2025Activity report​​Project-TeamANGE

Multilayer approach

As for​​​‌ the first shallow water​ assumption, multi-layer systems were​‌ proposed to describe the​​ flow as a superposition​​​‌ of Saint-Venant type systems​ 31, 34,​‌ 35. Even if​​ this approach has provided​​​‌ interesting results, layers are​ considered separate and non-miscible​‌ fluids, which implies strong​​ limitations. That is why​​​‌ we proposed a slightly​ different approach 32,​‌ 33 based on a​​ Galerkin type decomposition along​​​‌ the vertical axis of​ all variables and leading,​‌ both for the model​​ and its discretisation, to​​​‌ more accurate results.

A​ kinetic representation of our​‌ multilayer model allows to​​ derive robust numerical schemes​​ endowed with crucial properties​​​‌ such as: consistency, conservativity,‌ positivity, preservation of equilibria,‌​‌ ...  It is one​​ of the major achievements​​​‌ of the team but‌ it needs to be‌​‌ analyzed and extended in​​ several directions namely:

• The​​​‌ convergence of the multilayer‌ system towards the hydrostatic‌​‌ Euler system as the​​ number of layers goes​​​‌ to infinity is a‌ critical point. It is‌​‌ not fully satisfactory to​​ have only formal estimates​​​‌ of the convergence and‌ sharp estimates would provide‌​‌ an optimal number of​​ layers.
• The introduction of​​​‌ several source terms due‌ for instance to the‌​‌ Coriolis force or extra​​ terms from changes of​​​‌ coordinates seems necessary. Their‌ inclusion should lead to‌​‌ substantial modifications of the​​ numerical scheme.
• Its hyperbolicity​​​‌ has not yet been‌ proven and conversely the‌​‌ possible loss of hyperbolicity​​ cannot be characterised. Similarly,​​​‌ the hyperbolic feature is‌ essential in the propagation‌​‌ and generation of waves.​​

Non-hydrostatic models

The hydrostatic​​​‌ assumption consists in neglecting‌ the vertical acceleration of‌​‌ the fluid. It is​​ considered valid for a​​​‌ large class of geophysical‌ flows but is restrictive‌​‌ in various situations where​​ the dispersive effects (like​​​‌ wave propagation) cannot be‌ neglected. For instance, when‌​‌ a wave reaches the​​ coast, bathymetry variations give​​​‌ a vertical acceleration to‌ the fluid that strongly‌​‌ modifies the wave characteristics​​ and especially its height.​​​‌

Processing an asymptotic expansion‌ (w.r.t. the aspect ratio‌​‌ for shallow water flows)​​ into the Navier-Stokes equations,​​​‌ we obtain at the‌ leading order the Saint-Venant‌​‌ system. Going one step​​ further leads to a​​​‌ vertically averaged version of‌ the Euler/Navier-Stokes equations involving‌​‌ some non-hydrostatic terms. This​​ model has several advantages:​​​‌

• it admits an energy‌ balance law (that is‌​‌ not the case for​​ most dispersive models available​​​‌ in the literature),
• it‌ reduces to the Saint-Venant‌​‌ system when the non-hydrostatic​​ pressure term vanishes,
• it​​​‌ consists in a set‌ of conservation laws with‌​‌ source terms,
• it does​​ not contain high order​​​‌ derivatives.

Multi-physics modelling

The‌ coupling of hydrodynamic equations‌​‌ with other equations in​​ order to model interactions​​​‌ between complex systems represents‌ an important part of‌​‌ the team research. More​​ precisely, three multi-physics systems​​​‌ are investigated. More details‌ about the industrial impact‌​‌ of these studies are​​ presented in the following​​​‌ section.

• To estimate the‌ risk for infrastructures in‌​‌ coastal zones or close​​ to a river, the​​​‌ resolution of the shallow‌ water equations with moving‌​‌ bathymetry is necessary. The​​ first step consisted in​​​‌ the study of an‌ additional equation largely used‌​‌ in engineering science: The​​ Exner equation. The analysis​​​‌ enabled to exhibit drawbacks‌ of the coupled model‌​‌ such as the lack​​ of energy conservation or​​​‌ the strong variations of‌ the solution from small‌​‌ perturbations. A new formulation​​ is proposed to avoid​​​‌ these drawbacks. The new‌ model consists in a‌​‌ coupling between conservation laws​​ and an elliptic equation,​​​‌ like the Euler/Poisson system,‌ suggesting to use well-known‌​‌ strategies for the analysis​​ and the numerical resolution.​​​‌ In addition, the new‌ formulation is derived from‌​‌ classical complex rheology models​​​‌ and allowed physical phenomena​ like threshold laws.
• Interaction​‌ between flows and floating​​ structures is the challenge​​​‌ at the scale of​ the shallow water equations.​‌ This study requires a​​ better understanding of the​​​‌ energy exchanges between the​ flow and the structure.​‌ The mathematical model of​​ floating structures is very​​​‌ hard to solve numerically​ due to the non-penetration​‌ condition at the interface​​ between the flow and​​​‌ the structure. It leads​ to infinite potential wave​‌ speeds that could not​​ be solved with classical​​​‌ free surface numerical schemes.​ A relaxation model was​‌ derived to overcome this​​ difficulty. It represents the​​​‌ interaction with the floating​ structure with a free​‌ surface model-type.
• If the​​ interactions between hydrodynamics and​​​‌ biology phenomena are known​ through laboratory experiments, it​‌ is more difficult to​​ predict the evolution, especially​​​‌ for the biological quantities,​ in a real and​‌ heterogeneous system. The objective​​ is to model and​​​‌ reproduce the hydrodynamics modifications​ due to forcing term​‌ variations (in time and​​ space). We are typically​​​‌ interested in phenomena such​ as eutrophication, development of​‌ harmful bacteria (cyanobacteria) and​​ upwelling phenomena.

Data assimilation​​​‌ and inverse modelling

In​ environmental applications, the most​‌ accurate numerical models remain​​ subject to uncertainties that​​​‌ originate from their parameters​ and shortcomings in their​‌ physical formulations. It is​​ often desirable to quantify​​​‌ the resulting uncertainties in​ a model forecast. The​‌ propagation of the uncertainties​​ may require the generation​​​‌ of ensembles of simulations​ that ideally sample from​‌ the probability density function​​ of the forecast variables.​​​‌ Classical approaches rely on​ multiple models and on​‌ Monte Carlo simulations. The​​ applied perturbations need to​​​‌ be calibrated for the​ ensemble of simulations to​‌ properly sample the uncertainties.​​ Calibrations involve ensemble scores​​​‌ that compare the consistency​ between the ensemble simulations​‌ and the observational data.​​ The computational requirements are​​​‌ so high that designing​ fast surrogate models or​‌ metamodels is often required.​​

In order to reduce​​​‌ the uncertainties, the fixed​ or mobile observations of​‌ various origins and accuracies​​ can be merged with​​​‌ the simulation results. The​ uncertainties in the observations​‌ and their representativeness also​​ need to be quantified​​​‌ in the process. The​ assimilation strategy can be​‌ formulated in terms of​​ state estimation or parameter​​​‌ estimation (also called inverse​ modelling). Different algorithms are​‌ employed for static and​​ dynamic models, for analyses​​​‌ and forecasts. A challenging​ question lies in the​‌ optimization of the observational​​ network for the assimilation​​​‌ to be the most​ efficient at a given​‌ observational cost.

Non-hydrostatic scheme

The​​​‌ main challenge in the​ study of the non-hydrostatic​‌ model is to design​​ a robust and efficient​​​‌ numerical scheme endowed with​ properties such as: positivity,​‌ wet/dry interfaces treatment, consistency.​​ It must be noticed​​​‌ that even if the​ non-hydrostatic model looks like​‌ an extension of the​​ Saint-Venant system, most of​​​‌ the known techniques used​ in the hydrostatic case​‌ are not efficient as​​ we recover strong difficulties​​​‌ encountered in incompressible fluid​ mechanics due to the​‌ extra pressure term. These​​ difficulties are reinforced by​​ the absence of viscous/dissipative​​​‌ terms.

Space decomposition and‌ adaptive scheme

In the‌​‌ quest for a better​​ balance between accuracy and​​​‌ efficiency, a strategy consists‌ in the adaptation of‌​‌ models. Indeed, the systems​​ of partial differential equations​​​‌ we consider result from‌ a hierarchy of simplifying‌​‌ assumptions. However, some of​​ these hypotheses may turn​​​‌ out to be irrelevant‌ locally. The adaptation of‌​‌ models thus consists in​​ determining areas where a​​​‌ simplified model (e.g.‌ shallow water type) is‌​‌ valid and where it​​ is not. In the​​​‌ latter case, we may‌ go back to the‌​‌ “parent” model (e.g.​​ Euler) in the corresponding​​​‌ area. This implies to‌ know how to handle‌​‌ the coupling between the​​ aforementioned models from both​​​‌ theoretical and numerical points‌ of view. In particular,‌​‌ the numerical treatment of​​ transmission conditions is a​​​‌ key point. It requires‌ the estimation of characteristic‌​‌ values (Riemann invariant) which​​ have to be determined​​​‌ according to the regime‌ (torrential or fluvial).

Asymptotic-Preserving‌​‌ scheme for source terms​​

Hydrodynamic models comprise advection​​​‌ and sources terms. The‌ conservation of the balance‌​‌ between source terms, typically​​ viscosity and friction, has​​​‌ a significant impact since‌ the overall flow is‌​‌ generally a perturbation around​​ an equilibrium. The design​​​‌ of numerical schemes able‌ to preserve such balances‌​‌ is a challenge from​​ both theoretical and industrial​​​‌ points of view. The‌ concept of Asymptotic-Preserving (AP)‌​‌ methods is of great​​ interest in order to​​​‌ overcome these issues.

Another‌ difficulty occurs when a‌​‌ term, typically related to​​ the pressure, becomes very​​​‌ large compared to the‌ order of magnitude of‌​‌ the velocity. At this​​ regime, namely the so-called​​​‌ low Froude (shallow water)‌ or low Mach (Euler)‌​‌ regimes, the difference between​​ the speed of the​​​‌ gravity waves and the‌ physical velocity makes classical‌​‌ numerical schemes inefficient: firstly​​ because of the error​​​‌ of truncation which is‌ inversely proportional to the‌​‌ small parameters, secondly because​​ of the time step​​​‌ governed by the largest‌ speed of the gravity‌​‌ wave. AP methods made​​ a breakthrough in the​​​‌ numerical resolution of asymptotic‌ perturbations of partial-differential equations‌​‌ concerning the first point.​​ The second one can​​​‌ be fixed using partially‌ implicit scheme.

Multi-physics models‌​‌

Coupling problems also arise​​ within the fluid when​​​‌ it contains pollutants, density‌ variations or biological species.‌​‌ For most situations, the​​ interactions are small enough​​​‌ to use a splitting‌ strategy and the classical‌​‌ numerical scheme for each​​ sub-model, whether it be​​​‌ hydrodynamic or non-hydrodynamic.

The‌ sediment transport raises interesting‌​‌ issues from a numerical​​ aspect. This is an​​​‌ example of coupling between‌ the flow and another‌​‌ phenomenon, namely the deformation​​ of the bottom of​​​‌ the basin that can‌ be carried out either‌​‌ by bed load where​​ the sediment has its​​​‌ own velocity or suspended‌ load in which the‌​‌ particles are mostly driven​​ by the flow. This​​​‌ phenomenon involves different time‌ scales and nonlinear retroactions;‌​‌ hence the need for​​ accurate mechanical models and​​​‌ very robust numerical methods.‌ In collaboration with industrial‌​‌ partners (EDF–LNHE), the team​​​‌ already works on the​ improvement of numerical methods​‌ for existing (mostly empirical)​​ models but our aim​​​‌ is also to propose​ new (quite) simple models​‌ that contain important features​​ and satisfy some basic​​​‌ mechanical requirements. The extension​ of our 3D models​‌ to the transport of​​ weighted particles can also​​​‌ be here of great​ interest.

