2023Activity reportProjectTeamANGE
RNSR: 201221061V Research center Inria Paris Centre at Sorbonne University
 In partnership with:CNRS, Sorbonne Université
 Team name: Numerical Analysis, Geophysics and Environment
 In collaboration with:Laboratoire JacquesLouis Lions (LJLL)
 Domain:Digital Health, Biology and Earth
 Theme:Earth, Environmental and Energy Sciences
Keywords
Computer Science and Digital Science
 A6. Modeling, simulation and control
 A6.1. Methods in mathematical modeling
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.4. Multiscale modeling
 A6.1.5. Multiphysics modeling
 A6.2. Scientific computing, Numerical Analysis & Optimization
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.6. Optimization
 A6.3. Computationdata interaction
 A6.3.2. Data assimilation
 A6.3.4. Model reduction
 A6.3.5. Uncertainty Quantification
Other Research Topics and Application Domains
 B3. Environment and planet
 B3.3. Geosciences
 B3.3.2. Water: sea & ocean, lake & river
 B3.3.3. Nearshore
 B3.4. Risks
 B3.4.1. Natural risks
 B3.4.3. Pollution
 B4. Energy
 B4.3. Renewable energy production
 B4.3.1. Biofuels
 B4.3.2. Hydroenergy
1 Team members, visitors, external collaborators
Research Scientists
 Julien Salomon [Team leader, INRIA, Senior Researcher, HDR]
 Jacques SainteMarie [INRIA, HDR]
Faculty Members
 Nina Aguillon [SORBONNE UNIVERSITE, Associate Professor]
 Emmanuel Audusse [Université Sorbonne Paris Nord, Associate Professor Delegation, from Sep 2023, HDR]
 Bernard Di Martino [UNIV CORSE, Associate Professor Delegation, HDR]
 Julien Guillod [SORBONNE UNIVERSITE, Associate Professor Delegation, until Aug 2023]
PostDoctoral Fellow
 Louis Thiry [INRIA, PostDoctoral Fellow, from Oct 2023]
PhD Students
 Nelly Boulos Al Makary [UNIV PARIS XIII, ATER, until Aug 2023]
 Juliette Dubois [INRIA, until Oct 2023]
 Chourouk El Hassanieh [SorbonneUniversité, from Sep 2023]
 Chourouk El Hassanieh [UNIV LIBANAISE, until Aug 2023]
 Allan Gouvenaux [CEA]
 Antoine Leblond [SORBONNE UNIVERSITE, until Aug 2023]
 Léon Migus [SORBONNE UNIVERSITE, until Sep 2023]
 Lucas Perrin [INRIA]
 Djahou Norbert Tognon [INRIA]
Technical Staff
 Sibylle Techene [CNRS, Engineer, until Aug 2023]
Interns and Apprentices
 Dana Zilberberg [INRIA, Intern, from May 2023 until Sep 2023]
Administrative Assistants
 Laurence Bourcier [INRIA]
 Julien Guieu [INRIA]
Visiting Scientist
 MarieOdile Bristeau [Retired from INRIA, external collaborator of ANGE]
2 Overall objectives
2.1 Presentation
Among all aspects of geosciences, we mainly focus on gravity driven flows arising in many situations such as
 hazardous flows (flooding, rogue waves, landslides...),
 sustainable energies (hydrodynamicsbiology coupling, biofuel production, marine energies...),
 risk management and landuse planning (morphodynamic evolutions, early warning systems...)
There exists a strong demand from scientists and engineers in fluid mechanics for models and numerical tools able to simulate not only the water depth and the velocity field but also the distribution and evolution of external quantities such as pollutants or biological species and the interaction between flows and structures (seashores, erosion processes...). The key point of the researches carried out within ANGE is to answer this demand by the development of efficient, robust and validated models and numerical tools.
2.2 Scientific challenges
Due to the variety of applications with a wide range of spatial scales, reducedsize models like the shallow water equations are generally required. From the modelling point of view, the main issue is to describe the behaviour of the flow with a reducedsize model taking into account several physical processes such as nonhydrostatic terms, biological species evolution, topography and structure interactions within the flow. The mathematical analysis of the resulting model do not enter the field of hyperbolic equations anymore and new strategies have to be proposed. Moreover, efficient numerical resolutions of reducedsize models require particular attention due to the different time scales of the processes and in order to recover physical properties such as positivity, conservativity, entropy dissipation and equilibria.
The models can remain subject to uncertainties that originate from incomplete description of the physical processes and from uncertain parameters. Further development of the models may rely on the assimilation of observational data and the uncertainty quantification of the resulting analyses or forecasts.
3 Research program
3.1 Overview
The research activities carried out within the ANGE team strongly couple the development of methodological tools with applications to real–life problems and the transfer of numerical codes. The main purpose is to obtain new models adapted to the physical phenomena at stake, identify the main properties that reflect the physical meaning of the models (uniqueness, conservativity, entropy dissipation, ...), propose effective numerical methods to approximate their solution in complex configurations (multidimensional, unstructured meshes, wellbalanced, ...) and to assess the results with data in the purpose of potentially correcting the models.
The difficulties arising in gravity driven flow studies are threefold.
 Models and equations encountered in fluid mechanics (typically the free surface NavierStokes equations) are complex to analyze and solve.
 The underlying phenomena often take place over large domains with very heterogeneous length scales (size of the domain, mean depth, wave length, ...) and distinct time scales, e.g. coastal erosion, propagation of a tsunami, ...
 These problems are multiphysics with strong couplings and nonlinearities.
3.2 Modelling and analysis
Hazardous flows are complex physical phenomena that can hardly be represented by shallow water type systems of partial differential equations (PDEs). In this domain, the research program is devoted to the derivation and analysis of reduced complexity models compared to the NavierStokes equations, but relaxing the shallow water assumptions. The main purpose is then to obtain models welladapted to the physical phenomena at stake.
Even if the resulting models do not strictly belong to the family of hyperbolic systems, they exhibit hyperbolic features: the analysis and discretisation techniques we intend to develop have connections with those used for hyperbolic conservation laws. It is worth noticing that the need for robust and efficient numerical procedures is reinforced by the smallness of dissipative effects in geophysical models which therefore generate singular solutions and instabilities.
On the one hand, the derivation of the SaintVenant system from the NavierStokes equations is based on two approximations (the socalled shallow water assumptions), namely
 the horisontal fluid velocity is well approximated by its mean value along the vertical direction,
 the pressure is hydrostatic or equivalently the vertical acceleration of the fluid can be neglected compared to the gravitational effects.
As a consequence the objective is to get rid of these two assumptions, one after the other, in order to obtain models accurately approximating the incompressible Euler or NavierStokes equations.
On the other hand, many applications require the coupling with nonhydrodynamic equations, as in the case of microalgae production or erosion processes. These new equations comprise nonhyperbolic features and a special analysis is needed.
Multilayer approach
As for the first shallow water assumption, multilayer systems were proposed to describe the flow as a superposition of SaintVenant type systems 28, 31, 32. Even if this approach has provided interesting results, layers are considered separate and nonmiscible fluids, which implies strong limitations. That is why we proposed a slightly different approach 29, 30 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.
Nonhydrostatic 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 NavierStokes equations, we obtain at the leading order the SaintVenant system. Going one step further leads to a vertically averaged version of the Euler/NavierStokes equations involving some nonhydrostatic 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 SaintVenant system when the nonhydrostatic pressure term vanishes,
 it consists in a set of conservation laws with source terms,
 it does not contain high order derivatives.
Multiphysics 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 multiphysics 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 wellknown 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 nonpenetration 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 modeltype.
 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.
3.3 Numerical analysis
Nonhydrostatic scheme
The main challenge in the study of the nonhydrostatic 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 nonhydrostatic model looks like an extension of the SaintVenant 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).
AsymptoticPreserving 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 AsymptoticPreserving (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 socalled 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 partialdifferential equations concerning the first point. The second one can be fixed using partially implicit scheme.
Multiphysics 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 submodel, whether it be hydrodynamic or nonhydrodynamic.
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 welldefined 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.
4 Application domains
4.1 Overview
