‌, Florian Lemarié,‌​‌ Manolis Perrot.

A​​ few years ago, the​​​‌ AIRSEA team has started‌ to work on new‌​‌ topics around physics-dynamics coupling​​ 42. Schematically, numerical​​​‌ models consist of two‌ blocks generally identified as‌​‌ “physics” and “dynamics” which​​ are often developed separately.​​​‌ The “Physics” represents unresolved‌ or under-resolved processes with‌​‌ typical scales below model​​ resolution, while the “dynamics”​​​‌ corresponds to a discrete‌ representation in space and‌​‌ time of resolved processes.​​ Unresolved processes cannot be​​​‌ ignored because they directly‌ influence the resolved part‌​‌ of the flow since​​ energy is continuously transferred​​​‌ between scales. The interplay‌ between resolved and unresolved‌​‌ scales is a large,​​ incomplete, and complex topic​​​‌ for which there is‌ still much to do‌​‌ within the Earth system​​ modeling community 44.​​​‌ During the last year,‌ we worked on the‌​‌ following topics:

  1. Representation of​​ penetrative convection in oceanic​​​‌ models    Accounting for the‌ mean effect of subgrid-scale‌​‌ intermittent coherent structures like​​ convective plumes is very​​​‌ challenging. Currently, this is‌ done very crudely in‌​‌ ocean models (vertical diffusion​​ is locally increased to​​​‌ “mix'’ unstable density profiles).‌ A difficulty is that‌​‌ in convective conditions, turbulent​​ fluxes are dominated by​​​‌ processes unrelated to local‌ gradients, thus invalidating the‌​‌ usual downgradient (a.k.a. eddy-diffusion)​​ approach. In the framework​​​‌ of the PhD of‌ M. Perrot 21,‌​‌ a first step is​​ to study the derivation​​​‌ of mass-flux convection schemes‌ arising from a multi-fluid‌​‌ decomposition to extend them​​ specifically to the oceanic​​​‌ context 9. This‌ extension is done under‌​‌ certain “consistency" constraints: energetic​​ considerations and scale-awareness of​​​‌ the resulting model. Reference‌ LES simulations have been‌​‌ developed to guide the​​ formulation of unknown/uncertain free​​​‌ parameters (coefficients or functions)‌ in the proposed extended‌​‌ mass-flux scheme 10.​​ A first calibration of​​​‌ these free parameters was‌ carried out using Bayesian‌​‌ approaches and will be​​ further pursued within the​​​‌ ANR PLUME project.
  2. Link‌ between stochastic grid perturbation‌​‌ and Location Uncertainty (LU)​​ framework    Recent oceanic parameterizations​​​‌ "under Location Uncertainty" are‌ based on the hypothesis‌​‌ that the small-scale processes​​ are uncorrelated in time.​​​‌ Our work on this‌ topic investigates the theoretical‌​‌ connection between Stochastic Grid​​ Perturbation (SGP) and LU​​​‌ in ocean modeling. The‌ LU framework, based on‌​‌ random velocity fluctuations, has​​ proven effective in organizing​​​‌ large-scale flow and reproducing‌ long-term statistical properties. SGP‌​‌ offers a simpler alternative​​ by perturbing the computational​​​‌ grid across ensemble members‌ to represent small-scale uncertainties‌​‌ in high-resolution predictability studies.​​​‌ We derive SGP from​ the LU formalism, introduce​‌ time-correlated noise to preserve​​ grid structure, and demonstrate​​​‌ that a compensating advection​ term maintains LU properties​‌ and enables strict equivalence​​ between both approaches. Numerical​​​‌ experiments using a 3-layer​ Quasi-Geostrophic model confirm that​‌ the compensating advection term​​ is essential to achieve​​​‌ exact consistency between SGP​ and LU implementations. This​‌ work is summarized in​​ a publication 4.​​​‌

Those topics are addressed​ through collaborations with the​‌ climate and operational community​​ (Météo-France, SHOM, Mercator-Ocean, and​​​‌ IGE). The AIRSEA team​ is involved in the​‌ PLUME ANR project. One​​ of the objectives of​​​‌ this project is to​ use LES numerical simulations​‌ and laboratory experiments of​​ deep convection to calibrate​​​‌ and evaluate physical parameterizations​ like the one developped​‌ in 9 and 10​​.

8.2 Model Reduction​​​‌ and Multifidelity Methods

8.2.1​ Model Reduction

Participants: Clémentine​‌ Prieur, Katarina Radišić​​, Romain Verdière,​​​‌ Arthur Vidard, Olivier​ Zahm.

When numerical​‌ models are too costly​​ to evaluate, it is​​​‌ common to address the​ task of uncertainty quantification​‌ using an approximate model,​​ which is faster to​​​‌ compute. However, constructing such​ a reduced model (or​‌ surrogate) is challenging due​​ to the high number​​​‌ of variables involved. It​ is therefore crucial to​‌ identify the input variables​​ that are most important​​​‌ for building the reduced​ model.

In 23,​‌ we propose a nonlinear​​ dimensionality reduction method that​​​‌ leverages gradient evaluations of​ the model. The objective​‌ is to align the​​ Jacobian of the feature​​​‌ map (a nonlinear function​ that extracts the key​‌ components of the parameters)​​ with the model's gradients.​​​‌ Our main contribution is​ to use feature maps​‌ defined as the first​​ components of a diffeomorphism​​​‌ from d to​ d, parameterized​‌ by a Coupling Flows​​ neural network. This architecture​​​‌ preserves essential properties of​ the feature map, notably​‌ ensuring that its level​​ sets remain simply connected.​​​‌ In addition, we propose​ a dimension augmentation trick​‌ to increase the approximation​​ power of feature detection.​​​‌ A generalization to vector-valued​ functions demonstrate that our​‌ methodology directly applies to​​ learning autoencoders, showing the​​​‌ versatility of our proposed​ framework.

On a related​‌ topic, in her PhD​​ work, Katarina Radišić conducted​​​‌ an in-depth investigation into​ the use of stochastic​‌ polynomial chaos expansion, where​​ the coefficients of the​​​‌ polynomial basis are themselves​ treated as random variables.​‌ This approach allows for​​ an efficient representation of​​​‌ external uncertainties while retaining​ the computational efficiency of​‌ a surrogate emulator. Such​​ a framework proves particularly​​​‌ advantageous for problems involving​ complex systems with significant​‌ variability in external conditions.​​ This methodology was adaptated​​​‌ to a hydrological and​ pesticide transfer model, where​‌ the primary external uncertainty​​ arose from variability in​​​‌ rainfall. By incorporating this​ uncertainty directly into the​‌ stochastic framework, the model​​ achieved a flexible representation​​​‌ of system behavior under​ varying environmental conditions. This​‌ was in turn used​​ extensively in the context​​​‌ of sensitivity analysis and​ for robust parameter estimation,​‌ see (8.3.1,​​ 8.3.4).

8.2.2 Multifidelity​​

Participants: Elise Arnaud,​​​‌ Eric Blayo, Angélique‌ Saillet, Jean-Baptiste Seby‌​‌, Arthur Vidard,​​ Hélène Hénon.

Multifidelity​​​‌ methods seek to balance‌ the computational load across‌​‌ a hierarchy of models​​ with varying accuracy and​​​‌ evaluation cost, using lower-fidelity‌ models for inexpensive approximations‌​‌ and higher-fidelity ones only​​ when necessary. By integrating​​​‌ information across fidelities, it‌ ensures better performance for‌​‌ complex tasks. The efficiency​​ of such an approach,​​​‌ however, relies on our‌ ability to decide on‌​‌ how to allocate resources​​ on the different level​​​‌ of accuracy in order‌ to reduce overall computation‌​‌ while maintaining accuracy.

  1. Variational​​ data assimilation

    Incremental Variational​​​‌ Data Assimilation addresses the‌ non-linear least-square optimization challenges‌​‌ inherent in variational data​​ assimilation by minimizing a​​​‌ sequence of linear least-squares‌ cost functions iteratively. However,‌​‌ due to the high​​ dimensionality and ill-conditioning of​​​‌ the associated problems, the‌ computational burden can become‌​‌ prohibitive. To address these​​ challenges, we propose leveraging​​​‌ multifidelity methods and machine‌ learning to improve efficiency‌​‌ and reduce computational costs.​​

    This is explored in​​​‌ the context of Hélène‌ Hénon's PhD research, investigating‌​‌ the application of multifidelity​​ strategies to tackle the​​​‌ inner loop optimization problem.‌ The research focuses on‌​‌ leveraging a low-fidelity model​​ and randomization techniques to​​​‌ construct a limited-memory preconditioner,‌ while ensuring an improvement‌​‌ in the conditioning of​​ the Hessian. In particular,​​​‌ the goal is to‌ achieve a reduced condition‌​‌ number even when the​​ preconditioner is derived from​​​‌ a low-fidelity model and‌ thus an approximation of‌​‌ the true problem. A​​ key advantage of this​​​‌ approach lies in the‌ massively parallel nature of‌​‌ the preconditioner construction, which​​ enables efficient parallelization of​​​‌ the 4D-Var method. Her‌ work will be presented‌​‌ in two international conferences​​ early 2026