Optimisation

Numerical simulations​‌ are a very useful​​ tool for the design​​​‌ of new processes, for​ instance in renewable energy​‌ or water decontamination. The​​ optimisation of the process​​​‌ according to a well-defined​ objective such as the​‌ production of energy or​​ the evaluation of a​​​‌ pollutant concentration is the​ logical upcoming challenge in​‌ order to propose competitive​​ solutions in industrial context.​​​‌ First of all, the​ set of parameters that​‌ have a significant impact​​ on the result and​​​‌ on which we can​ act in practice is​‌ identified. Then the optimal​​ parameters can be obtained​​​‌ using the numerical codes​ produced by the team​‌ to estimate the performance​​ for a given set​​​‌ of parameters with an​ additional loop such as​‌ gradient descent or Monte​​ Carlo method. The optimisation​​​‌ is used in practice​ to determine the best​‌ profile for turbine pales,​​ the best location for​​​‌ water turbine implantation, in​ particular for a farm.​‌

7.1.1 Freshkiss

• Name:‌
  FREe Surface Hydrodynamics using‌​‌ KInetic SchemeS
• Keywords:
  Finite​​ volume methods, Hydrostatic Navier-Stokes​​​‌ equations, Free surface flows‌
• Functional Description:
  Freshkiss3D is‌​‌ a numerical code solving​​ the 3D hydrostatic and​​​‌ incompressible Navier-Stokes equations with‌ variable density.
• Contact:
  Jacques‌​‌ Sainte Marie
• Participants:
  Fabien​​ Souillé, Emmanuel Audusse, Jacques​​​‌ Sainte Marie, Marie-Odile Bristeau‌
• Partners:
  UPMC, CEREMA

7.1.2‌​‌ TSUNAMATHS

• Keywords:
  Modeling, Tsunamis​​
• Functional Description:
  Tsunamaths is​​​‌ an educational platform aiming‌ at simulating historical tsunamis.‌​‌ Real data and mathematical​​ explanations are provided to​​​‌ enable people to better‌ understand the overall process‌​‌ of tsunamis.
• URL:
  http://­tsunamath.­paris.­inria.­fr/​​
• Contact:
  Jacques Sainte Marie​​​‌
• Participants:
  Emmanuel Audusse, Jacques‌ Sainte Marie, Raouf Hamouda‌​‌

7.1.3 Freshkiss3D

• Keywords:
  Python,​​ Cython, Navier-Stokes
• Functional Description:​​​‌
  Tool for the numerical‌ solution of free surface‌​‌ Navier-Stokes equations
• Publication:
  hal-01393147​​
• Contact:
  Jacques Sainte Marie​​​‌
• Participants:
  Cedric Doucet, Apolline‌ El Baz, Jacques Sainte‌​‌ Marie
• Partner:
  UPMC

8.1.1‌ A comprehensive list of‌​‌ stationary solutions of shallow​​ water models

Participants: Nina​​​‌ Aguillon, Emmanuel Audusse‌.

The shallow water‌​‌ equation of Barré de​​ Saint-Venant describes the evolution​​​‌ of the water height‌ and of the horizontal‌​‌ velocity of a column​​​‌ of water. It is​ valid when the horizontal​‌ length scale of the​​ flow is much greater​​​‌ than its vertical length​ scale. This model is​‌ widely employed to model​​ rivers and lake. It​​​‌ can be enriched to​ take into account a​‌ shear velocity along the​​ vertical. In 21,​​​‌ we classify all the​ stationary solutions of the​‌ shallow water equation with​​ a shear velocity on​​​‌ a bounded domain. Boundary​ conditions are fixed at​‌ the inlet and the​​ outlet, and their number​​​‌ depends on whether the​ regime is supercritical (Froude​‌ number larger than 1)​​ or subcritical. The stationary​​​‌ solutions consist of a​ succession of regular parts​‌ where the momentum and​​ hydraulic head are constant,​​​‌ separated by discontinuity (also​ called hydraulic jumps) through​‌ which the hydraulic head​​ decreases but the momentum​​​‌ and momentum flux are​ constant. We exhibit the​‌ form of the stationary​​ solution and its conditions​​​‌ of existence for any​ set of boundary conditions​‌ on monotonic, bumped shaped​​ and hollow shaped topographies.​​​‌ We find that in​ some cases and for​‌ supercritical flow at the​​ inlet, two different stationary​​​‌ solutions can fulfilled the​ same set of boundary​‌ conditions. The solutions with​​ shocks on increasing topography​​​‌ are sparsely documented and​ seem to be instable.​‌ Eventually we consider a​​ topography made of a​​​‌ succession of N decreasing​ bumps and prove in​‌ the subcritical case that​​ up to $2^{\mathrm{N‌}-1}$ solutions with​ discontinuities on decreasing topography​‌ only may coexist.

8.1.2​​ Energy stable and linearly​​​‌ well-balanced numerical schemes for​ the non-linear Shallow Water​‌ equations with Coriolis force​​

Participants: Emmanuel Audusse.​​​‌

In 6, we​ analyse a class of​‌ energy-stable and linearly well-balanced​​ numerical schemes dedicated to​​​‌ the nonlinear Shallow Water​ equations with Coriolis force.​‌ The proposed algorithms rely​​ on colocated finite-difference approx-​​​‌ imations formulated on cartesian​ geometries. They involve appropriate​‌ diffusion terms in the​​ numerical fluxes, expressed as​​​‌ discrete versions of the​ linear geostrophic equilibrium. We​‌ show that the resulting​​ methods ensure semi-discrete energy​​​‌ estimates. Among the proposed​ algorithms a colocated finite-volume​‌ scheme is described. Numerical​​ results show a very​​​‌ clear improvement around the​ nonlinear geostrophic equilibrium when​‌ compared to those of​​ classic Godunov-type schemes.

8.1.3​​​‌ Hyperbolicity of a semi-Lagrangian​ formulation of the hydrostatic​‌ free-surface Euler system

Participants:​​ Jacques Sainte-Marie, Bernard​​​‌ Di Martino, Edwige​ Godlewski, Julien Guillod​‌.

In 9,​​ using a semi-Lagrangian change​​​‌ of coordinates, the hydrostatic​ Euler equations describing free-surface​‌ sheared flows is rewritten​​ as a system of​​​‌ quasilinear equations, where stability​ conditions can be determined​‌ by the analysis of​​ its hyperbolic structure. The​​​‌ system one obtains can​ be written as a​‌ quasi linear system in​​ time and horizontal variables​​​‌ and involves no more​ vertical derivatives. However, the​‌ coefficients in front of​​ the horizontal derivatives include​​​‌ an integral operator acting​ on the new vertical​‌ variable. The spectrum of​​ these operators is studied​​​‌ in detail, in particular​ it includes a continuous​‌ part. Riemann invariants are​​ then determined as conserved​​ quantities along the characteristic​​​‌ curves. Examples of solutions‌ are provided, in particular‌​‌ stationary solutions and solutions​​ blowing-up in finite time.​​​‌ Eventually, we propose an‌ exact multilayer P0-discretization, which‌​‌ could be used to​​ solve numerically this semi-Lagrangian​​​‌ system, and analyze the‌ eigenvalues of the corresponding‌​‌ discretized operator to investigate​​ the hyperbolic nature of​​​‌ the approximated system.

8.1.4‌ Implicit kinetic schemes for‌​‌ the Saint-Venant system

Participants:​​ Jacques Sainte-Marie.

Explicit​​​‌ (in time) kinetic schemes‌ applied to the nonlinear‌​‌ shallow water equations have​​ been extensively studied in​​​‌ the past. The novelty‌ of 10 is to‌​‌ investigate an implicit version​​ of such methods in​​​‌ order to improve their‌ stability properties. In the‌​‌ case of a flat​​ bathymetry we obtain a​​​‌ fully implicit kinetic solver‌ satisfying a discrete entropy‌​‌ inequality and keeping the​​ water height non negative​​​‌ without any restriction on‌ the time step. Remarkably,‌​‌ a simplified version of​​ this nonlinear implicit scheme​​​‌ allows to express the‌ update explicitly which we‌​‌ implement in practice. The​​ case of varying bottoms​​​‌ is then dealt with‌ through an iterative solver‌​‌ combined with the hydrostatic​​ reconstruction technique. We show​​​‌ that this scheme preserves‌ the water height non-negativity‌​‌ under a CFL condition​​ and satisfies a discrete​​​‌ entropy inequality without error‌ term, which is an‌​‌ improvement over its explicit​​ version. An extension of​​​‌ the implicit and iterative‌ methods to the two‌​‌ dimensional case is also​​ discussed. Finally we perform​​​‌ some numerical validations underlining‌ the advantages and the‌​‌ computational cost of our​​ strategy.

8.1.5 Unconditionally stable​​​‌ numerical scheme for the‌ 2D transport equation

Participants:‌​‌ Yohan Penel.

The​​ main goal of 11​​​‌ is to extend the‌ numerical scheme for the‌​‌ transport equation described in​​ previous works [Penel, 2012;​​​‌ Bernard et al., 2014]‌ from one to two‌​‌ dimensional problems. It is​​ based on the method​​​‌ of characteristics, which consists‌ in solving two ordinary‌​‌ dierential equations rather than​​ a partial dierential equation.​​​‌ Our scheme uses an‌ adaptive 6-point stencil in‌​‌ order to reach second-order​​ accuracy whenever it is​​​‌ possible, and preserves some‌ essential physical properties of‌​‌ the equation, such as​​ the maximum principle. The​​​‌ resulting scheme is proved‌ to be unconditionally stable‌​‌ and to reach second-order​​ accuracy. We show numerical​​​‌ examples with comparisons to‌ the well known Essentially‌​‌ Non-Oscillatory (ENO) scheme [Shu,​​ 1998], in order to​​​‌ illustrate the good properties‌ of our scheme (order‌​‌ of convergence, unconditional stability,​​ accuracy). Using a Gaussian​​​‌ initial condition, several test‌ cases are considered, using‌​‌ a constant or a​​ rotating velocity eld, taking​​​‌ into account or not‌ variable source terms. Also,‌​‌ a test is given​​ that shows the possibility​​​‌ of applying the scheme‌ in more realistic fluid‌​‌ mechanics case.

8.1.6 Barotropic-Baroclinic​​ Splitting for Multilayer Shallow​​​‌ Water Models with Exchanges‌

Participants: Jacques Sainte-Marie,‌​‌ Nina Aguillon.

The​​ paper 22 presents the​​​‌ numerical analysis of a‌ barotropic-baroclinic splitting in a‌​‌ nonlinear multilayer framework with​​ exchanges between the layers​​​‌ in terrain-following coordinates. The‌ splitting is formulated as‌​‌ an exact operator splitting.​​​‌ The barotropic step handles​ free surface evolution and​‌ depth-averaged velocity via a​​ well-balanced one-layer model, while​​​‌ the baroclinic step manages​ vertical exchanges between layers​‌ and adjusts velocities to​​ their mean values. We​​​‌ show that the barotropic-baroclinic​ splitting preserves total energy​‌ conservation and meets both​​ a discrete maximum principle​​​‌ and a discrete entropy​ inequality. Several numerical experiments​‌ are presented showing the​​ gain in computational cost,​​​‌ particularly in low Froude​ simulations, and the benefits​‌ of using well-balancing strategies​​ for the barotropic step.​​​‌

8.1.7 Topography optimization for​ enhancing microalgal growth in​‌ raceway ponds

Participants: Jacques​​ Sainte-Marie, Julien Salomon​​​‌.