Sustainable development and environment preservation have a growing importance and scientists have to address difficult issues such as: management of water resources, renewable energy production, bio/geochemistry of oceans, resilience of society w.r.t. hazardous flows, urban pollutions, ...
As mentioned above, the main issue is to propose models of reduced complexity, suitable for scientific computing and endowed with stability properties (continuous and/or discrete). In addition, models and their numerical approximations have to be confronted with experimental data, as analytical solutions are hardly accessible for these problems/models. A. Mangeney (IPGP) and N. Goutal (EDF) may provide useful data.
4.2 Geophysical flows
Reduced models like the shallow water equations are particularly welladapted to the modelling of geophysical flows since there are characterized by large time or/and space scales. For long time simulations, the preservation of equilibria is essential as global solutions are a perturbation around them. The analysis and the numerical preservation of nontrivial equilibria, more precisely when the velocity does not vanish, are still a challenge. In the fields of oceanography and meteorology, the numerical preservation of the socalled geostrophic state, which is the balance between the gravity field and the Coriolis force, can significantly improve the forecasts. In addition, data assimilation is required to improve the simulations and correct the dissipative effect of the numerical scheme.
The sediment transport modelling is of major interest in terms of applications, in particular to estimate the sustainability of facilities with silt or scour, such as canals and bridges. Dredging or fillingup operations are expensive and generally not efficient in the long term. The objective is to determine a configuration almost stable for the facilities. In addition, it is also important to determine the impact of major events like emptying dam which is aimed at evacuating the sediments in the dam reservoir and requires a large discharge. However, the downstream impact should be measured in terms of turbidity, river morphology and flood.
4.3 Hydrological disasters
It is a violent, sudden and destructive flow. Between 1996 and 2005, nearly 80% of natural disasters in the world have meteorological or hydrological origines. The main interest of their study is to predict the areas in which they may occur most probably and to prevent damages by means of suitable amenities. In France, floods are the most recurring natural disasters and produce the worst damages. For example, it can be a cause or a consequence of a dam break. The large surface they cover and the long period they can last require the use of reduced models like the shallow water equations. In urban areas, the flow can be largely impacted by the debris, in particular cars, and this requires fluid/structure interactions be well understood. Moreover, underground flows, in particular in sewers, can accelerate and amplify the flow. To take them into account, the model and the numerical resolution should be able to treat the transition between free surface and underground flows.
Tsunamis are another hydrological disaster largely studied. Even if the propagation of the wave is globally well described by the shallow water model in oceans, it is no longer the case close to the epicenter and in the coastal zone where the bathymetry leads to vertical accretions and produces substantial dispersive effects. The nonhydrostatic terms have to be considered and an efficient numerical resolution should be induced.
While viscous effects can often be neglected in water flows, they have to be taken into account in situations such as avalanches, debris flows, pyroclastic flows, erosion processes, ...i.e. when the fluid rheology becomes more complex. Gravity driven granular flows consist of solid particles commonly mixed with an interstitial lighter fluid (liquid or gas) that may interact with the grains and decrease the intensity of their contacts, thus reducing energy dissipation and favoring propagation. Examples include subaerial or subaqueous rock avalanches (e.g. landslides).
4.4 Biodiversity and culture
Nowadays, simulations of the hydrodynamic regime of a river, a lake or an estuary, are not restricted to the determination of the water depth and the fluid velocity. They have to predict the distribution and evolution of external quantities such as pollutants, biological species or sediment concentration.
The potential of microalgae as a source of biofuel and as a technological solution for CO2 fixation is the subject of intense academic and industrial research. Largescale production of microalgae has potential for biofuel applications owing to the high productivity that can be attained in highrate raceway ponds. One of the key challenges in the production of microalgae is to maximize algae growth with respect to the exogenous energy that must be used (paddlewheel, pumps, ...). There is a large number of parameters that need to be optimized (characteristics of the biological species, raceway shape, stirring provided by the paddlewheel). Consequently our strategy is to develop efficient models and numerical tools to reproduce the flow induced by the paddlewheel and the evolution of the biological species within this flow. Here, mathematical models can greatly help us reduce experimental costs. Owing to the high heterogeneity of raceways due to gradients of temperature, light intensity and nutrient availability through water height, we cannot use depthaveraged models. We adopt instead more accurate multilayer models that have recently been proposed. However, it is clear that many complex physical phenomena have to be added to our model, such as the effect of sunlight on water temperature and density, evaporation and external forcing.
Many problems previously mentioned also arise in larger scale systems like lakes. Hydrodynamics of lakes is mainly governed by geophysical forcing terms: wind, temperature variations, ...
4.5 Sustainable energy
One of the booming lines of business is the field of renewable and decarbonated energies. In particular in the marine realm, several processes have been proposed in order to produce electricity thanks to the recovering of wave, tidal and current energies. We may mention waterturbines, buoys turning variations of the water height into electricity or turbines motioned by currents. Although these processes produce an amount of energy which is less substantial than in thermal or nuclear power plants, they have smaller dimensions and can be set up more easily.
The fluid energy has kinetic and potential parts. The buoys use the potential energy whereas the waterturbines are activated by currents. To become economically relevant, these systems need to be optimized in order to improve their productivity. While for the construction of a harbour, the goal is to minimize swell, in our framework we intend to maximize the wave energy.
This is a complex and original issue which requires a fine model of energy exchanges and efficient numerical tools. In a second step, the optimisation of parameters that can be changed in reallife, such as bottom bathymetry and buoy shape, must be studied. Eventually, physical experiments will be necessary for the validation.
4.6 Urban environment
The urban environment is essentially studied for air and noise pollutions. Air pollution levels and noise pollution levels vary a lot from one street to next. The simulations are therefore carried out at street resolution and take into account the city geometry. The associated numerical models are subject to large uncertainties. Their input parameters, e.g. pollution emissions from road traffic, are also uncertain. Quantifying the simulation uncertainties is challenging because of the high computational costs of the numerical models. An appealing approach in this context is the use of metamodels, from which ensembles of simulations can be generated for uncertainty quantification.
The simulation uncertainties can be reduced by the assimilation of fixed and mobile sensors. Highquality fixed monitoring sensors are deployed in cities, and an increasing number of mobile sensors are added to the observational networks. Even smartphones can be used as noise sensors and dramatically increase the spatial coverage of the observations. The processing and assimilation of the observations raises many questions regarding the quality of the measurements and the design of the network of sensors.
4.7 SmartCity
There is a growing interest for environmental problems at city scale, where a large part of the population is concentrated and where major pollutions can occur. Numerical simulation is well established to study the urban environment, e.g. for road traffic modelling. As part of the smartcity movement, an increasing number of sensors collect measurements, at traditional fixed observation stations, but also on mobile devices, like smartphones. They must properly be taken into account given their number but also their potential low quality.
Pratical applications include air pollution and noise pollution. These directly relate to road traffic. Data assimilation and uncertainty propagation are key topics in these applications.
5 Social and environmental responsibility
5.1 Footprint of research activities
Only few travels were done last year (including one flight) as a consequence of a will of the team to avoid this type of transportation.
5.2 Impact of research results
Part of ANGE activity is devoted to research on renewable energy. In this way, the team took part to the organization of the EMRSim 22 conference, which devoted to Marine Energy Techniques and Simulation.
6 Highlights of the year
 J. Salomon has been promoted to the DR1 grade.