    In a​​​‌ related work, we propose‌ utilizing Deep Neural Networks‌​‌ to construct a preconditioner.​​ This preconditioner is trained​​​‌ on properties derived from‌ the singular value decomposition‌​‌ of the matrices, ensuring​​ it effectively mitigates the​​​‌ effects of ill-conditioning. To‌ further optimize resource utilization,‌​‌ the training dataset is​​ designed to be constructed​​​‌ dynamically during the optimization‌ process, thereby reducing storage‌​‌ requirements. This work is​​ detailed in a submitted​​​‌ paper 34

  2. Exploration of‌ climate scenarios

    Numerical models‌​‌ are important tools for​​ predicting climate change and​​​‌ helping policy-makers to make‌ decisions (e.g. in terms‌​‌ of protecting marine areas,​​ land use or defining​​​‌ fishing quotas). The huge‌ complexity of models and‌​‌ the generally very high​​ cost of numerical simulations​​​‌ make an exhaustive exploration‌ of the parameter space,‌​‌ corresponding to all possible​​ scenarios and all the​​​‌ model's internal options, completely‌ illusory. The idea is‌​‌ therefore to use statistical​​ tools for the design​​​‌ of experiments. These tools‌ enable us the parameter‌​‌ combinations that provide the​​ most information on a​​​‌ given quantity of interest‌ (QoI) calculated from the‌​‌ simulation carried out. The​​ design of experiments also​​​‌ has the advantage of‌ being able to be‌​‌ built adaptively, in order​​ to take into account​​​‌ the results of pre-existing‌ simulations, performed with various‌​‌ models, under various scenarios.​​​‌

    In Angelique Saillet's PhD,​ to address these issues,​‌ we use multi-fidelity Gaussian​​ process regression in the​​​‌ context of a marine​ biogeochemistry model, in collaboration​‌ with M. Baklouti (MIO​​ Marseille). A sensitivity analysis​​​‌ has been performed on​ a 1D (vertical) version​‌ of the model, in​​ order to identify the​​​‌ parameters that are most​ influential for certain quantities​‌ of interest (QoI). This​​ enables the construction of​​​‌ meta-models for these QoI,​ thanks to the use​‌ of Gaussian processes. The​​ current step consists in​​​‌ evaluating how the use​ of additional “low-fidelity’' simulations​‌ performed with one or​​ several degraded versions of​​​‌ the model can improve​ these metamodels. Simpler methods​‌ but on a more​​ realistic configuration have also​​​‌ been presented in 14​

    In Jean-Baptiste Seby's PhD​‌ (started on October 2025,​​ funded by Institut des​​​‌ Mathématiques pour la Planète​ Terre), we aim to​‌ explore these methodologies for​​ regional climate models, to​​​‌ try to make the​ best use of archived​‌ simulations. New theoretical developments​​ will probably be necessary.​​​‌ This work is done​ in collaboration with Pierre​‌ Nabat (Meteo France) and​​ Céline Helbert (Ecole Centrale​​​‌ Lyon).

8.3 Dealing with​ Uncertainties

8.3.1 Sensitivity Analysis​‌

Participants: Alexis Anagostakis,​​ Elise Arnaud, Clémentine​​​‌ Prieur, Arthur Vidard​, Ri Wang,​‌ Olivier Zahm, Mohamed​​ Doumbouya, Katarina Radišić​​​‌.

Sensitivity analysis is​ a crucial step in​‌ uncertainty quantification as it​​ helps identifying which input​​​‌ variables most influence the​ variability in a model's​‌ output. This understanding guides​​ model simplification, parameter prioritization,​​​‌ and robust decision-making. Our​ research results this year​‌ can be organized around​​ two main axes :​​​‌

  1. Gradient-based methods

    When model​ gradients are available, gradient-based​‌ sensitivity methods offer a​​ convenient and efficient alternative​​​‌ to traditional approaches. Over​ the past year, we​‌ have proposed several improvement​​ of such gradient-based sensitivity​​​‌ analysis:

    • The Active Subspaces​ (AS) method are quite​‌ effective for reducing input​​ dimensions of a smooth​​​‌ model, but its performance​ suffers when models have​‌ high-frequency, low-amplitude oscillations, leading​​ to poor feature selection.​​​‌ The work 35 introduces​ the Mollified Active Subspace​‌ (MAS) method, which smoothen​​ (or mollify) the model​​​‌ gradients in order to​ improve feature selection and​‌ surrogate accuracy, offering a​​ better error bound and​​​‌ practical guidelines for balancing​ smoothing and approximation quality.​‌ 51.
    • The optimal​​ sensor placement problem can​​​‌ be understood as a​ sensitivity analysis of an​‌ optimality system with respect​​ to the data. One​​​‌ canonical approach is to​ maximize the Expected Information​‌ Gain (EIG) associated with​​ a given system of​​​‌ obervable quantities. In the​ PhD project of Mohamed​‌ Doumbouya, we consider the​​ case of computationally expensive​​​‌ ocean models. Our approach​ is to optimize a​‌ tractable gradient-based bound of​​ the EIG instead of​​​‌ the EIG itself. We​ plan to compare different​‌ bound- based and EIG-based​​ solutions, and also to​​​‌ accelerate computations via randomized​ linear algebra.
    • Quantile oriented​‌ sensitivity analysis Quantiles provide​​ a rich information on​​​‌ model output. Quantile oriented​ sensitivity analysis measures the​‌ sensitivity of the quantiles​​ of model outputs to​​ inputs. In the framework​​​‌ of Ri Wang we‌ investigated random forest based‌​‌ inference of sensitivity measures​​ (QOSA and QOSE). A​​​‌ first paper is in‌ minor revision 52 and‌​‌ a second one should​​ be submitted in 2026.​​​‌
    • Sensitivity analysis for stochastic‌ models We proposed in‌​‌ 6 new algorithms for​​ global sensitivity analysis of​​​‌ non Markovian stochastic compartmental‌ models. The algorithms were‌​‌ implemented on a model​​ designed to the COVID19​​​‌ pandemics.
    • Sensitivity Analysis in‌ a Game-Theoretic Approach to‌​‌ an Environmental Management Problem​​ In 5, we​​​‌ analyzed the added value‌ of sensitivity analysis to‌​‌ solve environmental management problems.​​
  2. Given data inference for​​​‌ sensitivity analysis In 40‌, we introduce two‌​‌ semi-parametric estimators of Sobol'​​ indices of any order.​​​‌ These estimators can be‌ computed from a single‌​‌ input-output sample. We prove​​ assymptotic normality and efficiency.​​​‌
  3. GSA for hydrological models‌
    • Traditional global sensitivity analysis‌​‌ (GSA) often neglects natural​​ variability in forcing conditions,​​​‌ limiting result validity. In‌ 12, we treat‌​‌ Sobol’ indices as random​​ variables influenced by forcing​​​‌ variability and estimate them‌ efficiently using stochastic polynomial‌​‌ chaos expansions. Applying this​​ to a hydrological model,​​​‌ we found parameter rankings‌ vary with forcing, and‌​‌ proposed an aggregated sensitivity​​ index to enhance GSA​​​‌ robustness and decision reliability.‌
    • During Mélanie Villain's internship‌​‌ we performed a Sobol'​​ based GSA on Nihm,​​​‌ a realistic ground water‌ hydrological model of the‌​‌ Strengbach catchment area. It​​ enabled the identification of​​​‌ the parameters that most‌ influence the model outputs‌​‌ and provided additional insight​​ into the sources of​​​‌ variability and uncertainty. This‌ work form the basis‌​‌ for Mélanie's PhD (started​​ November 2025) and open​​​‌ the way to parameter‌ estimation. This work is‌​‌ our main contribution to​​ the ANR CASH project.​​​‌

8.3.2 Bayesian inversion

Participants:‌ Elise Arnaud, Arthur‌​‌ Vidard, Adama Barry​​, Clément Duhamel,​​​‌ Clémentine Prieur, Olivier‌ Zahm, Hippolyte Signargout‌​‌.

Bayesian inverse problems​​ become challenging when computational​​​‌ models are expensive, as‌ the repeated evaluations required‌​‌ for inference (e.g., in​​ Markov Chain Monte Carlo)​​​‌ become infeasible. Additionally, complex‌ priors, such as those‌​‌ with heavy tails or​​ multimodal distributions, complicate sampling​​​‌ and convergence, making efficient‌ exploration of the posterior‌​‌ space significantly harder.

In​​ 2025, we launched a​​​‌ collaboration with glaciologists at‌ IGE to estimate Antarctic‌​‌ ice-sheet deep temperatures profiles​​ using satellite data of​​​‌ the radiative emission of‌ the ice. Together with‌​‌ Ghislain Picard (IGE), Olivier​​ Zahm co-supervises Hippolyte Signargout's​​​‌ postdoctoral research, which focuses‌ on developing efficient numerical‌​‌ methods for Bayesian inversion.​​ The challenge lies in​​​‌ the problem's ill-posed nature‌ (weakly informative data) compounded‌​‌ by the sheer volume​​ of satellite data available​​​‌ (several measurement per image‌ pixels).