Modelling the evolution​ process for the growth​‌ of microalgae in an​​ artificial pond is a​​​‌ huge challenge, given the​ complex interaction between hydrodynamics​‌ and biological processes occurring​​ across various timescales. In​​​‌ 7, we consider​ a raceway, i.e., an​‌ oval pond where the​​ water is set in​​​‌ motion by a paddle​ wheel. Our aim is​‌ to investigate theoretically and​​ numerically the impact of​​​‌ bottom topography in such​ raceway ponds on microalgae​‌ growth. To achieve this​​ goal, we consider a​​​‌ biological model based on​ the Han model, coupled​‌ with the Saint–Venant systems​​ that model the fluid.​​​‌ We then formulate an​ optimization problem, for which​‌ we apply the weak​​ maximum principle to characterize​​​‌ optimal topographies that maximize​ biomass production over one​‌ lap of the raceway​​ pond or multiple laps​​​‌ with a paddle wheel.​ In contrast to a​‌ widespread belief in the​​ field of microalgae, we​​​‌ show that a flat​ topography in a periodic​‌ regime satisfies the necessary​​ optimality condition, and observe​​​‌ in the numerical experiments​ that the flat topography​‌ is actually optimal in​​ this case. However, non-trivial​​​‌ topographies may be more​ advantageous in alternative scenarios,​‌ such as when considering​​ the effects of mixing​​​‌ devices within the model.​ This study sheds light​‌ on the intricate relationship​​ between bottom topography, fluid​​​‌ dynamics, and microalgae growth​ in raceway ponds, offering​‌ valuable insights into optimizing​​ biomass production.

8.2.1 A linear​ model of separation for​‌ western boundary currents with​​ bathymetry

Participants: Anne-Laure Dalibard​​​‌, Corentin Gentil.​

This paper 24 is​‌ devoted to the asymptotic​​ analysis of strongly rotating​​​‌ and stratified fluids, under​ a $\beta$-plane approximation,​‌ and within a three-dimensional​​ spatial domain with strong​​​‌ topography. Our purpose is​ to propose a linear​‌ idealized model, which is​​ able to capture one​​​‌ of the key features​ of western boundary currents,​‌ in spite of its​​ simplicity: the separation of​​​‌ the currents from the​ coast. Our simplified framework​‌ allows us to perform​​ explicit computations, and to​​​‌ highlight the intricate links​ between rotation, stratification and​‌ bathymetry. In fact, we​​ are able to construct​​​‌ approximate solutions at any​ order for our system,​‌ and to justify their​​ validity. Each term in​​​‌ the asymptotic expansion is​ the sum of an​‌ interior part and of​​ two boundary layer parts:​​​‌ a “Munk” type boundary​ layer, which is quasi-geostrophic,​‌ and an “Ekman part”,​​ which is not. Even​​ though the Munk part​​​‌ of the approximation bears‌ some similarity with previously‌​‌ studied 2D models, the​​ analysis of the Ekman​​​‌ part is completely new,‌ and several of its‌​‌ properties differ strongly from​​ the ones of classical​​​‌ Ekman layers. Our theoretical‌ analysis is supplemented with‌​‌ numerical illustrations, which exhibit​​ the desired separation behavior.​​​‌

8.2.2 Long-time behavior of‌ the Stokes-transport system in‌​‌ a channel

Participants: Anne-Laure​​ Dalibard, Julien Guillod​​​‌.

In 8,‌ we consider here a‌​‌ two-dimensional incompressible fluid in​​ a periodic channel, whose​​​‌ density is advected by‌ pure transport, and whose‌​‌ velocity is given by​​ the Stokes equation with​​​‌ gravity source term. Dirichlet‌ boundary conditions are taken‌​‌ for the velocity field​​ on the bottom and​​​‌ top of the channel‌ and periodic conditions in‌​‌ the horizontal variable. We​​ prove that the affine​​​‌ stratified density profile is‌ stable under small perturbations‌​‌ in Sobolev spaces and​​ prove convergence of the​​​‌ density to another limiting‌ stratified density profile for‌​‌ large time with an​​ explicit algebraic decay rate.​​​‌ Moreover, we are able‌ to precisely identify the‌​‌ limiting profile as the​​ decreasing vertical rearrangement of​​​‌ the initial density. Finally,‌ we show that boundary‌​‌ layers are formed for​​ large times in the​​​‌ vicinity of the upper‌ and lower boundaries. These‌​‌ boundary layers, which had​​ not been identified in​​​‌ previous works, are given‌ by a self-similar ansatz‌​‌ and driven by a​​ linear mechanism. This allows​​​‌ us to precisely characterize‌ the long-time behavior beyond‌​‌ the constant limiting profile​​ and reach more optimal​​​‌ decay rates.

8.2.3 Modeling‌ gas flow in a‌​‌ looped thermosyphon with a​​ 1 D low-Mach number​​​‌ expansion

Participants: Yohan Penel‌.

In 16,‌​‌ we provide numerical results​​ for a laminar gas​​​‌ flow at small velocities‌ in the "looped thermosyphon",‌​‌ or "natural circulation loop"​​ : a closed configuration​​​‌ composed of two horizontal‌ adiabatic pipes and two‌​‌ vertical pipes with different​​ fixed wall temperature. To​​​‌ this extent, following Paolucci,‌ [39, 40] we construct‌​‌ a low-Mach number model​​ capable of taking into​​​‌ account the periodicity and‌ the discontinuities intrinsic to‌​‌ this configuration. This compressible​​ model is richer than​​​‌ the Boussinesq model since‌ it describes the pressure‌​‌ variation and is adapted​​ to the description of​​​‌ flows driven by large‌ temperature gradients. We settle‌​‌ averaged equations through the​​ pipes of small radius​​​‌ compared to the length,‌ this gives a one‌​‌ dimensional system of equations​​ of mass, momentum and​​​‌ energy with two pressures,‌ a dynamical one and‌​‌ a thermodynamical one only​​ function of time. We​​​‌ construct a quasi-exact solution‌ in a laminar and‌​‌ steady-state regime. We approach​​ the low-Mach averaged 1D​​​‌ Model with a coupled‌ numerical method based on‌​‌ the characteristics method considering​​ the presence of the​​​‌ periodic conditions and the‌ discontinuous gravity term with‌​‌ Dirac distributions as derivatives​​ at the corners. The​​​‌ numerical results are confronted‌ and validated by the‌​‌ aforementioned reference solution to​​ determine their accuracy.

8.2.4​​​‌ Theoretical and Numerical Study‌ of the Convergence of‌​‌ Luenberger Observers for a​​​‌ Linearized Water Wave Model​

Participants: Lucas Perrin.​‌

In 27, we​​ investigate the convergence properties​​​‌ of Luenberger observers applied​ to a linearized water​‌ wave model. The study​​ is motivated by the​​​‌ challenge of estimating wave​ dynamics when only partial​‌ free surface measurements are​​ available. We identify fundamental​​​‌ obstructions to convergence, showing​ that the classical Luenberger​‌ observer fails to achieve​​ full-state reconstruction due to​​​‌ challenges associated with mean-value​ modes and high-frequency components.​‌ To overcome these limitations,​​ we introduce modified observer​​​‌ schemes that incorporate frequency​ filtering and projection techniques.​‌ Our theoretical results are​​ reinforced by numerical experiments​​​‌ that demonstrate the practical​ effectiveness of these observer-based​‌ estimation methods for water​​ waves.

8.2.5 Forward self-similar​​​‌ solutions to the 2D​ Navier–Stokes equations

Participants: Julien​‌ Guillod.

In 23​​, we construct self-similar​​​‌ solutions to the 2D​ Navier–Stokes equations evolving from​‌ arbitrarily large $-\mathrm{1}$-homogeneous initial data and​​​‌ present numerical evidence for​ their non-uniqueness.

8.3.1 Parallel​​​‌ approximation of the exponential​ of semidefinite negative Hermitian​‌ matrices

Participants: Lucas Perrin​​, Julien Salomon.​​​‌

The numerical solution of​ parabolic equations often involves​‌ calculating the exponential of​​ Hermitian matrices. In 25​​​‌, we consider a​ rational approximation of the​‌ exponential function to design​​ an algorithm for computing​​​‌ the matrix exponential in​ the Hermitian case. Using​‌ partial fraction decomposition, we​​ derive a parallelizable method,​​​‌ reducing the computation to​ independent reso- lutions of​‌ linear systems. We analyze​​ the effects of rounding​​​‌ errors on the accuracy​ of our algorithm. This​‌ work is complemented by​​ numerical tests that demonstrate​​​‌ the efficiency of our​ method and compare its​‌ performance with standard implemen-​​ tations.

8.3.2 Convergence of​​​‌ ParaOpt for general Runge-Kutta​ time discretizations

Participants: Norbert​‌ Tognon, Julien Salomon​​.

ParaOpt is a​​​‌ time parallel method based​ on Parareal for solving​‌ optimality systems arising in​​ optimal control problems. The​​​‌ method was presented in​ [M.J. Gander, F. Kwok​‌ and J. Salomon, SIAM​​ J. Sci. Comput., 42​​​‌ (2020), A2773-A2802] together with​ a convergence analysis in​‌ the case where implicit​​ Euler is used to​​​‌ discretize the differential equations​ governing the system dynamics.​‌ However, its convergence behaviour​​ for higher order time​​​‌ discretizations has not been​ considered. In 26,​‌ we use an operator​​ norm analysis to prove​​​‌ that the convergence rate​ of ParaOpt applied to​‌ a linear-quadratic optimal control​​ problem has the same​​​‌ order as the Runge-Kutta​ time integration method used,​‌ provided that a few​​ auxiliary order conditions are​​​‌ satisfied. We illustrate our​ theoretical results with numerical​‌ examples, before showing an​​ additional test case not​​​‌ covered by our analysis,​ namely, a nonlinear optimal​‌ control problem involving a​​ Schrödinger type system.

8.3.3​​​‌ Learning to generate physical​ ocean states: Towards hybrid​‌ climate modeling

Participants: Etienne​​ Meunier.

Ocean General​​​‌ Circulation Models require extensive​ computational resources to reach​‌ equilibrium states, while deep​​ learning emulators, despite offering​​​‌ fast predictions, lack the​ physical interpretability and long-term​‌ stability necessary for climate​​ scientists to understand climate​​ sensitivity (to greenhouse gas​​​‌ emissions) and mechanisms of‌ abrupt % variability such‌​‌ as tipping points. In​​ 28, we propose​​​‌ to take the best‌ from both worlds by‌​‌ leveraging deep generative models​​ to produce physically consistent​​​‌ oceanic states that can‌ serve as initial conditions‌​‌ for climate projections. We​​ assess the viability of​​​‌ this hybrid approach through‌ both physical metrics and‌​‌ numerical experiments, and highlight​​ the benefits of enforcing​​​‌ physical constraints during generation.‌ Although we train here‌​‌ on ocean variables from​​ idealized numerical simulations, we​​​‌ claim that this hybrid‌ approach, combining the computational‌​‌ efficiency of deep learning​​ with the physical accuracy​​​‌ of numerical models, can‌ effectively reduce the computational‌​‌ burden of running climate​​ models to equilibrium, and​​​‌ reduce uncertainties in climate‌ projections by minimizing drifts‌​‌ in baseline simulations.

8.3.4​​ ParaOpt for unstable systems​​​‌

Participants: Norbert Tognon.‌

ParaOpt is a two-level‌​‌ time-parallel method to solve​​ the coupled forward/backward Euler-Lagrange​​​‌ system arising from partial‌ differential equations (PDEs) constrained‌​‌ optimization. In 29,​​ we present a convergence​​​‌ analysis of this algorithm‌ in the case where‌​‌ the system under consideration​​ is unstable. We complete​​​‌ this theoretical study with‌ numerical experiments, where the‌​‌ properties of the algorithm​​ are investigated on linear​​​‌ and nonlinear examples.