2023 was a year of evaluation for our projectteam. This evaluation, coordinated by Inria's Evaluation Committee, is an important step in the team's life cycle. In particular, it enabled us to elaborate collectively on the future of all teams involved in the environmental sciences theme. We have produced a summary of this foresight, which raises more questions than it answers, but which reflects the topic's complexity and the debate that has opened up within the institute itself.
This report can be found here.
7 New software, platforms, open data
7.1 New software
7.1.1 Freshkiss

Name:
FREe Surface Hydrodynamics using KInetic SchemeS

Keywords:
Finite volume methods, Hydrostatic NavierStokes equations, Free surface flows

Functional Description:
Freshkiss3D is a numerical code solving the 3D hydrostatic and incompressible NavierStokes equations with variable density.

Contact:
Jacques Sainte Marie

Participants:
Fabien Souillé, Emmanuel Audusse, Jacques Sainte Marie, MarieOdile 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:

Contact:
Jacques Sainte Marie

Participants:
Emmanuel Audusse, Jacques Sainte Marie, Raouf Hamouda
7.1.3 Verdandi

Keywords:
HPC, Model, Software Components, Partial differential equation

Functional Description:
Verdandi is a free and opensource (LGPL) library for data assimilation. It includes various such methods for coupling one or several numerical models and observational data. Mainly targeted at large systems arising from the discretization of partial differential equations, the library is devised as generic, which allows for applications in a wide range of problems (biology and medicine, environment, image processing, etc.). Verdandi also includes tools to ease the application of data assimilation, in particular in the management of observations or for a priori uncertainty quantification. Implemented in C++, the library may be used with models implemented in Fortran, C, C++ or Python.
 URL:

Contact:
Vivien Mallet

Participants:
Dominique Chapelle, Gautier Bureau, Nicolas Claude, Philippe Moireau, Vivien Mallet
7.1.4 Polyphemus

Keyword:
Simulation

Functional Description:
Polyphemus is a modeling system for air quality. As such, it is designed to yield uptodate simulations in a reliable framework: data assimilation, ensemble forecast and daily forecasts. Its completeness makes it suitable for use in many applications: photochemistry, aerosols, radionuclides, etc. It is able to handle simulations from local to continental scales, with several physical models. It is divided into three main parts:
libraries that gather data processing tools (SeldonData), physical parameterizations (AtmoData) and postprocessing abilities (AtmoPy),
programs for physical preprocessing and chemistrytransport models (Polair3D, Castor, two Gaussian models, a Lagrangian model),
model drivers and observation modules for model coupling, ensemble forecasting and data assimilation.
 URL:

Contact:
Vivien Mallet

Participants:
Sylvain Doré, Vivien Mallet
7.1.5 Urban noise analysis

Keyword:
Environment perception

Functional Description:
This software processes mobile observations collected by the application Ambiciti (previously known as SoundCity). It can merge simulated noise maps with the mobile observations.

Authors:
Raphaël Ventura, Vivien Mallet, Guillaume Chérel

Contact:
Vivien Mallet
7.1.6 Freshkiss3D

Keywords:
Python, Cython, NavierStokes

Functional Description:
Tool for the numerical solution of free surface NavierStokes equations
 Publication:

