2023Activity reportProject-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 28, 31, 32. 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 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.

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 Verdandi

• Keywords:
  HPC, Model, Software Components, Partial differential equation
• Functional Description:
  Verdandi is a free and open-source (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:
  http://­verdandi.­gforge.­inria.­fr/
• 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 up-to-date 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 post-processing abilities (AtmoPy),

  programs for physical pre-processing and chemistry-transport models (Polair3D, Castor, two Gaussian models, a Lagrangian model),

  model drivers and observation modules for model coupling, ensemble forecasting and data assimilation.

• URL:
  http://­cerea.­enpc.­fr/­polyphemus/
• 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, 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 Optimal periodic resource allocation in reactive dynamical systems: Application to microalgal production.

Participants: Liu-Di 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 Sainte-Marie.

other participants: Elise Basquin, Alain Rabaute, Maud Thomas, Sara Lafuerza, Abdelmounim El M'Rini, Denis Mercier, Elia D'acremont, Marie-Odile 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 discrete-time schemes

Participants: Pierre-Marie 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 coarse-scale 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 high-order discrete time evolution schemes for stochastic representation defined from stochastic transport.

8.1.4 Stability of implicit neural networks for long-term 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 auto-regressive methods and exhibit stability issues. Drawing inspiration from the stability property of implicit numerical schemes, we introduce in 14 a stable auto-regressive 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 long-term forecasting for two transports PDEs.

8.1.5 INFINITY: Neural Field Modeling for Reynolds-Averaged Navier-Stokes 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 real-world industrial use-cases. The experimental results demonstrate that our framework achieves state-of-the-art 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.

8.2.1 Low-Mach type approximation of the Navier-Stokes system with temperature and salinity for free surface flows.

Participants: Léa Boittin, Marie-Odile Bristeau, Anne Mangeney, Jacques Sainte-Marie, 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 hydrody-namic 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 Navier-Stokes system, we derive the so-called Navier-Stokes-Fourier system in an "incompressible" regime using the low-Mach 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 low-Mach asymptotics is proposed to obtain a model with thermo-mechanical 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 layer-averaged 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 layer-averaged Navier-Stokes-Fourier 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 Sainte-Marie.

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 non-barotropic 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 Non-uniqueness 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 one-parameter family of explicit scale-invariant axi-symmetric initial data, which is smooth away from the origin and invariant under the reflection with respect to the xy-plane. Working in the class of axi-symmetric fields, we calculate numerically scale-invariant 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 pitchfork-type bifurcation. By a variation of previous results by Jia and Šverák (Invent Math 196(1):233-265, 2013) it is known rigorously that if the behavior seen here numerically can be proved, optimal non-uniqueness examples for the Cauchy problem can be established, and two different solutions can exists for datum which is divergence-free, smooth away from the origin, compactly supported, and locally -homogeneous near the origin. In particular, assuming our (finite-dimensional) numerics represents faithfully the behavior of the full (infinite-dimensional) system, the problem of uniqueness of the Leray–Hopf solutions (with non-smooth initial data) has a negative answer and, in addition, the perturbative arguments such those by Kato (Math Z 187(4):471-480, 1984) and Koch and Tataru (Adv Math 157(1):22-35, 2001), or the weak-strong 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 computer-assisted 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.

8.3.1 On the Marginal Cost of the Duration of a Wildfire

Participants: Frédéric Allaire, Vivien Mallet.

Other participants: Antoine Belgodere, Jean-Baptiste 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 low-value 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.

8.4.1 A Parareal algorithm for a highly oscillating Vlasov-Poisson 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 two-dimensional Vlasov-Poisson systems by means of a specific version of the parareal algorithm. The novelty consists in using reduced models, obtained from the two-scale convergence theory, for the coarse solving. The reduced models are useful to approximate the original Vlasov-Poisson model at a low computational cost since they are free of high oscillations. Both models are numerically solved in a particle-in-cell 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.

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:
  11.2020-10.2024
• 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,
  • GO-SEE 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 state-of-the-art 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:
  MATH-AmSud
• 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.

Projet Emergence (2021-2023)

Participants: Julien Guillod.

• Project acronym: Emergence
• Project title: Etudes numériques d'équations fluides
• Coordinator: Julien Guillod (SU)
• Funding: 28 000 euros.

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.

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 (2022-2023)

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 (2019-2024)

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 Paris-Nord)
• Funding: 317 891 euros.

The goal of the ALLOWAPP project is the design of space-time parallel algorithms for large-scale 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. Time-parallel 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 space-time parallelization of these optimization problems.

ANR GeoFun (2020-2024)

Participants: Nina Aguillon.

• Project acronym: GeoFun
• Project title: Ecoulements géophysiques avec des modèles unifiés
• Coordinator: Martin Parisot (INRIA Bordeaux Sud-Ouest)
• 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 (2019-2023)

Participants: Julien Guillod.