8.3.5‌ Towards fully differentiable neural‌​‌ ocean model with Veros​​

Participants: Etienne Meunier.​​​‌

In 18, we‌ present a differentiable extension‌​‌ of the VEROS ocean​​ model, enabling automatic differentiation​​​‌ through its dynamical core.‌ We describe the key‌​‌ modifications required to make​​ the model fully compatible​​​‌ with JAX autodifferentiation framework‌ and evaluate the numerical‌​‌ consistency of the resulting​​ implementation. Two illustrative applications​​​‌ are then demonstrated: (i)‌ the correction of an‌​‌ initial ocean state through​​ gradient-based optimization, and (ii)​​​‌ the calibration of unknown‌ physical parameters directly from‌​‌ model observations. These examples​​ highlight how differentiable programming​​​‌ can facilitate end-to-end learning‌ and parameter tuning in‌​‌ ocean modeling. Our implementation​​ is available online.

8.4.1 Graph‌ and Mean-Field Limits for‌​‌ Interacting Particle Systems

Participants:​​ Nathalie Ayi.

Models​​​‌ of collective dynamics provide‌ a powerful framework to‌​‌ analyze phenomena such as​​ opinion formation in populations​​​‌ and flocking behaviors in‌ animal groups. While the‌​‌ classic mean-field limit approach​​ has provided valuable insights​​​‌ into indistinguishable particle systems,‌ it fails to capture‌​‌ the influence of individual​​ identities and specific interaction​​​‌ structures. Graph theory addresses‌ this limitation and allows‌​‌ to study large-population limits​​ of systems of interacting​​​‌ particles on weighted graphs.‌ The lecture notes presented‌​‌ in 17 begin by​​ exploring two approaches to​​​‌ large-population limits for non-exchangeable‌ particle systems: the graph‌​‌ limit and the (non-exchangeable)​​ mean-field limit. Rigorous convergence​​​‌ results are presented, emphasizing‌ their interplay. Building on‌​‌ this foundation, we consider​​ three variations: adaptive dynamical​​​‌ networks, which capture evolving‌ interaction structures, random graphs,‌​‌ which provide realistic models​​ for generating graphs, and​​​‌ hypergraphs, which extend analysis‌ to higher-order interactions, crucial‌​‌ in systems where joint​​ influences can be observed.​​​‌

8.4.2 Humanity's Last Exam‌

Participants: Julien Guillod.‌​‌

phan:hal-04915593, title = Humanity's​​​‌ Last Exam, Benchmarks are​ important tools for tracking​‌ the rapid advancements in​​ large language model (LLM)​​​‌ capabilities. However, benchmarks are​ not keeping pace in​‌ difficulty: LLMs now achieve​​ over 90% accuracy on​​​‌ popular benchmarks like MMLU,​ limiting informed measurement of​‌ state-of-the-art LLM capabilities. In​​ response, we introduce Humanity's​​​‌ Last Exam (HLE, see​ 15) a multi-modal​‌ benchmark at the frontier​​ of human knowledge, designed​​​‌ to be the final​ closed-ended academic benchmark of​‌ its kind with broad​​ subject coverage. HLE consists​​​‌ of 3,000 questions across​ dozens of subjects, including​‌ mathematics, humanities, and the​​ natural sciences. HLE is​​​‌ developed globally by subject-matter​ experts and consists of​‌ multiple-choice and short-answer questions​​ suitable for automated grading.​​​‌ Each question has a​ known solution that is​‌ unambiguous and easily verifiable,​​ but cannot be quickly​​​‌ answered via internet retrieval.​ State-of-the-art LLMs demonstrate low​‌ accuracy and calibration on​​ HLE, highlighting a significant​​​‌ gap between current LLM​ capabilities and the expert​‌ human frontier on closed-ended​​ academic questions. To inform​​​‌ research and policymaking upon​ a clear understanding of​‌ model capabilities, we publicly​​ release HLE at .​​​‌

8.4.3 Probing the partition​ function for temperature-dependent potentials​‌ with nested sampling

Participants:​​ Julien Salomon.

Thermodynamic​​​‌ properties can be in​ principle derived from the​‌ partition function, which, in​​ many-atom systems, is hard​​​‌ to evaluate as it​ involves a sum on​‌ the accessible microscopic states.​​ Recently, the partition function​​​‌ has been computed via​ nested sampling, relying on​‌ Bayesian statistics, which is​​ able to provide the​​​‌ density of states as​ a function of the​‌ energy in a single​​ run, independently of the​​​‌ temperature. This appealing property​ is lost whenever the​‌ potential energy that appears​​ in the partition function​​​‌ is temperature-dependent: for instance,​ mean-field effective potential energies​‌ or the quantum partition​​ function in the path-integral​​​‌ formalism. For these cases,​ the nested sampling must​‌ be carried out at​​ each temperature, which results​​​‌ in a massive increase​ of computational time. In​‌ 13, we introduce​​ and implement a new​​​‌ method, that is based​ on an extended partition​‌ function where the temperature​​ is considered as an​​​‌ additional parameter to be​ sampled. The extended partition​‌ function can be evaluated​​ by nested sampling in​​​‌ a single run, so​ to restore this highly​‌ desirable property even for​​ temperature-dependent effective potential energies.​​​‌ We apply this original​ method to compute the​‌ quantum partition function for​​ harmonic potentials and Lennard-Jones​​​‌ clusters at low temperatures​ and show that it​‌ outperforms the straightforward application​​ of nested sampling for​​​‌ each temperature within several​ temperature ranges.

8.4.4 Segmenting​‌ the motion components of​​ a video: A long-term​​​‌ unsupervised model

Participants: Etienne​ Meunier.

Human beings​‌ have the ability to​​ continuously analyze a video​​​‌ and immediately extract the​ motion components. We want​‌ to adopt this paradigm​​ to provide a coherent​​​‌ and stable motion segmentation​ over the video sequence.​‌ In this perspective, we​​ propose in 14 a​​​‌ novel long-term spatio-temporal model​ operating in a totally​‌ unsupervised way. It takes​​ as input the volume​​ of consecutive optical flow​​​‌ (OF) fields, and delivers‌ a volume of segments‌​‌ of coherent motion over​​ the video. More specifically,​​​‌ we have designed a‌ transformer-based network, where we‌​‌ leverage a mathematically well-founded​​ framework, the Evidence Lower​​​‌ Bound (ELBO), to derive‌ the loss function. The‌​‌ loss function combines a​​ flow reconstruction term involving​​​‌ spatio-temporal parametric motion models‌ combining, in a novel‌​‌ way, polynomial (quadratic) motion​​ models for the spatial​​​‌ dimensions and B-splines for‌ the time dimension of‌​‌ the video sequence, and​​ a regularization term enforcing​​​‌ temporal consistency on the‌ segments. We report experiments‌​‌ on four VOS benchmarks,​​ demonstrating competitive quantitative results​​​‌ while performing motion segmentation‌ on a sequence in‌​‌ one go. We also​​ highlight through visual results​​​‌ the key contributions on‌ temporal consistency brought by‌​‌ our method.

8.4.5 Surrogate​​ modeling of interactions in​​​‌ microbial communities through Physics-Informed‌ Neural Networks

Participants: Lucas‌​‌ Perrin.

Microorganisms form​​ complex communities known as​​​‌ microbiota, influencing various aspects‌ of host well-being. The‌​‌ Generalized Lotka-Volterra (GLV) model​​ is commonly used to​​​‌ understand microorganism population dynamics,‌ but its application to‌​‌ the microbiota faces challenges​​ due to limited bacterial​​​‌ data and complex interactions.‌ The preliminary work 12‌​‌ focuses on using a​​ Physics-Informed Neural Network (PINN)​​​‌ and synthetic data to‌ build a surrogate model‌​‌ of bacterial species evolution​​ driven by a GLV​​​‌ model. The approach is‌ calibrated and tested on‌​‌ several models differing in​​ size and dynamic behavior.​​​‌

9.1.1‌​‌ Participation in other International​​ Programs

Participants: Julien Salomon​​​‌, Jacques Sainte-Marie.‌

• OceanIA
• Partner Institution(s): INRIA‌​‌
  • INRIA Paris
  • INRIA Saclay​​
  • INRIA Sophia-Antipolis
  • INRIA Chile​​​‌
• Date/Duration: 2020-2025
• Additionnal info/keywords:‌
  OceanIA is a four-years‌​‌ project (11.2020–12.2025) involving Inria​​ teams in Chile, Paris,​​​‌ Saclay, and Sophia-Antipolis, and‌ the Fondation Tara Océan,‌​‌ the Center of Mathematical​​ Modeling (CMM, U.Chile), the​​​‌ Pontificia Universidad Católica de‌ Chile (PUC), the GO-SEE‌​‌ CNRS Federation, and the​​ Laboratoire des Sciences du​​​‌ Numérique de Nantes (LS2N).‌

9.1.2 Visits of international‌​‌ scientists

9.1.3​​ Visits to international teams​​​‌

9.1.4 Other european programs/initiatives‌​‌

Participants: Anne-Laure Dalibard.​​

• Visited institution:
  Mathematisches Forschungsinstitut​​​‌ Oberwolfach (MFO)
• Country:
  Germany‌
• Dates:
  12.05-16.05
• Mobility program/type‌​‌ of mobility:
  Organization of​​ a workshop.

Projet Emergence (2023-2025)‌

Participants: Nathalie Ayi.‌​‌

• Project acronym: Emergence
• Project​​ title: Numerical studies of​​​‌ STOChastic Kinetic partial differential‌ equations (STOCK)
• Coordinator: Nathalie‌​‌ Ayi (SU)
• Funding: 15​​​‌ 000 euros.

ANR NASSMOM​ (2024-2028)

Participants: Nina Aguillon​‌, Julie Deshayes,​​ Sybille Techené.

• Project​​​‌ acronym: NASSMOM
• Project title:​ Nondiffusive advection schemes and​‌ spurious mixing in ocean​​ model
• Coordinator: Nina Aguillon​​​‌
• Funding: 246 957 euros.​

Water masses of given​‌ temperature and salinity are​​ advected without much blending​​​‌ over long periods of​ time in the ocean.​‌ At the numerical level,​​ the discretization of the​​​‌ equation creates a spurious​ mixing (or numerical diffusion)​‌ that artificially mixes the​​ water masses. It can​​​‌ be of the same​ order of magnitude as​‌ the physical mixing. This​​ is especially true in​​​‌ climate simulations where the​ grid is coarse and​‌ the time of integration​​ is long. This project​​​‌ is concerned with two​ different aspects of the​‌ spurious mixing. First, we​​ will study a numerical​​​‌ procedure to quantify precisely​ in space and time​‌ the spurious mixing. The​​ method is both different​​​‌ from usual entropy inequality​ in maths that are​‌ limited to first order​​ schemes, and from global​​​‌ diagnosis based on water​ mass transformation in oceanography.​‌ It should allow us​​ to better understand the​​​‌ geography and effects of​ spurious mixing. It can​‌ be applied to any​​ transported quantity or to​​​‌ the evolution of total​ energy. Second, we will​‌ develop antidiffusive advection schemes​​ for the salinity and​​​‌ temperature in the European​ ocean general circulation model​‌ NEMO. This approach is​​ different from the usual​​​‌ « higher order, finer​ grids » strategy and​‌ has been successfully employed​​ for atmospheric pollution and​​​‌ biphasic flows. Preliminary results​ obtained by the principal​‌ investigator on a new​​ second order antidiffusive scheme​​​‌ show a gain of​ accuracy in the smooth​‌ regions and a correct​​ behavior in 2 space​​​‌ dimensions. This is a​ major improvement compared to​‌ the existing first order​​ antidiffusive schemes, which should​​​‌ allow us to go​ beyond its use in​‌ the vertical direction only.​​ In conclusion, this project​​​‌ proposes a mathematical approach​ on the question of​‌ spurious mixing in ocean​​ general circulation models. The​​​‌ team gathers experts on​ numerical analysis and ocean​‌ modeling. We will collaborate​​ closely together with the​​​‌ aim of having a​ direct contribution to NEMO.​‌

ANR BOURGEONS (2023-2027)

Participant:​​ Anne-Laure Dalibard.