Contact:
Jacques Sainte Marie

Participants:
Cedric Doucet, Apolline El Baz, Jacques Sainte Marie

Partner:
UPMC
8 New results
8.1 Numerical methods
8.1.1 Optimal periodic resource allocation in reactive dynamical systems: Application to microalgal production.
Participants: LiuDi Lu, Julien Salomon.
Coll. with Olivier Bernard In 8, we focus on a periodic resource allocation problem applied to a dynamical system which comes from a biological system. More precisely, we consider a system with $N$ resources and $N$ activities, each activity use the allocated resource to evolve up to a given time T > 0 where a control (represented by a given permutation) will be applied on the system to reallocate the resources. The goal is to find the optimal control strategies which optimize the cost or the benefit of the system. This problem can be illustrated by an industrial biological application, namely, the optimization of a mixing strategy to enhance the growth rate in a microalgal raceway system. A mixing device, such as a paddle wheel, is considered to control the rearrangement of the depth of the algae cultures, hence the light perceived at each lap. We prove that if the dynamics of the system is periodic, then the period corresponds to one reallocation whatever the order of the involved permutation matrix is. A nonlinear optimization problem for one reallocation process is then introduced. Since $N$! permutations need to be tested in the general case, it can be numerically solved only for a limited number of $N$. To overcome this difficulty, we introduce a second optimization problem which provides a suboptimal solution of the initial problem, but whose solution can be determined explicitly. A sufficient condition to characterize cases where the two problems have the same solution is given. Some numerical experiments are performed to assess the benefit of optimal strategies in various settings.
8.1.2 Evaluation of tsunami inundation in the plain of Martil (north Morocco): Comparison of four inundation estimation methods.
Participants: Apolline El Baz, Jacques SainteMarie.
other participants: Elise Basquin, Alain Rabaute, Maud Thomas, Sara Lafuerza, Abdelmounim El M'Rini, Denis Mercier, Elia D'acremont, MarieOdile Bristeau, Axel Creach
The Alboran Basin may be subject to tsunami hazards. If such an event were to occur, it is expected that the urbanised and densely populated areas of northern Moroccan coastline would be affected. Precise inundation hazard maps are needed for tsunami risk management in this region. In 6, we argue that the diversity of hazard mapping methods ensures the robustness of the scientific knowledge about the exposure of a territory. Hence, the main objective of this study is to analyse the exposure of the plain of Martil (north of Morocco), by using four hazard mapping methods to create inundation maps for two scenarios of tsunamis generated by extreme submarine mass failure (SMF) in the Alboran Sea, of 0.9 km3 and 3.8 km3 respectively. A digital terrain model of the plain was used to explore four methods of inundation mapping. The static method identified 4.32 km2 and 19.83 km2 of flooded areas for each scenario using water height values as inundation thresholds. The hybrid and the volumetric methods use the volume of water to determine the inundation extent. For the first scenario, 3.51 km2 of the plain were inundated using the hybrid method, and 20.11 km2 for the second scenario. The results of the volumetric methods are 2.32 km2 and 7.82 km2 respectively for the first and second scenario. Finally, the fourth method relies on numerical hydrodynamic modelling of tsunami inundation (Freshkiss3d® code). With this method, 4.55 km2 of the plain were flooded in the first scenario, and 24.12 km2 for the second. The comparison of the results highlights that the most sensitive areas to tsunami inundation are the lowest topographic ones, being the beaches and the wadis floodplains. This result raises questions on the current coastal development and the preparedness of its population, thus calling for more attention to engage on tsunami risk management related questions.
8.1.3 Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discretetime schemes
Participants: PierreMarie Boulvard.
other participant: Etienne Mémin
In 10, we characterize numerically through two criteria the Lévy area related to unresolved fluctuation velocities associated to a stochastic coarsescale representation of geophysical fluid flow dynamics. We study in particular whether or not the process associated to the random unresolved velocity components exhibits a Lévy area corresponding to a Wiener process, and if the law of this process can reasonably be approached by a centered Dirac measure. This exploration enables us to answer positively to a conjecture made for the constitution of highorder discrete time evolution schemes for stochastic representation defined from stochastic transport.
8.1.4 Stability of implicit neural networks for longterm forecasting in dynamical systems
Participants: Léon Migus, Julien Salomon.
other participant: Patrick Gallinari
Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been proposed. They are all based on autoregressive methods and exhibit stability issues. Drawing inspiration from the stability property of implicit numerical schemes, we introduce in 14 a stable autoregressive implicit neural network. We develop a theory based on the stability definition of schemes to ensure the stability in forecasting of this network. It leads us to introduce hard constraints on its weights and propagate the dynamics in the latent space. Our experimental results validate our stability property, and show improved results at longterm forecasting for two transports PDEs.
8.1.5 INFINITY: Neural Field Modeling for ReynoldsAveraged NavierStokes Equations
Participants: Leon Migus.
other participant: Louis Serrano, Yuan Yin, Jocelyn Ahmed Mazari, Patrick Gallinari
For numerical design, the development of efficient and accurate surrogate models is paramount. They allow us to approximate complex physical phenomena, thereby reducing the computational burden of direct numerical simulations. In 15, we propose INFINITY, a deep learning model that utilizes implicit neural representations (INRs) to address this challenge. Our framework encodes geometric information and physical fields into compact representations and learns a mapping between them to infer the physical fields. We use an airfoil design optimization problem as an example task and we evaluate our approach on the challenging AirfRANS dataset, which closely resembles realworld industrial usecases. The experimental results demonstrate that our framework achieves stateoftheart performance by accurately inferring physical fields throughout the volume and surface. Additionally we demonstrate its applicability in contexts such as design exploration and shape optimization: our model can correctly predict drag and lift coefficients while adhering to the equations.
8.2 Modelling
8.2.1 LowMach type approximation of the NavierStokes system with temperature and salinity for free surface flows.
Participants: Léa Boittin, MarieOdile Bristeau, Anne Mangeney, Jacques SainteMarie, Fabien Souillé.
Coll. with François Bouchut In 9, we are interested in free surface flows where density variations coming e.g. from temperature or salinity differences play a significant role in the hydrodynamic regime. In water, acoustic waves travel much faster than gravity and internal waves, hence the study of models arising from compressible fluid mechanics often requires a decoupling between these waves. Starting from the compressible NavierStokes system, we derive the socalled NavierStokesFourier system in an "incompressible" regime using the lowMach scaling, hence filtering the acoustic waves, neglecting the density dependency on the fluid pressure but keeping its variations in terms of temperature and salinity. A slightly modified lowMach asymptotics is proposed to obtain a model with thermomechanical compatibility. The case when the density depends only on the temperature is studied first. Then the variations of the fluid density with respect to temperature and salinity are considered, and it seems to be the first time that salinity dependency is considered in this low Mach limit. We give a layeraveraged formulation of the obtained models in an hydrostatic context, allowing to derive numerical schemes endowed with strong stability properties that are presented in a companion paper. Several stability properties of the layeraveraged NavierStokesFourier system are proved.
8.2.2 Acoustic and gravity waves in the ocean: a new derivation of a linear model from the compressible Euler equation
Participants: Juliette Dubois, Sébastien Imperiale, Anne Mangeney, François Bouchut, Jacques SainteMarie.
In 11, we construct an accurate linear model describing the propagation of both acoustic and gravity waves in water. This original model is obtained by the linearization of the compressible Euler equations, written in Lagrangian coordinates. The system is studied in the isentropic case, with a free surface, an arbitrary bathymetry, and vertical variations of the background temperature and density. We show that our model is an extension of some models from the literature to the case of a nonbarotropic fluid with a variable sound speed. Other models from the literature are recovered from our model through two asymptotic analyses, one for the incompressible regime and one for the acoustic regime. We also propose a method to write the model in Eulerian coordinates. Our model includes many physical properties, such as the existence of internal gravity waves or the variation of the sound speed with depth.
8.2.3 Numerical Investigations of Nonuniqueness for the Navier–Stokes Initial Value Problem in Borderline Spaces
Participants: Julien Guillod.
Other participants: Vladimír Šverák
In 13, we consider the Cauchy problem for the incompressible Navier–Stokes equations in for a oneparameter family of explicit scaleinvariant axisymmetric initial data, which is smooth away from the origin and invariant under the reflection with respect to the xyplane. Working in the class of axisymmetric fields, we calculate numerically scaleinvariant solutions of the Cauchy problem in terms of their profile functions, which are smooth. The solutions are necessarily unique for small data, but for large data we observe a breaking of the reflection symmetry of the initial data through a pitchforktype bifurcation. By a variation of previous results by Jia and Šverák (Invent Math 196(1):233265, 2013) it is known rigorously that if the behavior seen here numerically can be proved, optimal nonuniqueness examples for the Cauchy problem can be established, and two different solutions can exists for datum which is divergencefree, smooth away from the origin, compactly supported, and locally homogeneous near the origin. In particular, assuming our (finitedimensional) numerics represents faithfully the behavior of the full (infinitedimensional) system, the problem of uniqueness of the Leray–Hopf solutions (with nonsmooth initial data) has a negative answer and, in addition, the perturbative arguments such those by Kato (Math Z 187(4):471480, 1984) and Koch and Tataru (Adv Math 157(1):2235, 2001), or the weakstrong uniqueness results by Leray, Prodi, Serrin, Ladyzhenskaya and others, already give essentially optimal results. There are no singularities involved in the numerics, as we work only with smooth profile functions. It is conceivable that our calculations could be upgraded to a computerassisted proof, although this would involve a substantial amount of additional work and calculations, including a much more detailed analysis of the asymptotic expansions of the solutions at large distances.
8.3 Assessments of models by means of experimental data and assimilation
8.3.1 On the Marginal Cost of the Duration of a Wildfire
Participants: Frédéric Allaire, Vivien Mallet.
Other participants: Antoine Belgodere, JeanBaptiste Filippi, Florian Guéniot
Avoiding catastrophic wildfires is a natural rationale for fighting fires in their early stage. Beside this benefit, may a marginal decrease in the duration of smaller wildfires be worthwhile? The present article addresses this topic by estimating the marginal damage of the duration of forest fires. In 7, we perform two sets of wildfire simulations in Corsica, and estimate the damage based on the type of land use in burned areas. Results suggest that the marginal cost of the duration of fires rises by a factor of 4 during the first 400 minutes. The two reasons appear to be the increase in the marginal burned area (a physical mechanism) and the increase in the value of the marginal burned area, due to the ignition points being located in lowvalue places (a human mechanism). Using a conservative calibration, our results corroborate the principle of early initial attack already in use in countries with sufficient fire fighting forces, but subject to debate because of its cost.
8.4 Other contribution
8.4.1 A Parareal algorithm for a highly oscillating VlasovPoisson system with reduced models for the coarse solving
Participants: Julien Salomon.
Other participants: Laura Grigori, Sever A Hirstoaga
In 12, we introduce a new strategy for solving highly oscillatory twodimensional VlasovPoisson systems by means of a specific version of the parareal algorithm. The novelty consists in using reduced models, obtained from the twoscale convergence theory, for the coarse solving. The reduced models are useful to approximate the original VlasovPoisson model at a low computational cost since they are free of high oscillations. Both models are numerically solved in a particleincell framework. We illustrate this strategy with numerical experiments based on long time simulations of a charged beam in a focusing channel and under the influence of a rapidly oscillating external electric field. On the basis of computing times, we provide an analysis of the efficiency of the parareal algorithm in terms of speedup.
9 Bilateral contracts and grants with industry
Participants: Yohan Penel.
Yohan Penel, who left the team in 2022, supervised the PhD thesis of Giuseppe Parasiliti about the Physical, mathematical and numerical modelling of a gas flow for the transportation of liquified natural gas. This work is the result of a close collaboration with the corporation GTT, which has already collaborated with ANGE in the last years, through the Carnot institute SMILE. The defens
Participants: Jacques SainteMarie.
Jacques SainteMarie has a contract with Eaux de Paris about Hydraulic modeling, calibration and diagnosis. (20202023, with S. Labbé, Laboratoire D'Alembert and LPSM)
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