The PhD thesis‌​‌ of Adama Barry 18​​ was focused on metamodel​​​‌ based calibration of complex‌ computer codes. A first‌​‌ paper on the design​​ of physical and simulation​​​‌ experiments is in revision‌ 38.

The PhD‌​‌ thesis of Clément Duhamel​​ was focused on set​​​‌ inversion with application to‌ the calibration of wind‌​‌ turbines. In 28 we​​​‌ investigate active learning strategies​ for set inversion.

8.3.3​‌ Sampling algorithms

Participants: Olivier​​ Zahm, Benjamin Zanger​​​‌, Lorenzo Calzolari,​ Clémentine Prieur.

Sampling​‌ from high-dimensional distributions that​​ are multi-modal and/or heavy-​​​‌ tailed poses significant challenges​ across various fields. This​‌ is particularly true in​​ large-scale Bayesian inference with​​​‌ sparsity-inducing priors, but also,​ for example, in molecular​‌ dynamics, where the Boltzmann​​ distribution of a molecular​​​‌ system is highly multimodal,​ each of the mode​‌ corresponding to a distinct​​ physical conformation. Conventional sampling​​​‌ methods such as Markov​ Chain Monte Carlo (MCMC)​‌ face difficulties in accurately​​ exploring the entire landscape​​​‌ (modes, tails, etc) of​ the target distribution, resulting​‌ in poor numerical performances.​​ We have made diverse​​​‌ contributions which aim at​ addressing these challenges, focusing​‌ on a range of​​ applications including imaging, epidemiology,​​​‌ and also on providing​ proof-of-concepts for certain advanced​‌ pioneering algorithms.

These contributions​​ involve the development of:​​​‌

  1. dimension reduction techniques 47​
  2. transport maps methods 36​‌
  3. preconditioners for stochastic differential​​ equations (SDE) in order​​​‌ to enhance the convergence​ properties of sampling algorithms​‌ 39
  4. sampling algorithms for​​ functional data in a​​​‌ RKHS

8.3.4 Robust inversion​

Participants: Elise Arnaud,​‌ Exaucé Luweh Adjim Ngarti​​, Katarina Radišić,​​​‌ Arthur Vidard.

Estimating​ key parameters in numerical​‌ models is a crucial​​ aspect in numerical simulation,​​​‌ particularly when these parameters​ are not directly observable.​‌ Traditional estimation methods infer​​ parameters indirectly from their​​​‌ effects on observable variables,​ introducing inherent uncertainties. In​‌ addition to the parameters​​ to be estimated, numerical​​​‌ models often include uncertain​ and uncontrollable nuisance parameters,​‌ which can further complicate​​ the estimation process.

In​​​‌ Exaucé Ngarti’s PhD research,​ we investigate extending variational​‌ inference to account for​​ the presence of nuisance​​​‌ parameters. Ignoring the stochastic​ nature of these nuisance​‌ parameters can lead to​​ suboptimal parameter estimation due​​​‌ to error compensation effects.​ To address this, we​‌ model nuisance parameters as​​ random variables, redefining the​​​‌ numerical model itself as​ a random variable. This​‌ problem is formulated within​​ a Bayesian framework, where​​​‌ the goal is to​ estimate the posterior distribution​‌ by minimizing the Kullback-Leibler​​ divergence over a family​​​‌ of parameterized distributions. To​ increase the flexibility of​‌ this approach, we integrate​​ generative neural networks, such​​​‌ as normalizing flows, to​ enhance the expressiveness of​‌ the posterior approximation. These​​ methods are currently applied​​​‌ to a 1DV ocean​ model to estimate the​‌ subgrid scale convection parametrization.​​

In Katarina Radišić’s PhD​​​‌ research, we explored an​ alternative approach based on​‌ optimal control. Here, the​​ parameter estimation problem is​​​‌ addressed by minimising an​ objective function. When nuisance​‌ parameters are present, the​​ objective function becomes a​​​‌ random variable, adding a​ layer of complexity. To​‌ efficiently handle this uncertainty,​​ we employ stochastic polynomial​​​‌ chaos expansion as a​ surrogate for the "random"​‌ objective function. This technique​​ enables effective exploration of​​​‌ the uncertain parameter space​ and facilitates the computation​‌ of robust parameter estimates.​​ The methodology has been​​​‌ successfully applied to a​ hydrology and pesticide transfer​‌ model, demonstrating its feasibility.​​ This work is described​​ in 22 and is​​​‌ under revision in RESS‌ 31.

8.4 Analysis‌​‌ of reflected Langevin processes​​

Participants: Clémentine Prieur.​​​‌

In collaboration with Jose‌ R. Leon (Universidad de‌​‌ la República de Uruguay)​​ and Pierre Etoré (LJK/DATA)​​​‌ we study ergodicity properties‌ of reflected Langevin processes‌​‌ 29. Our aim​​ is then to propose​​​‌ statistical inference for such‌ models with environmental applications.‌​‌

8.5 High performance computing​​

8.5.1 Dynamic compute-resource utilization​​​‌

Participants: Martin Schreiber.‌

The way how applications‌​‌ are executed on supercomputers​​ still follows a traditional​​​‌ static resource allocation pattern:‌ Computing resources are allocated‌​‌ at the start of​​ a job which executes​​​‌ the application and are‌ only released at the‌​‌ end of the job's​​ runtime. This still follows​​​‌ the way of running‌ jobs since decades where‌​‌ a dynamic resource allocation​​ over the application's runtime​​​‌ would lead to several‌ benefits: higher utilization of‌​‌ the computing resources, ad-hoc​​ allocation of AI accelerator​​​‌ cards, less energy consumption,‌ faster response for interactive‌​‌ jobs, improved data locality​​ and I/O over the​​​‌ full runtime, support of‌ urgent computing without necessarily‌​‌ killing running jobs, etc.​​ Various attempts have been​​​‌ conducted under different terminologies‌ used such as “evolving”‌​‌ jobs (application-driven dynamic resource​​ changes) and “malleability” (system-driven​​​‌ dynamic resource changes) where‌ we see a hybridization‌​‌ of them required for​​ reaching optimal results.

We​​​‌ continued our roadmap to‌ further develop our new‌​‌ approach called “Dynamic Processes​​ with PSets (DPP)”:

  • We​​​‌ assessed the feasibility of‌ DPP to be even‌​‌ applied to asynchronous Many-Task​​ (AMT) Runtime System, 11​​​‌, special issue in‌ SN Computer Science Journal,‌​‌ in Springer Nature.
  • Large-scale​​ studies with DPP in​​​‌ collaboration with Barcelona Supercomputing‌ Center and the DataMOVE‌​‌ Inria team, see www.martin-schreiber.info/data/publications​​, accepted at HiPC​​​‌ 25 conference.
  • Design Principles‌ of Dynamic Resource Management‌​‌ for High-Performance Parallel Programming​​ Models, see 43,​​​‌ accepted in DynResHPC'25 workshop‌ at EuroPAR 2025
  • Bridging‌​‌ the Gap Between Genericity​​ and Programmability of Dynamic​​​‌ Resources in HPC, see‌ 15, accepted at‌​‌ ISC'25 in Hamburg
  • Forming​​ the “Dynamic Resources for​​​‌ HPC (DynResHPC) Consortium” to‌ provide a platform for‌​‌ including a variety of​​ experts.

External collaborators: Dominik​​​‌ Huber (TUM, DataMOVE), Pierre-François‌ Dutot (DataMOVE), Olivier Richard‌​‌ (DataMOVE), Howard Pritchard (LANL),​​ Martin Schulz (TUM)

8.5.2​​​‌ Hardware-aware numerics

Participants: Hugo‌ Brunie, Laurent Debreu‌​‌, Julien Remy,​​ Martin Schreiber.

The​​​‌ Poseidon project advanced further,‌ working on the vision‌​‌ to push the performance​​ of the NEMO and​​​‌ CROCO ocean simulation models‌ to the HPC limit‌​‌ with in-depth optimizations that​​ can't be done with​​​‌ currently existing compilers and‌ to simplify the development‌​‌ of highly performing code​​ for model developers.

The​​​‌ underlying idea is to‌ uplift the fluid dynamics‌​‌ equation solver to a​​ DSL-like intermediate representation (IR).​​​‌ This IR is based‌ on a hypergraph with‌​‌ nodes representing computations and​​ (hyper)edges the data flow.​​​‌ The strong formalism of‌ the IR representation forms‌​‌ the foundation for performing​​ the required HPC optimization.​​​‌ Poseidon supports writing back‌ code to the original‌​‌ CROCO ocean model, and​​​‌ two research codes TPDesHoughes​ and Schweinshaxe; hence, it​‌ doesn't require using a​​ different development which would​​​‌ require disruptive changes.