• Project​​​‌ acronym:BOURGEONS
• Project title: Boundaries,​ Congestion and Vorticity in​‌ Fluids: A connection with​​ environmental issues
• Coordinator: Anne-Laure​​​‌ DALIBARD
• Funding: 567301 euros.​

The purpose of the​‌ BOURGEONS project is to​​ investigate several aspects of​​​‌ fluid dynamics which all​ play an important role​‌ in geophysical flows and​​ their environmental applications. It​​​‌ is organized around two​ main topics which strongly​‌ expanded in recent years,​​ and for which we​​​‌ will address both fundamental​ and applied aspects: (i)​‌ the dynamics of floating​​ objects, congested flows and​​​‌ extreme waves; and (ii)​ the analysis of boundary​‌ layers and vortices.

PEPR​​ Climaths (2024-2029)

Participant: Anne-Laure​​​‌ Dalibard.

• Project acronym:​ CLIMATHS
• Project title: Fundamental​‌ advances in modelling key​​ processes for reducing climate​​​‌ change impacts
• Coordinator: Anne-Laure​ DALIBARD
• Funding: 1 000​‌ 000 euros.

The CLIMATHS​​ project targets fundamental developments​​ required to reduce uncertainties​​​‌ in the study of‌ the impacts of climate‌​‌ change. The climate and​​ its main components -​​​‌ including the atmosphere and‌ ocean - obey complex‌​‌ dynamics, some aspects of​​ which are still poorly​​​‌ understood, despite their crucial‌ importance for mankind in‌​‌ a context of climate​​ disruption.

ANR Saphir (2022-2026)​​​‌

Participants: Jacques Sainte-Marie,‌ Bernard Di Martino.‌​‌

• Project acronym: Saphir
• Project​​ title: Sensor Augmented weather​​​‌ Prediction at high Resolution‌
• Coordinator: J-F. Muzy (Université‌​‌ de Toulouse Paul Sabatier)​​
• Funding: 296 000 euros.​​​‌

Providing reliable forecasts of‌ severe weather events is‌​‌ a major issue in​​ many areas such as​​​‌ civil safety or renewable‌ energy production. SAPHIR proposes‌​‌ to combine high-resolution (sub-km)​​ atmospheric dynamics models and​​​‌ a set of direct‌ measurements from weather stations,‌​‌ atmospheric monitoring programs or​​ a dedicated sensor network​​​‌ within a «deep learning”‌ architecture specifically optimized for‌​‌ improving forecasting accuracy. We​​ plan to use this​​​‌ approach to improve the‌ forecast (at horizons ranging‌​‌ from few hours to​​ few days) of intense​​​‌ weather events including rainfalls‌ and electrical activity with‌​‌ an application to river​​ flooding forecasting. SAPHIR is​​​‌ also aiming for an‌ application in the field‌​‌ of renewable energies by​​ improving the forecast of​​​‌ cloudiness and wind strength,‌ which are determining factors‌​‌ for the production of​​ solar or wind power​​​‌ plants.

ANR DEEPNUM (2022-2026)‌

Participants: Julien Salomon,‌​‌ Jacques Sainte-Marie.

• Project​​ acronym: DEEPNUM
• Project title:​​​‌ Algorithmes pour l'optimisation à‌ grande échelle de problèmes‌​‌ de propagation d'ondes
• Coordinator:​​ Julien Salomon
• Funding: 493​​​‌ 799,20 euros.

The project‌ aims at developing the‌​‌ interplay between Deep Neural​​ Networks (DNNs) and Differential​​​‌ Equations (DEs), with the‌ goal of modeling complex‌​‌ dynamical systems arising from​​ the observation of natural​​​‌ phenomena. Two application domains‌ are targeted, environment and‌​‌ healthcare. We address three​​ fundamental questions: how to​​​‌ adapt and apply numerical‌ analysis theory to DNNs‌​‌ for analyzing them, providing​​ theoretical guaranties and improving​​​‌ their robustness, how to‌ combine simulation and data‌​‌ based models into hybrid​​ systems, how could DNNs​​​‌ help solving DEs and‌ complement numerical solvers. In‌​‌ addition, we evaluate our​​ methods on simulation and​​​‌ real world data in‌ the environment and health‌​‌ domains. DeepNuM gathers partners​​ with complementary skills: DEs​​​‌ and Environment (INRIA-ANGE), Machine‌ Learning and DNNs (Sorbonne‌​‌ – MLIA), DEs and​​ Biophysics (INRIA-EPIONE).

ANR MEGA​​​‌ (2023-2028)

Participants: Bernard Di‌ Martino, Jacques Sainte-Marie‌​‌, Nina Aguillon.​​

• Project acronym: MEGA
• Project​​​‌ title: Giant submarine landslides‌ in gas hydrate provinces:‌​‌ a comparison of the​​ Nile and Amazon deep-sea​​​‌ fans
• Coordinator: Sébastien Mingeon‌
• Funding: 533,348 euros.

Giant‌​‌ submarine landslides (10-2000 km3)​​ are found in the​​​‌ thick Quaternary sediment succession‌ of passive continental margins.‌​‌ Their ages coincide with​​ periods of sea-level fall​​​‌ and rise, but it‌ is unclear how such‌​‌ vast failures can be​​ triggered on low seafloor​​​‌ slopes (<2?) in the‌ absence of a triggering‌​‌ factor such as seismicity.​​ Key hypotheses involv. Beck,​​​‌ P. Bonneton, D. Bresch,‌ C. Collot, A.-L. Dalibard,‌​‌ E. Dormy, I. Gallagher,​​​‌ Th. Gallay, D. Gérard-Varet,​ E. Grenier, M. Hillairet,​‌ M. Kazakova, C. Lacave,​​ D. Lannes, F. Marbach,​​​‌ F. Marche, E. Miot,​ M. Parisot, C. Perrin,​‌ C. Prange, M. Rigal,​​ F. Rousset, L. Saint-Raymond,​​​‌ F. Sueur, M. Tucsnak,​ A. Venaille. e excess​‌ pore pressures linked to​​ reductions in gas-hydrate stability,​​​‌ driven by changes either​ in climate or in​‌ subsurface fluid flow. The​​ MEGA project wants to​​​‌ explore such hypotheses through​ the first modelling of​‌ linked changes in gas​​ hydrate and slope stability​​​‌ in response to ocean​ pressure and temperature changes,​‌ using an innovative comparison​​ of the Nile and​​​‌ Amazon deep-sea fans that​ experience different forms of​‌ climate forcing over glacial-interglacial​​ timescales. As such megaslides​​​‌ have never triggered in​ historical times, MEGA will​‌ provide input for the​​ first modelling of their​​​‌ tsunamogenic consequences on coastal​ zones.

ANR SMASH (2025-2029)​‌

Participants: Julien Guillod.​​

• Project acronym: SMASH
• Project​​​‌ title: Emergent Small Scale​ behaviors in Hydrodynamic models​‌
• Coordinator: F. Vigneron
• Funding:​​ 315000 euros.

ANR HEAD​​​‌ (2024-2029)

Participants: Nathalie Ayi​.

• Project acronym: HEAD​‌
• Project title: Hyperbolic Evolutions,​​ Approximations & Dynamics
• Coordinator:​​​‌ M. Rodrigues
• Funding: 422​ 820 euros.

Our project​‌ is focused on the​​ analysis of the long-time​​​‌ dynamics of first-order hyperbolic​ systems of nonlinear partial​‌ differential equations and their​​ approximations by numerical schemes,​​​‌ vanishing viscosity or in​ the dispersionless limit. It​‌ contributes to three general​​ aims:

1. The development of​​​‌ a stability theory applicable​ to singular waves, including​‌ discontinuous and/or characteristic ones.​​
2. Uniform stability results when​​​‌ the long-time limit and​ the approximation process commute.​‌
3. A refined description of​​ obstructions when they do​​​‌ not.

Its concrete applications​ are focused on models​‌ from fluid mechanics and​​ plasma dynamics.

RT "Terre​​​‌ & Énergies" (2023–)

Participants:​ Emmanuel Audusse, Bernard​‌ di Martino, Martin​​ Parisot, Jacques Sainte-Marie​​​‌.

The MathGeoPhy interdisciplinary​ research group was created​‌ in January 2022, for​​ five years. It is​​​‌ funded by the French​ National Center for Scientific​‌ Research (CNRS), with the​​ mission of animating the​​​‌ French scientific community around​ the theme of mathematics​‌ in interaction with the​​ geophysics of fluid and​​​‌ solid envelopes. The members​ of the GdR are​‌ interested in mathematical modeling,​​ scientific computing and the​​​‌ development of new numerical​ methods applied in particular​‌ to :

• offshore and​​ coastal ocean dynamics, gravity​​​‌ waves, coastal erosion problems​
• micro-macro approaches, granular and​‌ complex flows
• fluvial and​​ torrential hydrodynamics, extreme events​​​‌ and environmental risks, landslides,​ avalanches, volcanic eruptions, glaciology,​‌ etc.

GdR EOL-EMR (2021–2026)​​

Participants: Julien Salomon,​​​‌ Jacques Sainte-Marie.

The​ objectives of this project​‌ are the following:

• To​​ promote the dissemination of​​​‌ existing knowledge and expertise​ within and across disciplines.​‌
• The GDR EMR is​​ a forum for the​​​‌ exchange of expertise and​ know-how within and across​‌ disciplines.
• To promote the​​ implementation of collaborations, between​​​‌ partners of the GDR​ and with the industrial​‌ fabric.

The GDR is​​ an entry and orientation​​​‌ point. It provides a​ forum for the exchange​‌ of information concerning industrial​​ needs and the kills​​ of the academic community;​​​‌ and enables the bringing‌ together of players. Valuing‌​‌ the national scientific community​​ The GDR EMR gives​​​‌ visibility to the community,‌ in particular through the‌​‌ development of a mapping​​ of the actors and​​​‌ themes available on the‌ web platform

10.1.1 Seminar Organization

Participants:‌​‌ Julien Guillod.

• 2019-​​ : Séminaire Analyse non-linéaire​​​‌ et EDP (DMA, ENS)‌
• 2021- : Séminaire Infomath‌​‌

Participants: Anne-Laure Dalibard.​​

• 2016- : Comité d'organisation​​​‌ du séminaire du LJLL‌
• 2025- : Présidente du‌​‌ Comité scientifique du cycle​​ "1 Texte une aventure​​​‌ mathématique"

Participants: Nathalie Ayi‌.

2021- : Journée‌​‌ interne du LJLL

10.1.2​​ Scientific events: organisation

10.1.3​​ Journal

10.1.4 Invited talks

See‌ Table 2.

10.1.5 Research administration

Participants:​‌ Nathalie Ayi.

Membre​​ du comité de sélection​​​‌ pour les postes de​ Maître de confeérences a​‌ l'IMJ.

Participants: Julien Salomon​​.

• Membre du comité​​​‌ de sélection pour 2​ postes de Maiître de​‌ conférences au LJLL
• Membre​​ du comité de sélection​​​‌ pour les postes de​ CR/ISFP á l'INRIA-Bordeaux

Participants:​‌ Nina Aguillon.

• Membre​​ du comité de sélection​​​‌ pour 2 postes de​ Maître de conférences au​‌ LJLL
• Membre du Comité​​ de sélection pour 1​​​‌ poste de Maître de​ conférences au LIP6, Sorbonne​‌ Uni.

Long term responsabilities​​ are given in Table​​​‌ 3.

10.2.1​‌ Faculty responsabilities, committees

Participants:​​ Julien Guillod.

• 2019-​​​‌ : Membre du conseil​ de la Licence de​‌ Mathématiques pour l'UFR 929,​​ SU
• 2025 : Membre​​​‌ du comité d'attribution des​ primes, SU
• 2022 :​‌ Référent égalité et lutte​​ contre les discriminations pour​​​‌ l'UFR 929, SU
• 2025​ : Référent égalité du​‌ LJLL auprès du CNRS​​

Participants: Nathalie Ayi.​​​‌

• 2022- : Membre du​ conseil de département du​‌ cycle d'intégration
• 2023- :​​ Membre du CNU

Participants:​​​‌ Nina Aguillon.