Title:
Intelligence Artificielle, Données et Modèles pour Comprendre les Océans et le Changement Climatique (OCEANIA)
 Program:

Duration:
11.202010.2024

Local supervisor:
Julien Salomon

Partners:
 ANGE, BIOCORE, TAU Inria teams, France
 Universidad de Chile (Center of Mathematical Modeling), Chile
 Pontificia Universidad Catól ica de Chile, Chile
 Fondation TARA Océan, France,
 GOSEE CNRS Federation, France
 Université de Nantes (ComBi team), France

Inria contact:
Julien Salomon

Summary:
There is strong scientific evidence of the negative effects of climate change on the ocean. These changes will have a drastic impact on nearly all life forms in the ocean, as well as additional consequences for food security and ecosystems in coastal communities as well as inland. Despite these impacts, scientific data and infrastructure are still lacking to better understand and quantify the consequences of these disturbances on the marine ecosystem. There is a need not only to collect more data, but also to develop and apply stateoftheart mechanisms capable of transforming this data into real knowledge, policy, and action. This is where artificial intelligence, machine learning and modeling tools are needed. OceanIA, this ambitious interdisciplinary Inria Challenge, aims to develop new artificial intelligence and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the Ocean and its role in regulating and sustaining the biosphere and fighting climate change. OceanIA is also an opportunity to structure Inria's contributions around a global scientific challenge in the convergence of artificial intelligence, biodiversity and climate change.
10.1.2 STIC/MATH/CLIMAT AmSud projects

Title:
Mathematical analysis of neural networks for solving partial differential equations and inverse problems