Based​ on the extracted barotropic​‌ solver of the CROCO​​ model, our first HPC​​​‌ results are to perform​ a fully automatic kernel​‌ and loop fusion. This​​ already led to a​​​‌ substantial reduction of memory​ access, leading to speedups​‌ of over 2 for​​ GPU code that was​​​‌ considered to be highly​ optimized by HPC engineers.​‌ Our current work is​​ under review: 32.​​​‌

Due to the strong​ formalism, further work was​‌ conducted in collaboration with​​ Anna Mittermair & Martin​​​‌ Schulz (Technical University of​ Munich) on optimizing the​‌ communication for distributed memory​​ systems. Based on​​​‌ Poseidon and the data​ flow, we can automatically​‌ inject nodes into the​​ hypergraph to perform automatic​​​‌ MPI communication. Our current​ work is under review​‌ with a preprint available​​ here: 30.

As​​​‌ part of the Poseidon​ project, an overlapping Schwarz​‌ method for latency hiding​​ has been integrated to​​​‌ the barotropic solver of​ the Croco ocean model​‌ with substantial speedups of​​ around on larger-scale studies​​​‌ on Jean Zay (unpublished).​

External collaborators: Anna Mittermair​‌ (TUM), Andrew Porter (STFC),​​ Sergi Siso (STFC), Jörg​​​‌ Heinrichs (ABOM)

8.5.3 New​ time-integration methods

Participants: Martin​‌ Schreiber.

We investigated​​ the parallel performance of​​​‌ parallel spectral deferred corrections,​ a numerical method that​‌ enables fine-grained parallelism for​​ the solution of initial​​​‌ value problems. The scheme​ was applied to the​‌ shallow water equations and​​ employs an IMEX splitting,​​​‌ treating fast modes implicitly​ and slow modes explicitly​‌ to ensure efficiency. We​​ present OpenMP-based parallel implementations​​​‌ of parallel SDC in​ two well-established simulation codes:​‌ the finite-volume–based operational ocean​​ model ICON-O and the​​​‌ spherical-harmonics-based research code SWEET.​ The implementations were benchmarked​‌ on a single node​​ of the JUSUF (SWEET)​​​‌ and JUWELS (ICON-O) systems​ at the Jülich Supercomputing​‌ Centre. We demonstrate a​​ reduction in time-to-solution over​​​‌ a range of accuracy​ levels. For ICON-O, we​‌ show speedup compared to​​ the currently used Adams-Bashforth-2​​​‌ integrator with OpenMP loop​ parallelization. For SWEET, we​‌ demonstrate speedup over serial​​ spectral deferred corrections and​​​‌ a second-order implicit-explicit integrator.​ See 41 for more​‌ information.

We explored and​​ extended semi-Lagrangian exponential methods,​​​‌ which integrate stiff linear​ terms with exponential time​‌ integration and handle nonlinear​​ advection using a semi-Lagrangian​​​‌ approach. These techniques are​ relevant for partial differential​‌ equations found in atmospheric​​ models. A truncation error​​​‌ analysis reveals that existing​ methods are limited to​‌ first-order accuracy due to​​ linear term discretization. To​​​‌ address this, we develop​ a second-order scheme. Stability​‌ comparisons between various Eulerian​​ and semi-Lagrangian exponential methods​​​‌ and a widely used​ semi-Lagrangian semi-implicit method are​‌ conducted. Numerical tests on​​ shallow-water equations confirm the​​​‌ proposed method's improved stability​ and accuracy, albeit with​‌ higher computational costs. However,​​ its stability and cost​​​‌ are comparable to the​ semi-implicit method, making it​‌ a competitive option for​​ atmospheric modeling 3.​​​‌ This forms an extremely​ important part for future​‌ work on parallel-in-time methods.​​

Solving partial differential equations​​ is a central task​​​‌ in scientific computing, and‌ this work focuses on‌​‌ the numerical solution of​​ initial value problems governed​​​‌ partly or entirely by‌ linear PDEs using Rational‌​‌ Approximation of Exponential Integration​​ (REXI). REXI replaces sequential​​​‌ time-stepping with a sum‌ of rational terms, enabling‌​‌ parallelization across these terms​​ and thereby offering additional​​​‌ scalability for problems limited‌ by spatial parallelism. We‌​‌ introduce a unified REXI​​ framework, showing its algebraic​​​‌ equivalence to several classical‌ methods, including diagonalized implicit‌​‌ Runge–Kutta schemes, Cauchy-contour integration​​ approaches, and direct approximations,​​​‌ and provide the first‌ comprehensive numerical comparison of‌​‌ these techniques for challenging​​ hyperbolic problems. Performance is​​​‌ demonstrated for the nonlinear‌ shallow-water equations on the‌​‌ rotating sphere, showing that​​ diagonalized low-order Gauss Runge–Kutta​​​‌ methods formulated as REXI‌ achieve up to a‌​‌ 64-fold reduction in computational​​ resources at fixed accuracy​​​‌ compared to existing approaches.‌ See 33.

External‌​‌ collaborators: Pedro S. Peixoto​​ (USP), João C. Steinstraesser​​​‌ (USP), Elizaveta Boriskova (TUM)‌

9 Bilateral contracts and‌​‌ grants with industry

Participants:​​ Clémentine Prieur, Elise​​​‌ Arnaud, Clément Duhamel‌, Exaucé Luweh Adjim‌​‌ Ngarti, Lorenzo Calzolari​​.

9.1 Bilateral contracts​​​‌ with industry

  • Consortium CIROQUO‌ – Consortium Industrie Recherche‌​‌ pour l’Optimisation et la​​ QUantification d’incertitude pour les​​​‌ données Onéreuses – gathers‌ academical and technological partners‌​‌ to work on problems​​ related to the exploitation​​​‌ of numerical simulators. This‌ Consortium, created in January‌​‌ 2021, is the continuation​​ of the projects DICE,​​​‌ ReDICE and OQUAIDO which‌ respectively covered the periods‌​‌ 2006-2009, 2011-2015 and 2015-2020.​​ CIROQUO will be continued​​​‌ from 2025 as CIROQUO‌ 2 with new industrial‌​‌ partners such as EDF​​ or Michelin (cf ciroquo.ec-lyon.fr​​​‌).
  • The project "LOMIS"‌ (started in 2025) is‌​‌ a project funded by​​ ESA on ice-sheet temperature​​​‌ retriveal. The partners are‌ IGE-UGA, University of Trento‌​‌ and CNR-IFAC. It will​​ fund the postdoc of​​​‌ Hippolyte Signargout in 2026.‌

9.2 Bilateral grants with‌​‌ industry

  • Funding of Exaucé​​ Luweh Adjim Ngarti’s PhD​​​‌ with a CIFRE contract‌ with Eviden. PhD subject:‌​‌ Deep learning for inverse​​ problem in geophysics.
  • Funding​​​‌ of Clément Duhamel’s PhD‌ (sept. 2020-nov. 2024) by‌​‌ IFP Energies Nouvelles (IFPEN)​​ within the framework of​​​‌ IFPEN and Inria strategic‌ partnership. PhD subject: Gaussian‌​‌ processes-based excursion set estimation​​ for scalar or vector​​​‌ black box functions. Application‌ to the calibration of‌​‌ a numerical wind turbine​​ simulator.
  • Funding of Lorenzo​​​‌ Calzolari’s PhD (nov. 2024-…)‌ by IFP Energies Nouvelles‌​‌ (IFPEN). PhD subject: Active​​ learning with functional inputs:​​​‌ application to wind turbine‌ reliability design.

10 Partnerships‌​‌ and cooperations

10.1 International​​ initiatives

10.1.1 Associate Teams​​​‌ in the framework of‌ an Inria International Lab‌​‌ or in the framework​​ of an Inria International​​​‌ Program

Crocodiles (team.inria.fr/crocodiles/‌):

Optimization of PDE‌​‌ solvers is one of​​ the big challenges in​​​‌ High-Performance Computing (HPC). This‌ requires not only skills‌​‌ and a deeper understanding​​ of HPC from all​​​‌ the hardware and software‌ layers but also research‌​‌ on software solutions that​​ are sustainable and accepted​​​‌ by the developers and‌ users of these solvers.‌​‌

This associate team brings​​​‌ together members of ANL​ and the Inria AIRSEA​‌ team who are both​​ currently working on the​​​‌ HPC modernization of models​ under the aforementioned constraints.​‌ This allows us to​​ share, on the one​​​‌ hand, our experience and​ plans with the model​‌ developments. On the other​​ hand, we can strongly​​​‌ benefit from the experience​ of all the current​‌ developments, which share many​​ similarities.

OSCAR

The associate​​​‌ team OSCAR with the​ National University of Singapore​‌ started in 2025. It​​ is concerned with the​​​‌ design of new algorithms​ to address these issues,​‌ building on recent advances​​ in dimension reduction, transport​​​‌ map methods, and preconditioning​ strategies for stochastic differential​‌ equations. These developments are​​ motivated by applications in​​​‌ imaging, epidemiology, geophysics, and​ molecular dynamics.

10.1.2 STIC/MATH/CLIMAT​‌ AmSud projects

SMILE

Participants:​​ Clémentine Prieur, Alexis​​​‌ Anagnostakis.