• Project acronym: SingFlows
• Project title: Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure
• Coordinator: David Gerard-Varet (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 Navier-Stokes 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 non-smooth 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 (2022-2024)

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.

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 involve 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.

GdR MathGeoPhy (2022–2027)

Participants: Emmanuel Audusse, Bernard di Martino, Nicole Goutal, 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

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 co-organized the conference "Workshop on Assimilation, Control and Computational Speedup", Villetaneuse (France), 6-7 juin 2023.
• JS co-organizes the bi-monthly seminar "Rencontres INRIA-JLL en analyse numérique et calcul scientifique"
• JG co-organizes the monthly seminar "Analyse non-linéaire et EDP"
• JG co-organizes the monthly seminar "InfoMath"
• NAg co-organizes the yearly "Journée interne du Laboratoire J-L. Lions"
• NAg co-organizes Hyp 2023, Bordeaux

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 21/08-25/08
• 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 26-30/06/2023
• NAyi: Round mean field 2 Rome, Italie 13-14/06/2023
• NAyi: Classical and Quantum Mechanical Models of Many-Particle Systems Oberwolfach, Allemagne 04-08/09/2023
• 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 (2018-2023)

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 (2021-2023)
• JSM is belongs to External advisory board - ERC Synergy 2020-2024
• JSM Co-advisor of PEPR 'agroécologie et numérique' 2022-2028
• 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 (2020-2024)
• NAgui is member of Scientific Job commission (CES, 2023-)

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'Abomey-Calavi, Bénin CM

• Participants: Jacques Sainte-Marie.

  • Modélisation des écoulements gravitaires 40H, M1, Univ. Paris-Diderot et IPGP
  • Méthodes numériques en géosciences 50H, M2H, Univ. Paris-Diderot 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 Bi-DI Info-Math L2-L3", 12H, L2-L3, 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, TD-TP
  • Calcul scientifique, 30H, L2, USPN, CM-TD-TP
  • 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. Paris-Dauphine, 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, 2021-2024, Parallélisation en temps et assimilation de données
• JS (with Patrick Gallinari), PhD, Léon Migus, SU, 2020-2023, Deep Neural Networks and Differential Equations
• JS, PhD, Norbert Tognon, SU, 2022-2025, Techniques d'accélération pour le contrôle optimal
• JS (with Patrick Armand), PhD, Allan Gouvenaux, CEA, 2023-2026, Méta-modélisation pour la simulation rapide de phénomènes de transport
• BDM, JSM, JG, EG (with Samer Israwi, Libanese university), PhD, Chourouk El Hassanieh, Inria 2019-2023, Analysis and numerical approximation of some mathematical models free-surface flows
• JSM (with Sébastien Impériale), PhD, Juliette Dubois, Inria 2020-2023, 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 Pierre-Yves Lagrée), PhD, Giuseppe Parasiliti, SU, 2020-2023, Physical, mathematical and numerical modelling of a gas flow for the transportation of liquified natural gas
• JG, ALD, PhD, Antoine Leblond, SU, 09.2020-11.2023, Well-posedness and long-time behaviour of the Stokes-transport equation
• JSM (with Etienne Mémin), Post-doc, Pierre-Marie Boulvard, Inria 2021-2023, Location uncertainties in free surface flows models - Numerical analysis and implementation in Freshkiss3d
• EA, F. Benkhaldoun, PhD, Laila Baroukh, USPN, 2021-2024, 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 Free-Surface 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, LIP6-ISIR-LJLL (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, Sorbonne-Paris-Nord, Controle optimal et décomposition de domaines
• JG, 12.2023, PhD, Jury, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models free-surface flows
• EG, 12.2023, PhD, Jury, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models free-surface flows
• BDM, 12.2023, PhD, Jury, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models free-surface flows
• JSM, 12.2023, PhD, Jury, Advisor, Chourouk El Hassanieh, SU, Analysis and numerical approximation of some mathematical models free-surface flows
• JSM, 12.2023, PhD, Jury, Advisor, Juliette Dubois, SU, Acoustic-gravity 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

11.4.1 Interventions

• Julien Salomon
  • décembre 2023 : Accueil de Collégiens
  • janvier 2023 : Intervention "Chiche" au lycée Charlemagne
• Nina Aguillon
  • 2018- : co-organisation 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 Sainte-Marie
  • octobre 2022 : Ambassadeur pour la fête de la science 2022
  • 2022 : MOOC 'impact environnemental du numérique'
• Nathalie Ayi
  • Sept 2022 - ... : Création du podcast Tête-à-tête 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 Saint-Barthélémy, 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