Program:
MATHAmSud

Duration:
January 1, 2023 – December 31, 2024

Local supervisor:
Julien Salomon

Partners:
 Inria Chile
 Escuela Politecnica Nacional
 Pont. Cath. Univ. of Chile

Inria contact:
Julien Salomon

Summary:
This program aims at investigating techniques that combine neural network and PDE modelling. In a first work, we consider Holocene dust transport simulation using PINN.
10.2 International research visitors
 MayJune 2023: visit of F. Kwok (Université Laval, Canada). Work on time parallelization and preconditionning.
 June 2023: visit of G. Ciaramella (MOX, Polytechnico de Milano). Work about greedy approaches for identification.
 July 2023: visit of H. Carillon (Universidad de Chile (Center of Mathematical Modeling), Chile). Work on topography reconstruction.
 Oct. 2023: visit of G. Barennechea (U. Strathclyde, Ecosse) NS simulation incompressible with free surface.
 Dec. 2023: visit of S. Hörnschemeyer (RWTH Aachen, Allemagne).
10.3 National initiatives
Projet Emergence (20212023)
Participants: Julien Guillod.
 Project acronym: Emergence
 Project title: Etudes numériques d'équations fluides
 Coordinator: Julien Guillod (SU)
 Funding: 28 000 euros.
Projet Emergence (20232025)
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.
Bourses PEPS JCJC (2023)
Participants: Nathalie Ayi.
 Project title: Étude numérique et théorique d'équations cinétiques en présence de stochasticité
 Coordinator: Nathalie Ayi (SU)
 Funding: 4500 euros.
Tremplin Jeunes Chercheurs et Jeunes Chercheuses de SU (20222023)
Participants: Nina Aguillon.
 Project title: Antidiffusive advection scheme in the NEMO ocean global circulation model
 Coordinator: Nina Aguillon (SU)
 Funding: 10 000 euros.
ANR ALLOWAPP (20192024)
Participants: Julien Salomon.
 Project acronym: ALLOWAPP
 Project title: Algorithmes pour l'optimisation à grande échelle de problèmes de propagation d'ondes
 Coordinator: Laurence Halpern (Université ParisNord)
 Funding: 317 891 euros.
The goal of the ALLOWAPP project is the design of spacetime parallel algorithms for largescale optimization problems associated with wave propagation phenomena. Such problems appear in seismology, geophysics, but also in various applications from data assimilation. The large amount of data and the volume of computations required for the accurate numerical solution of wave propagation problems, within an optimization loop, requires the use of massively parallel computers. Timeparallel methods have experienced a great development in the last ten years, and for parabolic problems an almost perfect efficiency for a large number of processors has been achieved (scalability). It is quite different for wave propagation problems. In this project, we propose to develop robust, efficient and scalable methods for spacetime parallelization of these optimization problems.
ANR GeoFun (20202024)
Participants: Nina Aguillon.
 Project acronym: GeoFun
 Project title: Ecoulements géophysiques avec des modèles unifiés
 Coordinator: Martin Parisot (INRIA Bordeaux SudOuest)
 Funding: 524 880 euros.
The GeoFun project aims to improve the modeling and simulation of geophysical flows involving at least two different processes. Numerical simulation of watersheds and estimation of water resources is the main application of the project's achievements. In this context, a free surface flow (rivers, lakes) is the upper part of a groundwater flow (water table). Our vision of river transport is often naive, because we think first of rivers, lakes and floods, but in reality, 80 % of the water of the continents is underground. Sometimes, the porous substratum is covered by an impermeable rock stratum, which confines the flow as in pipes, except for some points where springs and resurgences appear.
ANR SingFlows (20192023)
Participants: Julien Guillod.
 Project acronym: SingFlows
 Project title: Ecoulements avec singularités : couches limites, filaments de vortex, interaction vaguestructure
 Coordinator: David GerardVaret (Institut de mathématiques de Jussieu  Paris Rive Gauche)
 Funding: 263 628 euros.
The objective of SingFlows is to develop mathematical and numerical tools for the analysis of three problems in fluid dynamics: the behaviour of anisotropic flows (boundary layers, shallow water flows), the dynamics of vortical structures, and the evolution of fixed or floating structures in water waves. Our will to unify these different problems is natural, because they share many mathematical features. The underlying keypoint is that they are described by singular solutions of Euler or NavierStokes equations. The word singular refers here:  either to a lack of smoothness: it applies for instance to vortex filaments, which are Dirac masses along curves, or to the contact line between water and the floating structure,  or to a singular dependence of the solution with respect to a parameter, typically the Reynolds number (like in boundary layers). The connection between the two points of view is usually made by viscous regularization of the nonsmooth structure, or conversely by taking the vanishing limit of the parameter. More generally, the three problems considered in SingFlows involve flows with very small scales. A relevant description then requires the derivation of reduced models.
ANR Saphir (20222024)
Participants: Jacques SainteMarie, Bernard Di Martino.
 Project acronym: Saphir
 Project title: Sensor Augmented weather Prediction at high Resolution
 Coordinator: JF. Muzy (Université de Toulouse Paul Sabatier)
 Funding: 296 000 euros.
ANR DEEPNUM (20222026)
Participants: Julien Salomon, Jacques SainteMarie.
 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 (INRIAANGE), Machine Learning and DNNs (Sorbonne – MLIA), DEs and Biophysics (INRIAEPIONE).
ANR MEGA (20232028)
Participants: Bernard Di Martino, Jacques SainteMarie, Nina Aguillon.
 Project acronym: MEGA
 Project title: Giant submarine landslides in gas hydrate provinces: a comparison of the Nile and Amazon deepsea fans
 Coordinator: Sébastien Mingeon
 Funding: 533,348 euros.
Giant submarine landslides (102000 km3) are found in the thick Quaternary sediment succession of passive continental margins. Their ages coincide with periods of sealevel 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 involve excess pore pressures linked to reductions in gashydrate 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 deepsea fans that experience different forms of climate forcing over glacialinterglacial 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.
GdR MathGeoPhy (2022–2027)
Participants: Emmanuel Audusse, Bernard di Martino, Nicole Goutal, Martin Parisot, Jacques SainteMarie.
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
 micromacro approaches, granular and complex flows
 fluvial and torrential hydrodynamics, extreme events and environmental risks, landslides, avalanches, volcanic eruptions, glaciology, etc.
GdR EOLEMR (2021–2026)
Participants: Julien Salomon, Jacques SainteMarie.
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 knowhow 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
11 Dissemination
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
Member of the organizing committees
 JG took part of the organization of the conference FoCM 2023 at Paris,
 JS coorganized the conference "Workshop on Assimilation, Control and Computational Speedup", Villetaneuse (France), 67 juin 2023.
 JS coorganizes the bimonthly seminar "Rencontres INRIAJLL en analyse numérique et calcul scientifique"
 JG coorganizes the monthly seminar "Analyse nonlinéaire et EDP"
 JG coorganizes the monthly seminar "InfoMath"
 NAg coorganizes the yearly "Journée interne du Laboratoire JL. Lions"
 NAg coorganizes Hyp 2023, Bordeaux
Reviewer
The team members served as referees for the following journals:
 JS: SIAM SISC, IEEE TAC,
 JG: Journal of Functional Analysis, Journal of Mathematical Fluid Mechanics, Journal of Differential Equations, Inventiones
 BDM: M2AN
 NAyi: Journal of Differential Equations, Kinetic and Related Models
 EA: Computer & Fluids, Calcolo, CMS
 NAgui: Journal of Advances in Modelling Earth Systems
 LM: NeurIPS 2023, ICLR 2024
 EG: M2AN, Siam SISC
 JSM: Nonlinear dynamics, M2AN, Acta Applicandae Mathematicae
11.1.2 Journal
JS is editor in chief of MATAPLI (national journal of the applied maths community). EA is responsible for its section "Du côté des écoles d’ingénieurs".
11.1.3 Invited talks
 JG: Prague summer school on Stochastic in Fluids Institute of Mathematics of the Academy of Sciences of Czech Republic 21/0825/08
 NAgui: séminaire RWTH, Aachen, 18/07
 NAgui: Séminaire de calcul scientifique et modélisation IMB, Bordeaux 23/03
 EG: NumHyp23: Numerical Methods for Hyperbolic Problems Bordeaux 2630/06/2023
 NAyi: Round mean field 2 Rome, Italie 1314/06/2023
 NAyi: Classical and Quantum Mechanical Models of ManyParticle Systems Oberwolfach, Allemagne 0408/09/2023
 NAyi: Séminaire du Laboratoire de Mathématiques de Bretagne Atlantique Brest 14/4
 NAyi: Groupe de travail Analyse, Modélisation & Simulation Paris Cité 21/05
 NAyi: Séminaire Denis Poisson Orléans 25/05
 NAyi: Séminaire Analyse Numérique et EDP Paris Saclay 15/06
 NAyi: Séminaire Modélisation, Analyse, Calcul Toulouse 17/10/23
 NAyi: Journées internes du laboratoire Jacques Louis Lions, 22/11/23
 NAyi: Séminaire de l'équipe EDP Analyse Numérique Nice 14/12/23
11.1.4 Leadership within the scientific community
 EA is adjoint director of GDR MathGeoPhy (2022)
 JS is member of the board of AMIES (20182023)
11.1.5 Research administration
 NAyi was in the selection committee of an assistant professor (Maître de Conférences) in Orsay and ENS Lyon
 JS is member of Scientific Job commission (CES, 2018)
 JS is an elected member of social administration council of INRIA (CSA de l'INRIA, 2023)
 JS is an elected member of the evaluation commission (2023)
 JSM is scientific director adjoint of INRIA (2019)
 JG is member of administration council of IHP (20212023)
 JSM is belongs to External advisory board  ERC Synergy 20202024
 JSM Coadvisor of PEPR 'agroécologie et numérique' 20222028
 JSM is responsible for the 'Numérique et environnement' program (2022)
 NAyi is a member of the LJLL laboratoire council (2020  )
 EA is a member of CR and CAC at USPN (20202024)
 NAgui is member of Scientific Job commission (CES, 2023)
11.2 Faculty administration
 JG belongs to Bonus allocation committee at (Comission d'attribution des primes à )
 NAyi Substitute on the Bonus Committee at (Comission d'attribution des primes à )
 JG belongd to Equality and antidiscrimination referent for UFR 929, SU (Référent égalité et luttre contre les discriminations pour l'UFR 929, SU)
 NAg is member of the integration cycle department council (conseil de département du cycle d'intégration)
 NAg is member of CAPSULE ( center for pedagogical support and experimentation  centre d'accompagnement à la pédagogie et support à l'expérimentation)
 NAyi belongs to University national council (CNU section 26)
 JG is member of the faculty council (UFR 929), SU
 NAgui is member of the faculty council (UFR 929), SU
 NAyi is member of the scientific committee of the faculty council (UFR 929), SU
11.3 Teaching  Supervision  Juries
11.3.1 Teaching
EG is the president of commission française pour l'enseignement des mathématiques (CFEM)
Teaching activities of ANGE are summarized in the following.