  • Title:
    Statistical​ modeling, nonparametric inference and​‌ model selection for complex​​ data
  • Program:
    MATH-AmSud
  • Duration:​​​‌
    January 1, 2024 –​ December 31, 2025
  • Local​‌ supervisor:
    Clementine Prieur
  • Partners:​​
    • Meza Becerra (Chili)
    • Jose​​​‌ R. Leon (Uruguay)
  • Inria​ contact:
    Clementine Prieur
  • Summary:​‌
    Statistical modelling for complex​​ data is an important​​​‌ framework for analyzing data​ in fields such as​‌ ecology, meteorology, health, and​​ telecommunications. These models are​​​‌ used to model population​ dynamics, animal movement, longitudinal​‌ data, spatial-temporal analysis, or​​ Poisson processes. In this​​​‌ proposal, we are interested​ in to propose novel​‌ estimation procedures in this​​ kind of complex data,​​​‌ considering restricted data (for​ instance, data on compact​‌ domain or longitudinal compositional​​ data), spatial weighted regression,​​​‌ and model selection with​ weakly dependent observations and​‌ non-homogeneous Poisson processes. We​​ will use parametric and​​​‌ nonparametric strategies.

10.1.3 Participation​ in other International Programs​‌

A Comprehensive Software Stack​​ for Dynamic Resources Management​​​‌

Participants: Sergio Iserte,​ Dominik Huber, Martin​‌ Schreiber, Pierre-François Dutot​​, Olivier Richard,​​​‌ Antonio J. Peña.​

  • Title:
    A Comprehensive Software​‌ Stack for Dynamic Resources​​ Management
  • Partner Institution(s):
    BSC,​​​‌ Inria
  • Date/Duration:
    2024-
  • Additionnal​ info/keywords:
    dynamic resource management​‌

10.2 International research visitors​​

10.2.1 Visits of international​​​‌ scientists

Other international visits​ to the team
Jose​‌ R. Leon
  • Status
    researcher​​
  • Institution of origin:
    Universidad​​​‌ de la República de​ Uruguay
  • Country:
    Uruguay
  • Dates:​‌
    January and December 2025​​ (2 visits of 2​​​‌ weeks)
  • Context of the​ visit:
    collaboration with Clémentine​‌ Prieur
  • Mobility program/type of​​ mobility:
    SMILE project
Sergio​​​‌ Iserte
  • Status
    researcher
  • Institution​ of origin:
    Barcelona Supercomputing​‌ Center
  • Country:
    Spain
  • Dates:​​
    February 2025
  • Context of​​​‌ the visit:
    collaboration with​ Martin Schreiber

10.2.2 Visits​‌ to international teams

Research​​ stays abroad
Clémentine Prieur​​​‌
  • Visited institution:
    Isaac Newton​ Institute Cambridge
  • Country:
    UK​‌
  • Dates:
    July
  • Context of​​ the visit:
    Kirk Distinguished​​​‌ Visiting Fellow for the​ Representing, calibrating & leveraging​‌ prediction uncertainty from statistics​​ to machine learning programme​​​‌
  • Mobility program/type of mobility:​
    research stay, plenary lecture​‌

10.3 European initiatives

10.3.1​​ Horizon Europe

DARE

Participants:​​​‌ Maurice Brémond, Laurent​ Debreu, Martin Schreiber​‌.

  • Title:
    DARE, Digital​​ Autonomy with RISC-V in​​​‌ Europe, dare-riscv.eu
  • Duration:
    2025-2030​
  • Abstract:
    The AIRSEA team​‌ is involved in the​​ DARE project, which aims​​ to develop an open​​​‌ and secure European processor‌ architecture based on RISC-V.‌​‌ The AIRSEA team's role​​ is to explore the​​​‌ application of RISC-V architecture‌ in high-performance computing for‌​‌ environmental modeling, particularly in​​ oceanographic simulations. This involves​​​‌ adapting existing models to‌ run efficiently on RISC-V‌​‌ processors. The focus is​​ on source to source​​​‌ code translation and optimization‌ techniques to ensure that‌​‌ the models can leverage​​ the capabilities of RISC-V​​​‌ architecture effectively. NEMO is‌ one of the ocean‌​‌ models targeted in this​​ project.

10.3.2 Other european​​​‌ programs/initiatives

  • Program: CMEMS
    • Project‌ acronym:
      ENMASSE
    • Project title:‌​‌
      Enhancing Nemo for Marine​​ Applications and Services
    • Coordinator:​​​‌
      F. Lemarié
    • Duration:
      Dec.‌ 2024 - Dec. 2027.‌​‌
    • Other partners:
      CMCC (Italy),​​ Sorbonne Université, MetOffice (UK),​​​‌ National Oceanography Center (UK),‌ STFC Hartree Centre (UK),‌​‌ Datlas (FR).
    • Abstract:
      The​​ Enhancing NEMO for Marine​​​‌ Applications and Services (ENMASSE)‌ project represents a pivotal‌​‌ initiative aimed at advancing​​ the capabilities of the​​​‌ NEMO (Nucleus for European‌ Modelling of the Ocean)‌​‌ modelling platform. This enhancement​​ is designed to address​​​‌ specific scientific and operational‌ requirements set by the‌​‌ Copernicus Marine Service (CMS)​​ program for the development​​​‌ and delivery of more‌ precise and sophisticated ocean‌​‌ modelling products. These products​​ are intended to support​​​‌ a wide range of‌ applications, including marine safety,‌​‌ climate prediction, and ecosystem​​ monitoring, ultimately contributing to​​​‌ informed decision-making and sustainable‌ ocean management.
  • Program: C3S2‌​‌
    • Project acronym:
      ERGO2
    • Project​​ title:
      Advancing ocean data​​​‌ assimilation methodology for climate‌ applications
    • Duration:
      August 2022‌​‌ - December 2025
    • Coordinator:​​
      Arthur Vidard
    • Other partners:​​​‌
      Cerfacs (France), CNR (Italy)‌
    • Abstract:
      The scope of‌​‌ this contract is to​​ improve ocean data assimilation​​​‌ capabilities at ECMWF, used‌ in both initialization of‌​‌ seasonal forecasts and generation​​ of coupled Earth System​​​‌ reanalyses. In particular it‌ shall focus on i)‌​‌ improving ensemble capabilities in​​ NEMO and NEMOVAR and​​​‌ the use of their‌ information to represent background‌​‌ error statistics; ii) extend​​ NEMOVAR capabilities to allow​​​‌ for multiple resolution in‌ multi-incremental 3D-Var; iii) make‌​‌ better use of ocean​​ surface observations. It shall​​​‌ also involve performing scout‌ experiments and providing relevant‌​‌ diagnostics to evaluate the​​ benefit coming from the​​​‌ proposed developments.

10.4 National‌ initiatives

10.4.1 ANR

  • A‌​‌ 4-year contract: ANR MOTIONS​​ (Multiscale Oceanic simulaTIONS based​​​‌ on mesh refinement strategies‌ with local adaptation of‌​‌ dynamics and physics).
    • PI:​​
      F. Lemarié
    • Duration:
      Jan.​​​‌ 2024 - Dec. 2027.‌
    • Other partners:
      • Laboratoire d’Aérologie,‌​‌ UMR 5560 (LAERO),
      • Service​​ Hydrographique et Océanographique de​​​‌ la Marine (SHOM),
      • Institut‌ Camille Jordan,
      • UMR5208 (ICJ),‌​‌
      • Laboratoire d’Etudes en Géophysique​​ et Océanographie Spatiales,
      • UMR5566​​​‌ (LEGOS).
    • Abstract:
      The MOTIONS‌ project aims at delivering‌​‌ robust and efficient numerical​​ algorithms allowing an innovative​​​‌ multiscale modeling strategy based‌ on block-structured mesh refinement‌​‌ with local adaptation of​​ model equations, numerics and​​​‌ physics in selected areas‌ of interest. The target‌​‌ application to evaluate numerical​​ developments is the simulation​​​‌ of important fine-scale non-hydrostatic‌ processes and their feedback‌​‌ to larger scales within​​ the Mediterranean / North-East​​​‌ Atlantic dynamical continuum.
  • A‌ 4-year contract: ANR PLUME‌​‌ (Observation and Parameterization of​​​‌ Oceanic Convection).
    • PI:
      B.​ Deremble (CNRS), Inria PI:​‌ F. Lemarié.
    • Objectives:
      1. build​​ a consistent database of​​​‌ convective events (both in​ the lab and with​‌ a numerical model) in​​ order to calibrate free​​​‌ parameters of parameterizations of​ deep convection.
      2. characterize the​‌ structure of the thermal​​ plumes in a well​​​‌ defined parameter space that​ characterizes the rotating/non rotating​‌ state and forced vs​​ free convection
      3. use a​​​‌ data driven approach to​ formulate a model of​‌ convection without any preconceived​​ bias about the mathematical​​​‌ formulation.
  • A 5-year contract:​ ANR MEDIATION: Methodological developments​‌ for a robust and​​ efficient digital twin of​​​‌ the ocean.
    • Duration:
      2022-2027​
    • Funding:
      French priority research​‌ program (PPR) ”Ocean and​​ Climate"
    • Partners:
      • Inria (DATAMOVE​​​‌ and ODYSSEY teams)
      • CNRS​
      • IFREMER
      • IMT-Atlantique
      • IRD
      • Metéo-France​‌
      • SHOM
      • Univ. Grenoble Alpes​​
      • Univ. Aix-Marseille.
    • Inria contact:​​​‌
      Laurent Debreu
    • Coordinator:
      Laurent​ Debreu
    • Summary:
      The MEDIATION​‌ project targets two questions:​​ how will global change​​​‌ impact the functioning of​ regional marine ecosystems, and​‌ how to evaluate the​​ effect of measures to​​​‌ preserve the environment? With​ two main demonstrators on​‌ the French coasts (Atlantic​​ and Mediterranean), MEDIATION combines​​​‌ methodological developments in numerical​ sciences (taking into account​‌ uncertainties, high performance computing​​ and artificial intelligence) with​​​‌ advances in the modeling​ of physical, biogeochemical and​‌ biological processes in the​​ ocean. It aims at​​​‌ setting up a modeling​ chain, integrating data and​‌ allowing to significantly increase​​ the number of scenarios​​​‌ (climate change, human activities)​ evaluated. The digital tools​‌ developed will also contribute​​ to a better science-society-policy​​​‌ interaction