• 2022-​ : Membre du conseil​‌ de l'UFR 929, SU​​
• 2022- : Comité de​​​‌ pilotage de CAPSULE (centre​ d'accompagnement á la pédagogie​‌ et support á l'expérimentation)​​

Participants: Anne-Laure Dalibard.​​​‌

Pôle écoute du LJLL​

10.2.2 Supervision

Supervision activities​‌ are given in Table​​ 4.

10.2.3 Juries

Participation to​​ committees is summarize in​​​‌ Table 5.

10.2.4 Teaching

Teaching‌​‌ activities are given in​​ Table 6.

10.2.5‌​‌ Educational and pedagogical outreach​​

Participants: Edwige Godlewski.​​​‌

2019- : president of‌ commission française pour l'enseignement‌​‌ des mathématiques (CFEM)

10.3.1 Others​​​‌ science outreach relevant activities​

Participants: Jacques Sainte-Marie.​‌

30.06.2025 : Colloque “Les​​ données au service des​​​‌ territoires intelligents” - Sénat​

International journals

• 6‌ articleE.Emmanuel Audusse‌​‌, V.Virgile Dubos​​, N.Noémie Gaveau​​​‌ and Y.Yohan Penel‌. Energy stable and‌​‌ linearly well-balanced numerical schemes​​ for the non-linear Shallow​​​‌ Water equations with Coriolis‌ force.SIAM Journal‌​‌ on Scientific Computing47​​01January 2025,​​​‌ A1-A23HALDOIback‌ to text
• 7 article‌​‌O.Olivier Bernard,​​ L.-D.Liu-Di Lu,​​​‌ J.Jacques Sainte-Marie and‌ J.Julien Salomon.‌​‌ Topography optimization for enhancing​​ microalgal growth in raceway​​​‌ ponds.SIAM Journal‌ on Control and Optimization‌​‌634July 2025​​, 2451-2471HALDOI​​​‌back to text
• 8‌ articleA.-L.Anne-Laure Dalibard‌​‌, J.Julien Guillod​​ and A.Antoine Leblond​​​‌. Long-time behavior of‌ the Stokes-transport system in‌​‌ a channel.Analysis​​ & PDE188​​​‌July 2025, 1955–2032‌HALDOIback to‌​‌ text
• 9 articleB.​​Bernard Di Martino,​​​‌ C.Chourouk El Hassanieh‌, E.Edwige Godlewski‌​‌, J.Julien Guillod​​ and J.Jacques Sainte-Marie​​​‌. Hyperbolicity of a‌ semi-Lagrangian formulation of the‌​‌ hydrostatic free-surface Euler system​​.Nonlinearity381​​​‌2025, 015018In‌ press. HALDOIback‌​‌ to text
• 10 article​​C.Chourouk El Hassanieh​​​‌, M.Mathieu Rigal‌ and J.Jacques Sainte-Marie‌​‌. Implicit kinetic schemes​​ for the Saint-Venant system​​​‌.ESAIM: Mathematical Modelling‌ and Numerical Analysis59‌​‌May 2025, 1863–1908​​HALDOIback to​​​‌ text
• 11 articleB.‌Bérénice Grec, D.‌​‌Davor Kumozec and Y.​​Yohan Penel. Unconditionally​​​‌ stable numerical scheme for‌ the 2D transport equation‌​‌.Computers & Mathematics​​ with Applications182March​​​‌ 2025, 275-290HAL‌DOIback to text‌​‌
• 12 articleP. J.​​Paguiel Javan Hossie,​​​‌ B.Béatrice Laroche,‌ T.Thibault Malou,‌​‌ L.Lucas Perrin,​​ T.Thomas Saigre and​​​‌ L.Lorenzo Sala.‌ Surrogate modeling of interactions‌​‌ in microbial communities through​​ Physics-Informed Neural Networks..​​​‌ESAIM: Proceedings and Surveys‌81October 2025,‌​‌ 104-122HALDOIback​​ to text
• 13 article​​​‌L.Lune Maillard,‌ P.Philippe Depondt,‌​‌ F.Fabio Finocchi,​​ S.Simon Huppert,​​​‌ T.Thomas Plé,‌ J.Julien Salomon and‌​‌ M.Martino Trassinelli.​​ Probing the partition function​​​‌ for temperature-dependent potentials with‌ nested sampling.The‌​‌ Journal of Chemical Physics​​16318November 2025​​​‌HALDOIback to‌ text
• 14 articleE.‌​‌Etienne Meunier and P.​​​‌Patrick Bouthemy. Segmenting​ the motion components of​‌ a video: A long-term​​ unsupervised model.IEEE​​​‌ Transactions on Pattern Analysis​ and Machine IntelligenceEarly​‌ accessSeptember 2025,​​ 1-12HALDOIback​​​‌ to text
• 15 article​L.Long Phan,​‌ A.Alice Gatti,​​ Z.Ziwen Han,​​​‌ N.Nathaniel Li,​ J.Josephina Hu,​‌ H.Hugh Zhang,​​ S.Sean Shi,​​​‌ M.Michael Choi,​ A.Anish Agrawal,​‌ A.Arnav Chopra,​​ A.Adam Khoja,​​​‌ R.Ryan Kim,​ J.Jason Hausenloy,​‌ O.Oliver Zhang,​​ M.Mantas Mazeika,​​​‌ D.Daron Anderson,​ T.Tung Nguyen,​‌ M.Mobeen Mahmood,​​ F.Fiona Feng,​​​‌ S. Y.Steven Y.​ Feng, H.Haoran​‌ Zhao, M.Michael​​ Yu, V.Varun​​​‌ Gangal, C.Chelsea​ Zou, Z.Zihan​‌ Wang, J. P.​​Jessica P. Wang,​​​‌ P.Pawan Kumar,​ O.Oleksandr Pokutnyi,​‌ R.Robert Gerbicz,​​ S.Serguei Popov,​​​‌ J.-C.John-Clark Levin,​ M.Mstyslav Kazakov,​‌ J.Johannes Schmitt,​​ G.Geoff Galgon,​​​‌ A.Alvaro Sanchez,​ Y.Yongki Lee,​‌ W.Will Yeadon,​​ S.Scott Sauers,​​​‌ M.Marc Roth,​ C.Chidozie Agu,​‌ S.Søren Riis,​​ F.Fabian Giska,​​​‌ S.Saiteja Utpala,​ Z.Zachary Giboney,​‌ G. M.Gashaw M.​​ Goshu, J. o.​​​‌Joan of Arc Xavier​, S.-J.Sarah-Jane Crowson​‌, M. M.Mohinder​​ Maheshbhai Naiya, N.​​​‌Noah Burns, L.​Lennart Finke, Z.​‌Zerui Cheng, H.​​Hyunwoo Park, F.​​​‌Francesco Fournier-Facio, J.​John Wydallis, M.​‌Mark Nandor, A.​​Ankit Singh, T.​​​‌Tim Gehrunger, J.​Jiaqi Cai, B.​‌Ben Mccarty, D.​​Darling Duclosel, J.​​​‌Jungbae Nam, J.​Jennifer Zampese, R.​‌ G.Ryan G. Hoerr​​, A.Aras Bacho​​​‌, G. A.Gautier​ Abou Loume, A.​‌Abdallah Galal, H.​​Hangrui Cao, A.​​​‌ C.Alexis C Garretson​, D.Damien Sileo​‌, Q.Qiuyu Ren​​, D.Doru Cojoc​​​‌, P.Pavel Arkhipov​, U.Usman Qazi​‌, L.Lianghui Li​​, S.Sumeet Motwani​​​‌, C. S.Christian​ Schroeder de Witt,​‌ E.Edwin Taylor,​​ J.Johannes Veith,​​​‌ E.Eric Singer,​ T. D.Taylor D.​‌ Hartman, P.Paolo​​ Rissone, J.Jaehyeok​​​‌ Jin, J. W.​Jack Wei Lun Shi​‌, C. G.Chris​​ G. Willcocks, J.​​​‌Joshua Robinson, A.​Aleksandar Mikov, A.​‌Ameya Prabhu, L.​​Longke Tang, X.​​​‌Xavier Alapont, J.​ L.Justine Leon Uro​‌, K.Kevin Zhou​​, E. d.Emily​​​‌ de Oliveira Santos,​ A. P.Andrey Pupasov​‌ Maksimov, E.Edward​​ Vendrow, K.Kengo​​​‌ Zenitani, J.Julien​ Guillod, Y.Yuqi​‌ Li, J.Joshua​​ Vendrow, V.Vladyslav​​​‌ Kuchkin, N.Ng​ Ze-An, P.Pierre​‌ Marion, D.Denis​​ Efremov, J.Jayson​​ Lynch, K.Kaiqu​​​‌ Liang, A.Andrew‌ Gritsevskiy, D.Dakotah‌​‌ Martinez, B.Ben​​ Pageler, N.Nick​​​‌ Crispino, D.Dimitri‌ Zvonkine, N. W.‌​‌Natanael Wildner Fraga,​​ S.Saeed Soori,​​​‌ O.Ori Press,‌ H.Henry Tang,‌​‌ J.Julian Salazar,​​ S. R.Sean R.​​​‌ Green, L.Lina‌ Brüssel, M.Moon‌​‌ Twayana, A.Aymeric​​ Dieuleveut, T. R.​​​‌T. Ryan Rogers,‌ W.Wenjin Zhang,‌​‌ B.Bikun Li,​​ J.Jinzhou Yang,​​​‌ A.Arun Rao,‌ G.Gabriel Loiseau,‌​‌ M.Mikhail Kalinin,​​ M.Marco Lukas,​​​‌ C.Ciprian Manolescu,‌ S.Subrata Mishra,‌​‌ A. G.Ariel Ghislain​​ Kemogne Kamdoum, T.​​​‌Tobias Kreiman, T.‌Tad Hogg, A.‌​‌Alvin Jin, C.​​Carlo Bosio, G.​​​‌Gongbo Sun, B.‌ P.Brian P Coppola‌​‌, T.Tim Tarver​​, H.Haline Heidinger​​​‌, R.Rafael Sayous‌, S.Stefan Ivanov‌​‌, J. M.Joseph​​ M Cavanagh, J.​​​‌Jiawei Shen, J.‌ M.Joseph Marvin Imperial‌​‌, P.Philippe Schwaller​​, S.Shaipranesh Senthilkuma​​​‌, A. M.Andres‌ M Bran, A.‌​‌Ali Dehghan, A.​​Andres Algaba, B.​​​‌Brecht Verbeken, D.‌David Noever, R.‌​‌Ragavendran P V,​​ L.Lisa Schut,​​​‌ I.Ilia Sucholutsky,‌ E.Evgenii Zheltonozhskii,‌​‌ D.Derek Lim,​​ R.Richard Stanley,​​​‌ S.Shankar Sivarajan,‌ T.Tong Yang,‌​‌ J.John Maar,​​ J.Julian Wykowski,​​​‌ M.Martí Oller,‌ J.Jennifer Sandlin,‌​‌ A.Anmol Sahu,​​ Y.Yuzheng Hu,​​​‌ S.Sara Fish,‌ N.Nasser Heydari,‌​‌ A.Archimedes Apronti,​​ K.Kaivalya Rawal,​​​‌ T. G.Tobias Garcia‌ Vilchis, Y.Yuexuan‌​‌ Zu, M.Martin​​ Lackner, J.James​​​‌ Koppel, J.Jeremy‌ Nguyen, D. S.‌​‌Daniil S. Antonenko,​​ S.Steffi Chern,​​​‌ B.Bingchen Zhao,‌ P.Pierrot Arsene,‌​‌ A.Alan Goldfarb,​​ S.Sergey Ivanov,​​​‌ R.Rafał Poświata,‌ C.Chenguang Wang,‌​‌ D.Daofeng Li,​​ D.Donato Crisostomi,​​​‌ A.Andrea Achilleos,‌ B.Benjamin Myklebust,‌​‌ A.Archan Sen,​​ D.David Perrella,​​​‌ N.Nurdin Kaparov,‌ M. H.Mark H‌​‌ Inlow, A.Allen​​ Zang, E.Elliott​​​‌ Thornley, D.Daniil‌ Orel, V.Vladislav‌​‌ Poritski, S.Shalev​​ Ben-David, Z.Zachary​​​‌ Berger, P.Parker‌ Whitfill, M.Michael‌​‌ Foster, D.Daniel​​ Munro, L.Linh​​​‌ Ho, D. B.‌Dan Bar Hava,‌​‌ A.Aleksey Kuchkin,​​ R.Robert Lauff,​​​‌ D.David Holmes,‌ F.Frank Sommerhage,‌​‌ K.Keith Schneider,​​ Z.Zakayo Kazibwe,​​​‌ N.Nate Stambaugh,‌ M.Mukhwinder Singh,‌​‌ I.Ilias Magoulas,​​ D.Don Clarke,​​​‌ D. H.Dae Hyun‌ Kim, F. M.‌​‌Felipe Meneguitti Dias,​​ V.Veit Elser,​​​‌ K. P.Kanu Priya‌ Agarwal, V. E.‌​‌Victor Efren Guadarrama Vilchis​​​‌, I.Immo Klose​, C.Christoph Demian​‌, U.Ujjwala Anantheswaran​​, A.Adam Zweiger​​​‌, G.Guglielmo Albani​, J.Jeffery Li​‌, N.Nicolas Daans​​, M.Maksim Radionov​​​‌, V.Václav Rozhoň​, Z.Ziqiao Ma​‌, C.Christian Stump​​, M.Mohammed Berkani​​​‌, J.Jacob Platnick​, V.Volodymyr Nevirkovets​‌, L.Luke Basler​​, M.Marco Piccardo​​​‌, F.Ferenc Jeanplong​, N.Niv Cohen​‌, J.Josef Tkadlec​​, P.Paul Rosu​​​‌, P.Piotr Padlewski​, S.Stanislaw Barzowski​‌, K.Kyle Montgomery​​, A.Aline Menezes​​​‌, A.Arkil Patel​, Z.Zixuan Wang​‌, J.Jamie Tucker-Foltz​​, J.Jack Stade​​​‌, T.Tom Goertzen​, F.Fereshteh Kazemi​‌, J.Jeremiah Milbauer​​, J. A.John​​​‌ Arnold Ambay, A.​Abhishek Shukla, Y.​‌ C.Yan Carlos Leyva​​ Labrador, A.Alan​​​‌ Givré, H.Hew​ Wolff, V.Vivien​‌ Rossbach, M. F.​​Muhammad Fayez Aziz,​​​‌ Y.Younesse Kaddar,​ Y.Yanxu Chen,​‌ R.Robin Zhang,​​ J.Jiayi Pan,​​​‌ A.Antonio Terpin,​ N.Niklas Muennighoff,​‌ H.Hailey Schoelkopf,​​ E.Eric Zheng,​​​‌ A.Avishy Carmi,​ A.Adam Jones,​‌ J.Jainam Shah,​​ E. D.Ethan D.