Participants: Julien Salomon.
 Méthodes numériques pour des modèles incluants des EDP, 45,M2,Université d'AbomeyCalavi, Bénin CM

Participants: Jacques SainteMarie.
 Modélisation des écoulements gravitaires 40H, M1, Univ. ParisDiderot et IPGP
 Méthodes numériques en géosciences 50H, M2H, Univ. ParisDiderot et IPGP
 Hyperbolic models for complex flows 25H, M2, SU

Participants: Nathalie Ayi.
 Approximation des EDPs 36H M1 CM
 EDO 18H L2 TD
 Algèbre linéaire 10H L2 Colles
 " Responsabilité du parcours BiDI InfoMath L2L3", 12H, L2L3, SU, responsabilité

Participants: Juliette Dubois.
 Structures mathématiques, 22H, L3, Polytech Sorbonne TD

Participants: Nina Aguillon.
 Directrice des études de L2 mathématiques, 64H, L2, , responsabilité
 Topologie et calcul différentiel 1, 36H, L2, , TD
 Modèles hyperboliques d'écoulements complexes dans le domaine de l'environnement, 10H, M2, SU, CM
 Formation des nouveaux moniteurs en mathématiques 8H, D, SU, responsabilité
 Atelier de Recherche Encadrée 30H, L1, SU, TD

Participants: Bernard Di Martino.
 Calcul différentiel 54H, L3, Université de Corse, CM,TD
 Pratiques d'Algèbre 18H, L1, Université de Corse, TP
 Pratique d'Analyse 18H, L1, Université de Corse, TP
 Pratique d'Algèbre 18H, L2, Université de Corse, TP
 Pratique d'Analyse 18H, L2, Université de Corse, TP

Participants: Emmanuel Audusse.
 Optimisation, 30H, ING2, USPN, TDTP
 Calcul scientifique, 30H, L2, USPN, CMTDTP
 TP analyse numérique avec Matlab, 30H, L3 (ING1), USPN

Participants: Julien Guillod.
 Programmation Python pour les mathématiques, 45H, L2, SU, TP/TD
 Fondements des méthodes numériques, 48H, M1, SU, TD

Participants: Nelly Boulos.
 Mathématiques pour les études scientifiques, 36H, L1, SU, TP

Participants: Lucas Perrin.
 Méthodes numériques : algèbre matricielle et fonctions d'une variable réelle, 40H, L2, Univ. ParisDauphine, TP+TD
 Analyse de Fourier, 28H, L3, Polytech Sorbonne, TD

Participants: Antoine Leblond.
 Analyse numérique, 72H, L3, TP, TD+TP

Participants: Léon Migus.
 Informatique 2 (fortran), 40H, M1, Polytech Sorbonne, TP