10.4.2 Other Initiatives​

  • E. Blayo is co-advising​‌ the PhD thesis of​​ Valentin Bellemin-Laponnaz with IGE​​​‌ Lab, in the framework​ of the NASA-CNES working​‌ group on the SWOT​​ satellite.
  • MIAM (Multi-fIdelity Approach​​​‌ for climate Models): Institut​ des Mathématiques pour la​‌ Planète Terre, PI: Elise​​ Arnaud, Pierre Nabat (Météo-​​​‌ France).Collaboration with Météo France​ and Ecole Centrale Lyon​‌

11 Dissemination

11.1 Promoting​​ scientific activities

11.1.1 Scientific​​​‌ events: organisation

  • In 2025,​ the AIRSEA team has​‌ organised the SAMO conference​​ in Grenoble. SAMO is​​​‌ a cross-disciplinary conference, held​ every three years, related​‌ to the fields of​​ sensitivity analysis, design of​​​‌ experiments, model calibration and​ validation, structural reliability, uncertainty​‌ quantification, machine learning interpretability,​​ explainable AI, and related​​​‌ application areas (engineering, environment,​ agronomy, finance, etc.).
  • Since​‌ 2024, the AIRSEA team​​ has been organizing an​​​‌ annual workshop on the​ topic of Digital Twins.​‌ The two first editions​​ (2024-2025) were held at​​​‌ CIRM and brought together​ an international audience of​‌ mathematicians and computational scientists,​​ fostering interdisciplinary exchanges in​​​‌ this field. In 2026,​ this workshop will be​‌ organised at the Institut​​ d'Études Scientifiques of Cargèse.​​​‌
General chair, scientific chair​
  • Clémentine Prieur was the​‌ general chair of SAMO​​ 2025 conference.
Member of​​​‌ the organizing committees
  • Martin​ Schreiber was a co-organiser​‌ of “(EuroHPC) Workshop on​​ Dynamic Resources in HPC”,​​​‌ 25 – 29 Août​ 2025, Dresden, Germany
  • Martin​‌ Schreiber was a co-organiser​​ of “PDEs on the​​​‌ sphere workshop” 12 –​ 16 Mai 2025 in​‌ Sao Paulo, Brazil 0​​ participants
  • Martin Schreiber was​​ a principal organiser of​​​‌ the “Birds of feather:‌ Dynamic resources” at International‌​‌ Super Computing, 10 –​​ 13 Juin 2025, Hambourg,​​​‌ Germany

11.1.2 Scientific events:‌ selection

Member of the‌​‌ conference program committees
  • Clémentine​​ Prieur was a member​​​‌ of the conference program‌ committee of the SMAI‌​‌ conference.
  • Martin Schreiber was​​ a member of the​​​‌ conference program committee of‌ EuroMPI
  • Martin Schreiber was‌​‌ a member of the​​ conference program committee of​​​‌ ICCS 2025
  • Martin Schreiber‌ was a member of‌​‌ the conference program committee​​ of IWOCL 2025
  • Martin​​​‌ Schreiber was a member‌ of the conference program‌​‌ committee of Supercomputing (applications,​​ doctoral showcase, best paper​​​‌ award)

11.1.3 Journal

Member‌ of the editorial boards‌​‌
  • F. Lemarié is associate​​ editor of the Journal​​​‌ of Advances in Modeling‌ Earth Systems (JAMES)
  • Clémentine‌​‌ Prieur is associate editor​​ for SIAM/ASA Journal of​​​‌ Uncertainty Quantification journal.
  • Clémentine‌ Prieur is a member‌​‌ of the reading committee​​ of Annales Mathématiques Blaise​​​‌ Pascal.
  • M.Schreiber is associate‌ editor for “The International‌​‌ Journal of High Performance​​ Computing Applications”.

11.1.4 Invited​​​‌ talks

  • Clémentine Prieur was‌ invited to iMSi (Institute‌​‌ for Mathematical and Statistical​​ Innovation) to give a​​​‌ talk "Kernel Methods in‌ Uncertainty Quantification and Experimental‌​‌ Design", Chicago, USA, March​​ 31 - April 4,​​​‌ 2025.
  • Clémentine Prieur was‌ a Kirk Distinguished Visiting‌​‌ Fellow in the Isaac​​ Newton Institute for Mathematical​​​‌ Sciences, Cambridge. She participated‌ in the Programme "Representing,‌​‌ calibrating & leveraging prediction​​ uncertainty, from statistics to​​​‌ machine learning" and delivered‌ a lecture titled "On‌​‌ feasible set estimation with​​ Bayesian active learning" on​​​‌ the July 22, 2025.‌
  • E. Blayo was invited‌​‌ to give a 2-hour​​ lecture “Introduction to data​​​‌ assimilation’’ in the Workshop‌ on Uncertainty Quantification for‌​‌ Climate Science co-organized by​​ IMPT, RT UQ and​​​‌ GdR Défis théoriques pour‌ les sciences du climat‌​‌ (Paris, Nov. 2025)

11.1.5​​ Leadership within the scientific​​​‌ community

  • In 2022-2025, C.‌ Prieur was the president‌​‌ of SAMO group, international​​ research group on sensitivity​​​‌ analysis.
  • F. Lemarié is‌ a member of the‌​‌ international CLIVAR Ocean Model​​ Development Panel since Jan.​​​‌ 2024. CLIVAR (Climate and‌ Ocean: Variability, Predictability, and‌​‌ Change) is a core​​ project of the World​​​‌ Climate Research Programme (WCRP).‌
  • F. Lemarié is a‌​‌ member of the scientific​​ board of the GDR​​​‌ "Défis théorique pour les‌ sciences du climat" (since‌​‌ Dec. 2024)
  • F. Lemarié​​ is the coordinator of​​​‌ the national inter-agency program‌ SUN (computational sciences for‌​‌ Earth and Space sciences),​​ affiliated with CNRS-INSU. The​​​‌ program includes a call‌ for projects component as‌​‌ well as a broader​​ focus on scientific networking​​​‌ and training activities (since‌ may 2025).
  • M. Schreiber‌​‌ is a Co-chair of​​ the “Dynamic Resources for​​​‌ HPC” (DynResHPC) consortium

11.1.6‌ Scientific expertise

  • Clémentine Prieur‌​‌ is advisor to the​​ scientific council of IFPEN.​​​‌
  • E. Blayo is a‌ member of the scientific‌​‌ committee of IMPT (Institut​​ Mathématique pour la Planète​​​‌ Terre)
  • E. Blayo is‌ a member of the‌​‌ scientific committee of the​​ Labex Persyval-3
  • F. Lemarié​​​‌ is the co-leader with‌ Sybille Téchené (CNRS) and‌​‌ Mike Bell (UK Met​​​‌ Office) of the NEMO​ (www.nemo-ocean.eu) Working​‌ Group on numerical kernel​​ development.
  • F. Lemarié is​​​‌ a member of the​ CROCO (www.croco-ocean.org)​‌ Development Committee.
  • F. Lemarié​​ is a member of​​​‌ the CE56 scientific evaluation​ committee, Interfaces: mathematics, computational​‌ sciences - Earth system​​ and environmental sciences of​​​‌ the ANR (French National​ Research Agency)
  • Martin Schreiber​‌ is a member of​​ the OpenMP ARB (representing​​​‌ Inria).