International journals

• 6 articleE.Elise Basquin, A.Apolline El Baz, J.Jacques Sainte-Marie, A.Alain Rabaute, M.Maud Thomas, S.Sara Lafuerza, A.Abdelmounim El M'Rini, D.Denis Mercier, E.Elia D’acremont, M.-O.Marie-Odile Bristeau and A.Axel Creach. Evaluation of tsunami inundation in the plain of Martil (north Morocco): Comparison of four inundation estimation methods.Natural Hazards ResearchJune 2023HALDOIback to text
• 7 articleA.Antoine Belgodere, F.Frédéric Allaire, J.-B.Jean-Baptiste Filippi, V.Vivien Mallet and F.Florian Guéniot. On the Marginal Cost of the Duration of a Wildfire.Journal of Forest Economics3832023, 265-292HALDOIback to text
• 8 articleO.Olivier Bernard, L.Liu‐di Lu and J.Julien Salomon. Optimal periodic resource allocation in reactive dynamical systems: Application to microalgal production.International Journal of Robust and Nonlinear Control339June 2023, 4989-5010HALDOIback to text
• 9 articleL.Léa Boittin, M.-O.Marie-Odile Bristeau, F.François Bouchut, A.Anne Mangeney, J.Jacques Sainte-Marie and F.Fabien Souillé. Low-Mach type approximation of the Navier-Stokes system with temperature and salinity for free surface flows.Communications in Mathematical Sciences211January 2023, 151-172HALDOIback to text
• 10 articleP.-M.Pierre-Marie Boulvard and E.Etienne Mémin. Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes.Foundations of Data Science2023, 1-25HALDOIback to text
• 11 articleJ.Juliette Dubois, S.Sébastien Imperiale, A.Anne Mangeney, F.François Bouchut and J.Jacques Sainte-Marie. Acoustic 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 articleL.Laura Grigori, S. A.Sever A Hirstoaga and J.Julien Salomon. A Parareal algorithm for a highly oscillating Vlasov-Poisson system with reduced models for the coarse solving.Computers & Mathematics with Applications1302023, 137-148HALback to text
• 13 articleJ.Julien Guillod and V.Vladimír Šverák. Numerical Investigations of Non-uniqueness for the Navier–Stokes Initial Value Problem in Borderline Spaces.Journal of Mathematical Fluid Mechanics253August 2023, 46HALDOIback to text

Conferences without proceedings

• 14 inproceedingsL.Léon Migus, J.Julien Salomon and P.Patrick Gallinari. Stability of implicit neural networks for long-term forecasting in dynamical systems.ICLR 2023 Workshop on Physics for Machine LearningKigali, RwandaMay 2023HALback to text
• 15 inproceedingsL.Louis Serrano, L.Leon Migus, Y.Yuan Yin, J. A.Jocelyn Ahmed Mazari and P.Patrick Gallinari. INFINITY: Neural Field Modeling for Reynolds-Averaged Navier-Stokes 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 thesisN.Nelly Boulos Al Makary. Stationary solutions and well-balanced schemes for the shallow water model with two velocities and topography.Sorbonne Paris Nord; Inria Paris, Équipe ANGE2022, URL: https://hal.science/tel-03990996
• 17 thesisC.Chourouk El Hassanieh. Analysis and numerical approximation of some mathematical models of free-surface flows.Sorbonne Université; Université Libanaise; Inria Paris, Équipe ANGEDecember 2023HAL
• 18 thesisA.Antoine Leblond. Well-posedness and long-time behaviour of the Stokes-transport equation.Sorbonne UniversitéNovember 2023HAL
• 19 thesisL.Léon Migus. Deep neural networks and partial differential equations.Sorbonne UniversitéDecember 2023HAL

Reports & preprints

• 20 miscE.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.July 2023HAL
• 21 miscN.Nathalie Ayi and N.Nastassia Pouradier Duteil. Graph Limit for Interacting Particle Systems on Weighted Random Graphs.July 2023HAL
• 22 miscA.-L.Anne-Laure Dalibard, J.Julien Guillod and A.Antoine Leblond. Long-time behavior of the Stokes-transport system in a channel.June 2023HAL
• 23 miscB.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.August 2023HAL
• 24 miscC.Chourouk El Hassanieh, S.Samer Israwi, H.Henrik Kalisch, D.Dimitrios Mitsotakis and A.Amutha Senthilkumar. Mechanical balance laws for two-dimensional Boussinesq systems.January 2024HAL
• 25 miscC.Chourouk El Hassanieh, M.Mathieu Rigal and J.Jacques Sainte-Marie. Implicit kinetic schemes for the Saint-Venant system.March 2023HAL
• 26 miscE.Emmanuel Franck, I.Ibtissem Lannabi, Y.Youssouf Nasseri, L.Laurent Navoret, G.Giuseppe Parasiliti and G.Guillaume Steimer. Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision.April 2023HAL
• 27 miscF.Frédéric Hecht, S.-M.Sidi-Mahmoud Kaber, L.Lucas Perrin, A.Alain Plagne and J.Julien Salomon. Parallel approximation of the exponential of Hermitian matrices.June 2023HAL