Participants: Chourouk El Hassanieh.
 Mathématiques pour les études scientifiques 2, 38H, L1, SU, TD
11.3.2 Supervision
The format is here supervisior, grade, student, institution, period, title.
 JS, PhD, Lucas Perrin, SU, 20212024, Parallélisation en temps et assimilation de données
 JS (with Patrick Gallinari), PhD, Léon Migus, SU, 20202023, Deep Neural Networks and Differential Equations
 JS, PhD, Norbert Tognon, SU, 20222025, Techniques d'accélération pour le contrôle optimal
 JS (with Patrick Armand), PhD, Allan Gouvenaux, CEA, 20232026, Métamodélisation pour la simulation rapide de phénomènes de transport
 BDM, JSM, JG, EG (with Samer Israwi, Libanese university), PhD, Chourouk El Hassanieh, Inria 20192023, Analysis and numerical approximation of some mathematical models freesurface flows
 JSM (with Sébastien Impériale), PhD, Juliette Dubois, Inria 20202023, Modélisation et approximation numérique de la propagation des ondes acoustique et des ondes de gravité dans les fluides à surface libre
 YP (with Nora Aissiouene and PierreYves Lagrée), PhD, Giuseppe Parasiliti, SU, 20202023, Physical, mathematical and numerical modelling of a gas flow for the transportation of liquified natural gas
 JG, ALD, PhD, Antoine Leblond, SU, 09.202011.2023, Wellposedness and longtime behaviour of the Stokestransport equation
 JSM (with Etienne Mémin), Postdoc, PierreMarie Boulvard, Inria 20212023, Location uncertainties in free surface flows models  Numerical analysis and implementation in Freshkiss3d
 EA, F. Benkhaldoun, PhD, Laila Baroukh, USPN, 20212024, Simulation numérique pour des écoulements partiellement congestionnés avec rhéologie complexe
 BDM, Master, Dana Zilberberg, SU, Ecole des ponts, 2023, On the Caracterization of Hyberbolicity of FreeSurface Euler Equations
11.3.3 Juries
 JS, 23.11.2023, PhD, Referee, Rishabh BHATT, LJK, Univ. Grenoble Parallel In Time Algorithms for Data Assimilation
 JS, 01.12.2023, PhD, Jury, Advisor, Leon Migus, LIP6ISIRLJLL (SU), Réseaux de neurones profonds et équations aux dérivées partiellles
 JS, 12.2023, PhD, Jury, Yohan Poirier, ECN, Contribution à l’accélération d’un code de calcul des interactions vagues/structures basée sur la théorie potentielle instationnaire des écoulements à surface libre
 JS, 12.2023, PhD, Jury, Vuong, LAGA, SorbonneParisNord, Controle optimal et décomposition de domaines
 JG, 12.2023, PhD, Jury, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models freesurface flows
 EG, 12.2023, PhD, Jury, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models freesurface flows
 BDM, 12.2023, PhD, Jury, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models freesurface flows
 JSM, 12.2023, PhD, Jury, Advisor, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models freesurface flows
 JSM, 12.2023, PhD, Jury, Advisor, Juliette Dubois, SU, Acousticgravity waves in free surface flows: modeling: analysis and simulation towards tsunami early warning systems
 NAyi, 09.2023, PhD, Jury, Corentin Le Bihan, ENS Lyon, Effets de bord et comportement en temps long en théorie cinétique collisionnelle
11.4 Popularization
 JSM organized Journée de la FSMP : "A l'eau les maths"
 JS coorganized a roundtable discussion at the forum emploimaths ("Pollution, des mesures aux solutions" )
11.4.1 Interventions
 Julien Salomon
 décembre 2023 : Accueil de Collégiens
 janvier 2023 : Intervention "Chiche" au lycée Charlemagne
 Nina Aguillon
 2018 : coorganisation de Mathematic Park (public licence et prépa)
 janvier 2023 : présentation métier dans un lycée
 (with N. Ayi) mars 2023 : organisation d'une journée filles, maths et info, une équation lumineuse à SU: accueil de 100 lycéennes, programme 2 conférences scientifiques, rencontre avec des étudiantes, visite du campus, speed meeting métier (20 intervenantes), théâtre forum
 mai 2023 :exposé lors de la journée "maths en mouvement" de la FSMP
 Jacques SainteMarie
 octobre 2022 : Ambassadeur pour la fête de la science 2022
 2022 : MOOC 'impact environnemental du numérique'
 Nathalie Ayi
 Sept 2022  ... : Création du podcast Têteàtête Chercheuse(s) et réseaux sociaux associés
 Mai 2022  ... : Participation à l'exposition "Mathématiques, Informatique ... avec elles" par l'association Femmes et Mathématiques
 2023 ... : ambassadrice de la Maison Poincaré
 mai 2023 : exposé grand public lors de l'évènement "L'IHES célèbre les mathématiciennes"
 mai 2023 : exposé grand public lors du salon de la cuture et jeux mathématiques
 octobre 2023 : exposé grand public lors de la cérémonie de remise des prix des Olympiades de Mathématiques
 novembre 2023 : exposé en ligne aux étudiantes du lycée Nelson Mandela, Pibrac
 novembre 2023 : exposé dans le lycée dans le cadre des "Villon conférences", Beaugency
 novembre 2023 : exposé et atelier mathématiques dans le collège Henri Becquerel, Avoine
 décembre 2023 : exposé dans le lycée SaintBarthélémy, Nice
 Juliette Dubois
 décembre 2022 : Intervention devant des lycéens et lycéennes, Lycée Racine Paris
 Julien Guillod
 mai 2023 : stage de formation pour les enseignantes et enseignants du secondaire
12 Scientific production
12.1 Major publications
 1 articleApproximation of the hydrostatic NavierStokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation.J. Comput. Phys.2302011, 34533478URL: http://dx.doi.org/10.1016/j.jcp.2011.01.042DOI
 2 articleA multilayer SaintVenant system with mass exchanges for Shallow Water flows. Derivation and numerical validation.ESAIM Math. Model. Numer. Anal.452011, 169200URL: http://dx.doi.org/10.1051/m2an/2010036DOI
 3 articleAn energyconsistent depthaveraged Euler system: derivation and properties.Discrete and Continuous Dynamical Systems  Series B2042015, 28
 4 unpublishedAnalysis of the Blade Element Momentum Theory.April 2020, working paper or preprintHAL
 5 articleVertically averaged models for the free surface Euler system. Derivation and kinetic interpretation.Math. Models Methods Appl. Sci. (M3AS)2132011, 459490URL: http://dx.doi.org/10.1142/S0218202511005118DOI
12.2 Publications of the year
International journals
 6 articleEvaluation of tsunami inundation in the plain of Martil (north Morocco): Comparison of four inundation estimation methods.Natural Hazards ResearchJune 2023HALDOIback to text
 7 articleOn the Marginal Cost of the Duration of a Wildfire.Journal of Forest Economics3832023, 265292HALDOIback to text
 8 articleOptimal periodic resource allocation in reactive dynamical systems: Application to microalgal production.International Journal of Robust and Nonlinear Control339June 2023, 49895010HALDOIback to text
 9 articleLowMach type approximation of the NavierStokes system with temperature and salinity for free surface flows.Communications in Mathematical Sciences211January 2023, 151172HALDOIback to text
 10 articleDiagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discretetime schemes.Foundations of Data Science2023, 125HALDOIback to text
 11 articleAcoustic and gravity waves in the ocean: a new derivation of a linear model from the compressible Euler equation.Journal of Fluid Mechanics970September 2023, A28HALDOIback to text
 12 articleA Parareal algorithm for a highly oscillating VlasovPoisson system with reduced models for the coarse solving.Computers & Mathematics with Applications1302023, 137148HALback to text
 13 articleNumerical Investigations of Nonuniqueness for the Navier–Stokes Initial Value Problem in Borderline Spaces.Journal of Mathematical Fluid Mechanics253August 2023, 46HALDOIback to text
Conferences without proceedings
 14 inproceedingsStability of implicit neural networks for longterm forecasting in dynamical systems.ICLR 2023 Workshop on Physics for Machine LearningKigali, RwandaMay 2023HALback to text
 15 inproceedingsINFINITY: Neural Field Modeling for ReynoldsAveraged NavierStokes Equations.Workshop on Synergy of Scientific and Machine Learning Modeling (ICML 2023)Honolulu, HI, United StatesJuly 2023HALback to text
Doctoral dissertations and habilitation theses
 16 thesisStationary solutions and wellbalanced schemes for the shallow water model with two velocities and topography.Sorbonne Paris Nord; Inria Paris, Équipe ANGE2022, URL: https://hal.science/tel03990996
 17 thesisAnalysis and numerical approximation of some mathematical models of freesurface flows.Sorbonne Université; Université Libanaise; Inria Paris, Équipe ANGEDecember 2023HAL
 18 thesisWellposedness and longtime behaviour of the Stokestransport equation.Sorbonne UniversitéNovember 2023HAL
 19 thesisDeep neural networks and partial differential equations.Sorbonne UniversitéDecember 2023HAL
Reports & preprints
 20 miscEnergy stable and linearly wellbalanced numerical schemes for the nonlinear Shallow Water equations with Coriolis force.July 2023HAL
 21 miscGraph Limit for Interacting Particle Systems on Weighted Random Graphs.July 2023HAL
 22 miscLongtime behavior of the Stokestransport system in a channel.June 2023HAL
 23 miscHyperbolicity of a semiLagrangian formulation of the hydrostatic freesurface Euler system.August 2023HAL
 24 miscMechanical balance laws for twodimensional Boussinesq systems.January 2024HAL
 25 miscImplicit kinetic schemes for the SaintVenant system.March 2023HAL
 26 miscHyperbolic reduced model for VlasovPoisson equation with FokkerPlanck collision.April 2023HAL
 27 miscParallel approximation of the exponential of Hermitian matrices.June 2023HAL
12.3 Cited publications
 28 articleA multilayer SaintVenant model~: Derivation and numerical validation.Discrete Contin. Dyn. Syst. Ser. B522005, 189214back to text
 29 articleApproximation of the hydrostatic NavierStokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation.J. Comput. Phys.2302011, 34533478URL: http://dx.doi.org/10.1016/j.jcp.2011.01.042DOIback to text
 30 articleA multilayer SaintVenant system with mass exchanges for Shallow Water flows. Derivation and numerical validation.ESAIM Math. Model. Numer. Anal.452011, 169200URL: http://dx.doi.org/10.1051/m2an/2010036DOIback to text
 31 article A robust wellbalanced scheme for multilayer shallow water equations.Discrete Contin. Dyn. Syst. Ser. B132010, 739758back to text
 32 articleNumerical simulation of twolayer shallow water flows through channels with irregular geometry.J. Comput. Phys.19512004, 202235back to text