11.1.7 Research administration​

  • E. Blayo is a​‌ deputy director of the​​ Jean Kuntzmann Lab.
  • F.​​​‌ Lemarié is the Inria​ local scientific correspondent for​‌ national calls for projects​​ (work in coordination with​​​‌ Inria contract managers to​ identify national project calls​‌ and the teams that​​ may be suited to​​​‌ respond to these calls.​ Since July 2020, as​‌ part of this mission,​​ I provide support to​​​‌ (1) analyze the objectives​ of project calls to​‌ assess their relevance. (2)​​ track trends and innovations​​​‌ in the relevant sector).​
  • Clémentine Prieur was a​‌ member of the jury​​ for the "Prix de​​​‌ thèse - LMBP -​ Université Clermont Auvergne" in​‌ 2025.
  • Clémentine Prieur was​​ a member of the​​​‌ jury for the Blaise​ Pascal Prize from the​‌ Académie des Sciences in​​ 2024 and 2025.
  • Clémentine​​​‌ Prieur is Vice President​ of the french society​‌ of statistics (SFdS) since​​ July 2024.
  • Clémentine Prieur​​​‌ is currently a member​ of the Executive and​‌ Scientific Committees of the​​ RT Quantification d’Incertitudes (RT2172​​​‌ funded by INSMI @​ CNRS) which she chaired​‌ during the period 2010-2017.​​
  • Clémentine Prieur is currently​​​‌ a member of the​ Scientific Committee of the​‌ RT Terre et Energies​​ (RT2166 funded by INSMI​​​‌ @ CNRS).
  • Clémentine Prieur​ is local correspondent in​‌ Grenoble for the Mathematical​​ Society of France (SMF).​​​‌
  • Clémentine Prieur was a​ member of the MSTIC​‌ pole council of UGA(nov.​​ 2020-oct. 2024).
  • Clémentine Prieur​​​‌ is responsible for the​ applied math specialty for​‌ doctoral school MSTII edmstii.univ-grenoble-alpes.fr​​
  • E. Arnaud is in​​​‌ charge of the parity​ diversity commission at Jean​‌ Kuntzmann Lab

11.2 Teaching​​ - Supervision - Juries​​​‌ - Educational and pedagogical​ outreach

  • Licence: E. Arnaud,​‌ Mathematics for engineers, 50h,​​ L2, UGA, France
  • Licence:​​​‌ E. Arnaud, Statistics, 20h,​ L2, UGA, France
  • Licence:​‌ E. Blayo, analysis and​​ algebra, 107h, L1, University​​​‌ Grenoble Alpes, France
  • Licence:​ C. Kazantsev, Mathématiques approfondies​‌ pour l'ingénieur, 36h, L2,​​ UGA, France
  • Licence: C.​​​‌ Kazantsev, Mathématiques pour les​ sciences de l'ingénieur, 36h,​‌ L2, UGA, France
  • Licence:​​ Martin Schreiber, Advanced Analysis​​​‌ & Algebra, L1, 69h,​ UGA, France
  • Master: E.​‌ Blayo, Partial Differential Equations,​​ 55h, M1, University Grenoble​​​‌ Alpes, France
  • Master: E.​ Arnaud, Critical thinking, 30h,​‌ M1, UGA, France
  • Master:​​ E. Arnaud, Supervision of​​​‌ student in apprenticeship, 30h,​ M2, UGA, France
  • Master:​‌ Martin Schreiber, High-Performance Computing,​​ M1, 31.1h, UGA, France​​​‌
  • Master: Martin Schreiber, Parallel​ Algorithms and Programming, M1,​‌ 11.25h, UGA, France
  • Master:​​ Martin Schreiber, Object oriented​​​‌ programming with C++, M1,​ 18h, UGA, France
  • Master:​‌ Martin Schreiber, Partial differential​​ equations, M1, 34.5h, UGA,​​​‌ France
  • E-learning: E. Arnaud​ is in charge of​‌ the pedagogic platform math@uga:​​ implementation of a collaborative​​ moodle platform to share​​​‌ pedagogical resources within teachers‌ and towards students.
  • E.‌​‌ Blayo is in charge​​ of the Ecole des​​​‌ Mathématiques Appliquées: organization and‌ coordination of pedagogical and‌​‌ administrative aspects related to​​ teaching for the applied​​​‌ maths department.

11.2.1 Supervision‌

  • PhD in progress: Angélique‌​‌ Saillet, Multi fidelity for​​ marine biogeochemical model, Octobre​​​‌ 2023, Eric Blayo and‌ Elise Arnaud.
  • PhD in‌​‌ progress: Exaucé Luweh Adjim​​ Ngarti, Deep learning for​​​‌ inverse problem in geophysics,‌ Université Grenoble-Alpes Avril 2023,‌​‌ E. Arnaud, L. Nicoletti​​ (Atos) and A. Vidard.​​​‌
  • PhD in progress: Lorenzo‌ Calzolari, Active learning with‌​‌ functional inputs: application to​​ wind turbine reliability design,​​​‌ Novembre 2024, C. Helbert‌ (Ecole Centrale Lyon), C.‌​‌ Prieur, promoted by M.​​ Munoz Zuniga, D. Sinoquet​​​‌ (IFPEN)
  • PhD in progress‌ : Jean-Baptise Seby, Multi‌​‌ fidelity for regional climate​​ models, October 2025, Eric​​​‌ Blayo and Elise Arnaud‌
  • PhD in progress :‌​‌ Mélanie Villain, Méthodes avancées​​ d’assimilation de données pour​​​‌ l’estimation des paramètres et‌ des états dans les‌​‌ modèles hydrologiques en contexte​​ montagneux, November 2025, Arthur​​​‌ Vidard and Elise Arnaud‌
  • PhD in progress: Hélène‌​‌ Hénon, Assimilation de données​​ variationnelles multi-fidélité pour les​​​‌ prévisions océaniques , Université‌ Grenoble-Alpes Octobre 2023, A.‌​‌ Vidard.
  • PhD in progress:​​ Doaa Akil, Placement optimal​​​‌ de capteurs pour des‌ équations aux dérivées partielles‌​‌ hyperboliques de Saint-Venant par​​ approche « Physics-Informed Machine​​​‌ Learning » : application‌ à la détection de‌​‌ tsunamis, October 2025, co-supervised​​ with D. Georges (Gipsa​​​‌ lab) and O. Millet‌ (Université de La Rochelle)‌​‌
  • PhD in progress: Mohamed​​ Doumbouya, Computational Bayesian optimal​​​‌ sensor placement for ocean‌ models, October 2024, supervised‌​‌ by A. Vidard and​​ O. Zahm.
  • PhD in​​​‌ progress: Gabriel Derrida, Design‌ of flexible and numerically-sound‌​‌ generalised vertical coordinates with​​ vertical ALE (V-ALE) algorithm​​​‌ for operational ocean forecasting.‌ October 2023, L. Debreu‌​‌ and F. Lemarié.
  • Defended​​ PhD: Adama Barry, Plans​​​‌ d’expériences pour la calibration‌ et la validation d’un‌​‌ simulateur numérique, June 2025,​​ supervised by F. Bachoc​​​‌ (Institut de Mathématiques de‌ Toulouse), C. Prieur, promoted‌​‌ by M. Munoz Zuniga​​ and S. Bouquet.
  • Defended​​​‌ PhD: Pierre Lozano, Coupling‌ hydrostatic and nonhydrostatic ocean‌​‌ circulation models. December 2025,​​ E. Blayo and L.​​​‌ Debreu
  • Defended PhD: Manolis‌ Perrot, Modeling Oceanic and‌​‌ Atmospheric Convection : Energy,​​ Uncertainties and Rotation 21​​​‌, April 2025, supervised‌ by E. Blayo and‌​‌ F. Lemarié.
  • Defended PhD:​​ Benjamin Zanger, Compositional surrogates​​​‌ for reduced order modeling‌ 24, supervised by‌​‌ M. Schreiber, O. Zahm​​ since 2022
  • Defended PhD:​​​‌ Katarina Radisic, Prise en‌ compte d'incertitudes externes dans‌​‌ l'estimation de paramètres d'un​​ modèle de transfert d'eau​​​‌ et de pesticides à‌ l'échelle du bassin versant‌​‌ 22, Université Grenoble-Alpes,​​ supervised by C. Lauvernet​​​‌ (Inrae) and A. Vidard,‌ defended in March 2025.‌​‌
  • Defended PhD: Romain Verdière,​​ Nonlinear dimension reduction for​​​‌ uncertainty quantification problems 23‌, supervised by C.‌​‌ Prieur and O. Zahm​​ since 2022
  • Defended PhD:​​​‌ Ri Wang, Apprentissage statistique‌ pour l’analyse de sensibilité‌​‌ globale avec entrées dépendantes,​​ supervised by C. Prieur​​​‌ and V. Maume-Deschamps (Université‌ Lyon 1) since 2021‌​‌
  • Internship: M. Aharmouch (co-encadrement​​​‌ à 50 % avec​ C. Helbert, Ecole Centrale​‌ de Lyon), M2 internship,​​ Active learning for Gaussian​​​‌ processes with functional inputs:​ application to wind turbine​‌ reliability design, C. Helbert,​​ M. Munoz Zuniga, C.​​​‌ Prieur and D. Sinoquet.​
  • Internship: M. Villain. Advanced​‌ data assimilation methods for​​ estimating parameters and states​​​‌ in hydrological models in​ mountainous contexts. M2 internship,​‌ supervised by Arthur Vidard​​ and Elise Arnaud