​​​‌ L. Brown, K.​Kelin Zhu, M.​‌Max Bartolo, R.​​Richard Wheeler, A.​​​‌Andrew Ho, S.​Shaul Barkan, J.​‌Jiaqi Wang, M.​​Martin Stehberger, E.​​​‌Egor Kretov, K.​Kaustubh Sridhar, Z.​‌Zienab El-Wasif, A.​​Anji Zhang, D.​​​‌Daniel Pyda, J.​Joanna Tam, D.​‌ M.David M. Cunningham​​, V.Vladimir Goryachev​​​‌, D.Demosthenes Patramanis​, M.Michael Krause​‌, A.Andrew Redenti​​, D.Daniel Bugas​​​‌, D.David Aldous​, J.Jesyin Lai​‌, S.Shannon Coleman​​, M.Mohsen Bahaloo​​​‌, J.Jiangnan Xu​, S.Sangwon Lee​‌, S.Sandy Zhao​​, N.Ning Tang​​​‌, M. K.Michael​ K. Cohen, M.​‌Micah Carroll, O.​​Orr Paradise, J.​​​‌ H.Jan Hendrik Kirchner​, S.Stefan Steinerberger​‌, M.Maksym Ovchynnikov​​, J. O.Jason​​​‌ O. Matos, A.​Adithya Shenoy, B.​‌ A.Benedito Alves de​​ Oliveira Junior, M.​​​‌Michael Wang, Y.​Yuzhou Nie, P.​‌Paolo Giordano, P.​​Philipp Petersen, A.​​​‌Anna Sztyber-Betley, P.​Priti Shukla, J.​‌Jonathan Crozier, A.​​Antonella Pinto, S.​​​‌Shreyas Verma, P.​Prashant Joshi, Z.-X.​‌Zheng-Xin Yong, A.​​Allison Tee, J.​​​‌Jérémy Andréoletti, O.​Orion Weller, R.​‌Raghav Singhal, G.​​Gang Zhang, A.​​​‌Alexander Ivanov, S.​Seri Khoury, H.​‌Hamid Mostaghimi, K.​​Kunvar Thaman, Q.​​​‌Qijia Chen, T.​ Q.Tran Quoc Khánh​‌, J.Jacob Loader​​, S.Stefano Cavalleri​​​‌, H.Hannah Szlyk​, Z.Zachary Brown​‌, J.Jonathan Roberts​​, W.William Alley​​, K.Kunyang Sun​​​‌, R.Ryan Stendall‌, M.Max Lamparth‌​‌, A.Anka Reuel​​, T.Ting Wang​​​‌, H.Hanmeng Xu‌, S. G.Sreenivas‌​‌ Goud Raparthi, P.​​Pablo Hernández-Cámara, F.​​​‌Freddie Martin, D.‌Dmitry Malishev, T.‌​‌Thomas Preu, T.​​Tomek Korbak, M.​​​‌Marcus Abramovitch, D.‌Dominic Williamson, Z.‌​‌Ziye Chen, B.​​Biró Bálint, M.​​​‌ S.M Saiful Bari‌, P.Peyman Kassani‌​‌, Z.Zihao Wang​​, B.Behzad Ansarinejad​​​‌, L. P.Laxman‌ Prasad Goswami, Y.‌​‌Yewen Sun, H.​​Hossam Elgnainy, D.​​​‌Daniel Tordera, G.‌George Balabanian, E.‌​‌Earth Anderson, L.​​Lynna Kvistad, A.​​​‌ J.Alejandro José Moyano‌, R.Rajat Maheshwari‌​‌, A.Ahmad Sakor​​, M.Murat Eron​​​‌, I. C.Isaac‌ C. Mcalister, J.‌​‌Javier Gimenez, I.​​Innocent Enyekwe, A.​​​‌ F.Andrew Favre D.‌ O., S.Shailesh‌​‌ Shah, X.Xiaoxiang​​ Zhou, F.Firuz​​​‌ Kamalov, R.Ronald‌ Clark, S.Sherwin‌​‌ Abdoli, T.Tim​​ Santens, K.Khalida​​​‌ Meer, H. K.‌Harrison K Wang,‌​‌ K.Kalyan Ramakrishnan,​​ E.Evan Chen,​​​‌ A.Alessandro Tomasiello,‌ G. B.G. Bruno‌​‌ de Luca, S.-Z.​​Shi-Zhuo Looi, V.-K.​​​‌Vinh-Kha Le, N.‌Noam Kolt, N.‌​‌Niels Mündler, A.​​Avi Semler, E.​​​‌Emma Rodman, J.‌Jacob Drori, C.‌​‌ J.Carl J Fossum​​, M.Milind Jagota​​​‌, R.Ronak Pradeep‌, H.Honglu Fan‌​‌, T.Tej Shah​​, J.Jonathan Eicher​​​‌, M.Michael Chen‌, K.Kushal Thaman‌​‌, W.William Merrill​​, C.Carter Harris​​​‌, J.Jason Gross‌, I.Ilya Gusev‌​‌, A.Asankhaya Sharma​​, S.Shashank Agnihotri​​​‌, P.Pavel Zhelnov‌, S.Siranut Usawasutsakorn‌​‌, M.Mohammadreza Mofayezi​​, S.Sergei Bogdanov​​​‌, A.Alexander Piperski‌, M.Marc Carauleanu‌​‌, D. K.David​​ K. Zhang, D.​​​‌Dylan Ler, R.‌Roman Leventov, I.‌​‌Ignat Soroko, T.​​Thorben Jansen, P.​​​‌Pascal Lauer, J.‌Joshua Duersch, V.‌​‌Vage Taamazyan, W.​​Wiktor Morak, W.​​​‌Wenjie Ma, W.‌William Held, T.‌​‌ Đ.Tran Đuc Huy​​, R.Ruicheng Xian​​​‌, A. R.Armel‌ Randy Zebaze, M.‌​‌Mohanad Mohamed, J.​​ N.Julian Noah Leser​​​‌, M. X.Michelle‌ X Yuan, L.‌​‌Laila Yacar, J.​​Johannes Lengler, H.​​​‌Hossein Shahrtash, E.‌Edson Oliveira, J.‌​‌ W.Joseph W. Jackson​​, D. E.Daniel​​​‌ Espinosa Gonzalez, A.‌Andy Zou, M.‌​‌Muthu Chidambaram, T.​​Timothy Manik, H.​​​‌Hector Haffenden, D.‌Dashiell Stander, A.‌​‌Ali Dasouqi, A.​​Alexander Shen, E.​​​‌Emilien Duc, B.‌Bita Golshani, D.‌​‌David Stap, M.​​Mikalai Uzhou, A.​​​‌ B.Alina Borisovna Zhidkovskaya‌, L.Lukas Lewark‌​‌, M.Mátyás Vincze​​​‌, D.Dustin Wehr​, C.Colin Tang​‌, Z.Zaki Hossain​​, S.Shaun Phillips​​​‌, J.Jiang Muzhen​, F.Fredrik Ekström​‌, A.Angela Hammon​​, O.Oam Patel​​​‌, N.Nicolas Remy​, F.Faraz Farhidi​‌, G.George Medley​​, F.Forough Mohammadzadeh​​​‌, M.Madellene Peñaflor​, H.Haile Kassahun​‌, A.Alena Friedrich​​, C.Claire Sparrow​​​‌, T.Taom Sakal​, O.Omkar Dhamane​‌, A. K.Ali​​ Khajegili Mirabadi, E.​​​‌Eric Hallman, M.​Mike Battaglia, M.​‌Mohammad Maghsoudimehrabani, H.​​Hieu Hoang, A.​​​‌Alon Amit, D.​Dave Hulbert, R.​‌Roberto Pereira, S.​​Simon Weber, S.​​​‌Stephen Mensah, N.​Nathan Andre, A.​‌Anton Peristyy, C.​​Chris Harjadi, H.​​​‌Himanshu Gupta, S.​Stephen Malina, S.​‌Samuel Albanie, W.​​Will Cai, M.​​​‌Mustafa Mehkary, F.​Frank Reidegeld, A.-K.​‌Anna-Katharina Dick, C.​​Cary Friday, J.​​​‌Jasdeep Sidhu, W.​Wanyoung Kim, M.​‌Mariana Costa, H.​​Hubeyb Gurdogan, B.​​​‌Brian Weber, H.​Harsh Kumar, T.​‌Tong Jiang, A.​​Arunim Agarwal, C.​​​‌Chiara Ceconello, W.​ S.Warren S. Vaz​‌, C.Chao Zhuang​​, H.Haon Park​​​‌, A. R.Andrew​ R. Tawfeek, D.​‌Daattavya Aggarwal, M.​​Michael Kirchhof, L.​​​‌Linjie Dai, E.​Evan Kim, J.​‌Johan Ferret, Y.​​Yuzhou Wang, M.​​​‌Minghao Yan, K.​Krzysztof Burdzy, L.​‌Lixin Zhang, A.​​Antonio Franca, D.​​​‌ T.Diana T. Pham​, K. Y.Kang​‌ Yong Loh, J.​​Joshua Robinson, S.​​​‌Shreen Gul, G.​Gunjan Chhablani, Z.​‌Zhehang Du, A.​​Adrian Cosma, C.​​​‌Colin White, R.​Robin Riblet, P.​‌Prajvi Saxena, J.​​Jacob Votava, V.​​​‌Vladimir Vinnikov, E.​Ethan Delaney, S.​‌Shiv Halasyamani, S.​​ M.Syed M. Shahid​​​‌, J.-C.Jean-Christophe Mourrat​, L.Lavr Vetoshkin​‌, R.Renas Bacho​​, V.Vincent Ginis​​​‌, A.Aleksandr Maksapetyan​, F.Florencia de​‌ la Rosa, X.​​Xiuyu Li, G.​​​‌Guillaume Malod, L.​Leon Lang, J.​‌Julien Laurendeau, F.​​Fatimah Adesanya, J.​​​‌Julien Portier, L.​Lawrence Hollom, V.​‌Victor Souza, Y.​​ A.Yuchen Anna Zhou​​​‌, Y.Yiğit Yalın​, G. D.Gbenga​‌ Daniel Obikoya, L.​​Luca Arnaboldi, F.​​​‌Filippo Bigi, K.​Kaniuar Bacho, P.​‌Pierre Clavier, G.​​Gabriel Recchia, M.​​​‌Mara Popescu, N.​Nikita Shulga, N.​‌ M.Ngefor Mildred Tanwie​​, T. C.Thomas​​​‌ C. H. Lux,​ B.Ben Rank,​‌ C.Colin Ni,​​ A.Alesia Yakimchyk,​​​‌ H.Huanxu Liu,​ O.Olle Häggström,​‌ E.Emil Verkama,​​ H.Himanshu Narayan,​​​‌ H.Hans Gundlach,​ L.Leonor Brito-Santana,​‌ B.Brian Amaro,​​ V.Vivek Vajipey,​​ R.Rynaa Grover,​​​‌ Y.Yiyang Fan,‌ G. P.Gabriel Poesia‌​‌ Reis E Silva,​​ L.Linwei Xin,​​​‌ Y.Yosi Kratish,‌ J.Jakub Łucki,‌​‌ W.-D.Wen-Ding Li,​​ J.Justin Xu,​​​‌ K. J.Kevin Joseph‌ Scaria, F.Freddie‌​‌ Vargus, F.Farzad​​ Habibi, E.Emanuele​​​‌ Rodolà, J.Jules‌ Robins, V.Vincent‌​‌ Cheng, D.Declan​​ Grabb, I.Ida​​​‌ Bosio, T.Tony‌ Fruhauff, I.Ido‌​‌ Akov, E. J.​​Eve J. Y. Lo​​​‌, H.Hao Qi‌, X.Xi Jiang‌​‌, B.Ben Segev​​, J.Jingxuan Fan​​​‌, S.Sarah Martinson‌, E. Y.Erik‌​‌ Y. Wang, K.​​Kaylie Hausknecht, M.​​​‌ P.Michael P. Brenner‌, M.Mao Mao‌​‌, Y.Yibo Jiang​​, X.Xinyu Zhang​​​‌, D.David Avagian‌, E. J.Eshawn‌​‌ Jessica Scipio, M.​​ R.Muhammad Rehan Siddiqi​​​‌, A.Alon Ragoler‌, J.Justin Tan‌​‌, D.Deepakkumar Patil​​, R.Rebeka Plecnik​​​‌, A.Aaron Kirtland‌, R. G.Roselynn‌​‌ Grace Montecillo, S.​​Stephane Durand, O.​​​‌ F.Omer Faruk Bodur‌, Z.Zahra Adoul‌​‌, M.Mohamed Zekry​​, G.Guillaume Douville​​​‌, A.Ali Karakoc‌, T. C.Tania‌​‌ C. B. Santos,​​ S.Samir Shamseldeen,​​​‌ L.Loukmane Karim,‌ A.Anna Liakhovitskaia,‌​‌ N.Nate Resman,​​ N.Nicholas Farina,​​​‌ J. C.Juan Carlos‌ Gonzalez, G.Gabe‌​‌ Maayan, S.Sarah​​ Hoback, R. d.​​​‌Rodrigo de Oliveira Pena‌, G.Glen Sherman‌​‌, H.Hodjat Mariji​​, R.Rasoul Pouriamanesh​​​‌, W.Wentao Wu‌, G.Gözdenur Demir‌​‌, S.Sandra Mendoza​​, I.Ismail Alarab​​​‌, J.Joshua Cole‌, D.Danyelle Ferreira‌​‌, B.Bryan Johnson​​, H.Hsiaoyun Milliron​​​‌, M.Mohammad Safdari‌, L.Liangti Dai‌​‌, S.Siriphan Arthornthurasuk​​, A.Alexey Pronin​​​‌, J.Jing Fan‌, A.Angel Ramirez-Trinidad‌​‌, A.Ashley Cartwright​​, D.Daphiny Pottmaier​​​‌, O.Omid Taheri‌, D.David Outevsky‌​‌, S.Stanley Stepanic​​, S.Samuel Perry​​​‌, L.Luke Askew‌, R. A.Raúl‌​‌ Adrián Huerta Rodríguez,​​ A.Abdelkader Dendane,​​​‌ S.Sam Ali,‌ R.Ricardo Lorena,‌​‌ K.Krishnamurthy Iyer,​​ S. M.Sk Md​​​‌ Salauddin, M.Murat‌ Islam, J.Juan‌​‌ Gonzalez, J.Josh​​ Ducey, R.Russell​​​‌ Campbell, M.Maja‌ Somrak, V.Vasilios‌​‌ Mavroudis, E.Eric​​ Vergo, J.Juehang​​​‌ Qin, B.Benjámin‌ Borbás, E.Eric‌​‌ Chu, J.Jack​​ Lindsey, A.Anil​​​‌ Radhakrishnan, A.Antoine‌ Jallon, I. M.‌​‌I. M. J. Mcinnis​​, A.Alex Hoover​​​‌, S.Sören Möller‌, S.Song Bian‌​‌, J.John Lai​​, T.Tejal Patwardhan​​​‌, S.Summer Yue‌, A.Alexandr Wang‌​‌ and D.Dan Hendrycks​​. A benchmark of​​​‌ expert-level academic questions to‌ assess AI capabilities.‌​‌Nature6498099January​​​‌ 2026, 1139-1146HAL​DOIback to text​‌
• 16 articleG. P.​​Giuseppe Parasiliti Rantone,​​​‌ N.Nora Aïssiouene,​ Y.Yohan Penel and​‌ P.-Y.Pierre-Yves Lagrée.​​ Modeling gas flow in​​​‌ a looped thermosyphon with​ a 1 D low-Mach​‌ number expansion.International​​ Journal of Thermal Sciences​​​‌220July 2025,​ 110323In press. HAL​‌DOIback to text​​