11.2.2​​​‌ Juries

  • F. Lemarié:
    • Dec​ 11, 2025 — PhD​‌ thesis of Adrien Marcel,​​ Université Toulouse III —​​​‌ Paul Sabatier, (reviewer​)
  • M. Schreiber:
    • 2025​‌ — PhD thesis of​​ Arsène Marzorati, l'INSA Lyon,​​​‌ (reviewer)
    • July​ 2, 2025 — PhD​‌ thesis of Abdessalam BENHARI,​​ UGA, (jury member​​​‌)
  • A. Vidard:
    • February​ 20, 2025 — PhD​‌ thesis of Olivier Goux,​​ ISAE Supaero, (jury​​​‌ member)
    • June 30,​ 2025 — PhD thesis​‌ of Djahou Norbert Tognon,​​ Sorbonne University, (reviewer​​​‌)
  • E. Blayo:
    • May​ 7, 2025 — PhD​‌ thesis of Jacopo Iollo​​ (president)
    • Oct​​​‌ 14, 2025 — PhD​ thesis of Jean-Paul Travert​‌ (reviewer)
    • Nov​​ 18, 2025 — Habilitation​​​‌ thesis of Florian Lemarié​ (president)
    • Dec​‌ 9, 2025 — PhD​​ thesis of Arthur Grange​​​‌ (president)
  • C.​ Prieur:
    • 27 nov. 2025​‌ thèse de Mohamed Bahi​​ Yahiaoui, Université Grenoble Alpes​​​‌ (examinatrice)
    • 22​ oct. 2025 thèse de​‌ Benjamin Zanger, Université Grenoble​​ Alpes (présidente)​​​‌
    • 25 sept. 2025 thèse​ de Marine Dumon, Université​‌ Gustave Eiffel (rapportrice​​)
    • 15 sept. 2025​​​‌ thèse de Romain Ait​ Abdelmalek-Lomenech, CentraleSupélec (rapportrice​‌)
    • 2 juin 2025​​ thèse de Justin Reverdi,​​​‌ Université de Toulouse (​présidente)
    • 24 mars​‌ 2025 thèse de Katarina​​ Radisik, Université Grenoble Alpes​​​‌ (présidente)
    • 12​ déc. 2025 membre du​‌ jury d'HDR de J.​​ Chevallier, Université Grenoble Alpes​​​‌ (présidente)
    • 4​ juin 2025 membre du​‌ jury d'HDR de J.​​ Garnier, Université Savoie-Mont-Blanc (​​​‌examinatrice)
    • 2025-... Membre​ du jury du prix​‌ Blaise Pascal, décerné chaque​​ année par l'Académie des​​​‌ Sciences, après consultation de​ la SMAI et du​‌ groupe SMAI-GAMNI.

11.3 Popularization​​

11.3.1 Productions (articles, videos,​​​‌ podcasts, serious games, ...)​

  • Ch. Kazantsev and E.​‌ Blayo are strongly involved​​ in the creation and​​​‌ dissemination of pedagogic suitcases​ with mathematical activities designed​‌ for primary and secondary​​ schools, as well as​​​‌ an escape game. These​ actions are led in​‌ the context of the​​ association La Grange des​​​‌ Maths.
  • E. Blayo and​ A. Vidard have produced​‌ a series of pedagogical​​ videos on numerical ocean​​​‌ modeling, in collaboration with​ L’Esprit Sorcier TV, available​‌ here).

11.3.2 Participation​​ in Live events

  • E.​​​‌ Blayo gave several outreach​ talks, in particular for​‌ high school students, and​​ for more general audiences.​​​‌

11.3.3 Others science outreach​ relevant activities

  • E. Blayo​‌ is in charge of​​ the project Terra Numerica​​​‌ Grenoble. This project​ brings together numerous institutional​‌ partners (Inria, UGA, Territoire​​ de Sciences, etc.) and​​​‌ associations (La Grange des​ Maths, Info sans Ordi,​‌ Aconit, etc.). It aims​​ to open two venues​​ (La Casemate in Grenoble​​​‌ and a space on‌ the university campus) dedicated‌​‌ to popularizing mathematics and​​ computer sciences within the​​​‌ next two years. In‌ addition, a program offering‌​‌ a range of activities​​ (educational kits, exhibitions, escape​​​‌ games, conferences, etc.) in‌ a network of partner‌​‌ venues (schools, colleges, high​​ schools, media libraries, third​​​‌ places, etc.) across the‌ region will be developed.‌​‌

12 Scientific production

12.1​​ Major publications

  • 1 article​​​‌V.Valentina Schüller,‌ F.Florian Lemarié,‌​‌ P.Philipp Birken and​​ E.Eric Blayo.​​​‌ Quantifying coupling errors in‌ atmosphere-ocean-sea ice models: A‌​‌ study of iterative and​​ non-iterative approaches in the​​​‌ EC-Earth AOSCM.Geoscientific‌ Model Development1822‌​‌November 2025, 9167-9187​​HALDOIback to​​​‌ text

12.2 Publications of‌ the year

International journals‌​‌

International peer-reviewed​ conferences

  • 15 inproceedingsD.​‌Dominik Huber, S.​​Sergio Iserte, M.​​​‌Martin Schreiber, A.​ J.Antonio J. Peña​‌ and M.Martin Schulz​​. Bridging the Gap​​​‌ Between Genericity and Programmability​ of Dynamic Resources in​‌ HPC.ISC High​​ Performance 2025 - 40th​​​‌ ISC High Performance International​ ConferenceHamburg, Germany2025​‌, 1-11HALback​​ to text

Conferences without​​​‌ proceedings

Doctoral dissertations and habilitation​​ theses

Reports & preprints

Software

12.3 Cited publications

  • 38​​ unpublishedA.Adama Barry​​​‌, F.François Bachoc​, S.Sarah Bouquet​‌, M. M.Miguel​​ Munoz Munoz Zuniga and​​​‌ C.Clémentine Prieur.​ Design of experiments for​‌ computer code calibration.​​June 2024, working​​​‌ paper or preprintHAL​back to text
  • 39​‌ unpublishedT.Tiangang Cui​​, X.Xin Tong​​​‌ and O.Olivier Zahm​. Optimal Riemannian metric​‌ for Poincaré inequalities and​​ how to ideally precondition​​​‌ Langevin dymanics.2024​, working paper or​‌ preprintHALback to​​ text
  • 40 unpublishedS.​​​‌Sébastien Da Veiga,​ F.Fabrice Gamboa,​‌ A.Agnès Lagnoux,​​ T.Thierry Klein and​​​‌ C.Clémentine Prieur.​ Efficient estimation of Sobol'​‌ indices of any order​​ from a single input/output​​​‌ sample.2024,​ working paper or preprint​‌HALback to text​​
  • 41 unpublishedP.Philip​​​‌ Freese, S.Sebastian​ Götschel, T.Thibaut​‌ Lunet, D.Daniel​​ Ruprecht and M.Martin​​​‌ Schreiber. Parallel performance​ of shared memory parallel​‌ spectral deferred corrections.​​2024, 14 pages,​​​‌ 4 figuresHALback​ to text
  • 42 article​‌M.Markus Gross,​​ H.Hui Wan,​​ P. J.Philip J.​​​‌ Rasch, P. M.‌Peter M. Caldwell,‌​‌ D. L.David L.​​ Williamson, D.Daniel​​​‌ Klocke, C.Christiane‌ Jablonowski, D. R.‌​‌Diana R. Thatcher,​​ N.Nigel Wood,​​​‌ M.Mike Cullen,‌ B.Bob Beare,‌​‌ M.Martin Willett,​​ F.Florian Lemarié,​​​‌ E.Eric Blayo,‌ S.Sylvie Malardel,‌​‌ P.Piet Termonia,​​ A.Almut Gassmann,​​​‌ P. H.Peter H.‌ Lauritzen, H.Hans‌​‌ Johansen, C. M.​​Colin M. Zarzycki,​​​‌ K.Koichi Sakaguchi and‌ R.Ruby Leung.‌​‌ Physics--Dynamics Coupling in Weather,​​ Climate, and Earth System​​​‌ Models: Challenges and Recent‌ Progress.Monthly Weather‌​‌ Review14611November​​ 2018, 3505--3544HAL​​​‌DOIback to text‌
  • 43 unpublishedD.Dominik‌​‌ Huber, M.Martin​​ Schreiber, M.Martin​​​‌ Schulz, H.Howard‌ Pritchard and D.Daniel‌​‌ Holmes. Design Principles​​ of Dynamic Resource Management​​​‌ for High-Performance Parallel Programming‌ Models.2024,‌​‌ working paper or preprint​​HALback to text​​​‌
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  • 45‌ unpublishedF.Florian Lemarié‌​‌. Formulation of a​​ three-dimensional atmospheric boundary layer​​​‌ model for an improved‌ representation of air-sea interactions‌​‌ in eddying oceanic models​​.March 2024,​​​‌ working paper or preprint‌HALback to text‌​‌
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  • 49​​​‌ techreportO.Olivier Marti​, S.Sébastien Nguyen​‌, P.Pascale Braconnot​​, S.Sophie Valcke​​​‌, F.Florian Lemarié​ and E.Eric Blayo​‌. Diagnosing the ocean-atmosphere​​ coupling schemes by using​​​‌ a mathematically consistent Schwarz​ iterative method.Research​‌ activities in Earth system​​ modelling. Working Group on​​​‌ Numerical Experimentation. Report No.​ 51. WCRP Report No.4/2021.​‌ WMO, GenevaJuly 2021​​HALback to text​​​‌
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