Conferences without proceedings

• 17​​​‌ inproceedingsN.Nathalie Ayi​. Graph and Mean-Field​‌ Limits for Interacting Particle​​ Systems.Festum Pi​​​‌ 2024La Canée, Crète,​ Greece2025HALback​‌ to text
• 18 inproceedings​​E.Etienne Meunier,​​​‌ S.Said Ouala,​ H.Hugo Frezat,​‌ J. L.Julien Le​​ Sommer and R.Ronan​​​‌ Fablet. Towards fully​ differentiable neural ocean model​‌ with Veros.EurIPS​​ 2025 - Differentiable Systems​​​‌ and Scientific Machine Learning​ - A workshop @​‌Copenhagen, DenmarkNovember 2025​​, 1-8HALback​​​‌ to text

Scientific books​

• 19 bookJ.Julien​‌ Guillod. Python Programming​​ for Mathematics.The​​​‌ Python SeriesChapman &​ Hall/CRCJanuary 2025HAL​‌DOI

Doctoral dissertations and​​ habilitation theses

• 20 thesis​​​‌D. N.Djahou Norbert​ Tognon. Time parallelization​‌ and machine learning for​​ optimal control and inverse​​​‌ problems.Sorbonne Université​June 2025HAL

Reports​‌ & preprints

• 21 misc​​N.Nina Aguillon,​​​‌ E.Emmanuel Audusse,​ N.Nelly Boulos and​‌ M.Martin Parisot.​​ A comprehensive list of​​​‌ stationary solutions of shallow​ water models.April​‌ 2025HALback to​​ text
• 22 miscN.​​​‌Nina Aguillon and S.​Sophie Hörnschemeyer. Barotropic-Baroclinic​‌ Splitting for Multilayer Shallow​​ Water Models with Exchanges​​​‌.January 2026HAL​back to text
• 23​‌ miscD.Dallas Albritton​​, J.Julien Guillod​​​‌, M.Mikhail Korobkov​ and X.Xiao Ren​‌. Forward self-similar solutions​​ to the 2D Navier--Stokes​​​‌ equations.January 2026​HALback to text​‌
• 24 miscA.-L.Anne-Laure​​ Dalibard and C.Corentin​​​‌ Gentil. A linear​ model of separation for​‌ western boundary currents with​​ bathymetry.December 2025​​​‌HALback to text​
• 25 miscF.Frédéric​‌ Hecht, S.-M.Sidi-Mahmoud​​ Kaber, L.Lucas​​​‌ Perrin, A.Alain​ Plagne and J.Julien​‌ Salomon. Parallel approximation​​ of the exponential of​​​‌ semidefinite negative Hermitian matrices​.February 2025HAL​‌back to text
• 26​​ miscF.Felix Kwok​​​‌, J.Julien Salomon​ and D. N.Djahou​‌ N Tognon. Convergence​​ of ParaOpt for general​​​‌ Runge-Kutta time discretizations.​March 2025HALback​‌ to text
• 27 misc​​P.Pierre Lissy and​​​‌ L.Lucas Perrin.​ Theoretical and Numerical Study​‌ of the Convergence of​​ Luenberger Observers for a​​​‌ Linearized Water Wave Model​.February 2025HAL​‌back to text
• 28​​ miscÉ.Étienne Meunier​​​‌, D.David Kamm​, G.Guillaume Gachon​‌, R.Redouane Lguensat​​ and J.Julie Deshayes​​​‌. Learning to generate​ physical ocean states: Towards​‌ hybrid climate modeling.​​February 2025HALback​​​‌ to text
• 29 misc​D. N.Djahou N​‌ Tognon. ParaOpt for​​ unstable systems.February​​ 2025HALback to​​​‌ text

Software

• 30 software‌O.Olivier Delestre,‌​‌ C.Carine Lucas,​​ P.-A.Pierre-Antoine Ksinant Garcia​​​‌, F.Frédéric Darboux‌, C.Christian Laguerre‌​‌, A.-C.Anne-Céline Boulanger​​, N.Noémie Gaveau​​​‌, M.Maxime Rougier‌, M.Marco Mancini‌​‌, S.Stéphane Cordier​​ and F.François James​​​‌. SWASHES: Shallow Water‌ Analytic Solutions for Hydraulic‌​‌ and Environmental Studies.​​1.05.00April 2025Université​​​‌ d'Orléans (UO), Orléans, FRA.;‌ INRA Institut National de‌​‌ la Recherche Agronomique; CNRS​​ - Centre National de​​​‌ la Recherche Scientifique lic:‌ CeCILL Free Software License‌​‌ Agreement v2.0.HAL​​Software HeritageVCS