RESEARCH CENTRE

Inria Paris Centre
at Sorbonne University

IN PARTNERSHIP WITH:

CNRS, Sorbonne Université

2023
ACTIVITY REPORT

Project-Team

ANGE

Numerical Analysis, Geophysics and
Environment

IN COLLABORATION WITH: Laboratoire Jacques-Louis Lions (LJLL)

DOMAIN

Digital Health, Biology and Earth

THEME

Earth, Environmental and Energy
Sciences

Contents

Project-Team ANGE

1 Team members, visitors, external collaborators

2 Overall objectives

2.1 Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Scientific challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Research program

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Modelling and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Geophysical flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Hydrological disasters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Biodiversity and culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Sustainable energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Urban environment
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 SmartCity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Social and environmental responsibility

5.1 Footprint of research activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Impact of research results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Highlights of the year

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7 New software, platforms, open data

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7.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Freshkiss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
7.1.2 TSUNAMATHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7.1.3 Verdandi
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7.1.4 Polyphemus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7.1.5 Urban noise analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
7.1.6 Freshkiss3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

8 New results

11
8.1 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.1.1 Optimal periodic resource allocation in reactive dynamical systems: Application to

microalgal production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

8.1.2 Evaluation of tsunami inundation in the plain of Martil (north Morocco): Compar-

ison of four inundation estimation methods. . . . . . . . . . . . . . . . . . . . . . . . . 12

8.1.3 Diagnostic of the Lévy area for geophysical flow models in view of defining high

order stochastic discrete-time schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.1.4 Stability of implicit neural networks for long-term forecasting in dynamical systems
12
8.1.5 INFINITY: Neural Field Modeling for Reynolds-Averaged Navier-Stokes Equations . 13
8.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
8.2.1 Low-Mach type approximation of the Navier-Stokes system with temperature and

salinity for free surface flows.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8.2.2 Acoustic and gravity waves in the ocean: a new derivation of a linear model from the

compressible Euler equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8.2.3 Numerical Investigations of Non-uniqueness for the Navier–Stokes Initial Value

Problem in Borderline Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8.3 Assessments of models by means of experimental data and assimilation . . . . . . . . . . . 14

8.3.1 On the Marginal Cost of the Duration of a Wildfire . . . . . . . . . . . . . . . . . . . . 14
8.4 Other contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.4.1 A Parareal algorithm for a highly oscillating Vlasov-Poisson system with reduced

models for the coarse solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9 Bilateral contracts and grants with industry

15

10 Partnerships and cooperations

15
10.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework

10.1.2 STIC/MATH/CLIMAT AmSud projects

of an Inria International Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
10.2 International research visitors
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
10.3 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

11 Dissemination

21
11.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11.1.2 Journal
11.1.3 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
11.1.4 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 22
11.1.5 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
11.2 Faculty administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
11.3 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
11.3.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
11.3.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
11.3.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.4 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
11.4.1 Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

12 Scientific production

27
12.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
12.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
12.3 Cited publications

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Project-Team ANGE

Creation of the Project-Team: 2014 January 01

Keywords

Computer sciences and digital sciences

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. – Computation-data 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. – Hydro-energy

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Julien Salomon [Team leader, INRIA, Senior Researcher, HDR]

• Jacques Sainte-Marie [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]

Post-Doctoral Fellow

• Louis Thiry [INRIA, Post-Doctoral 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 [Sorbonne-Université, 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

• Marie-Odile Bristeau [Retired from INRIA, external collaborator of ANGE]

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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 (hydrodynamics-biology coupling, biofuel production, marine energies. . . ),

• risk management and land-use 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, reduced-size 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 reduced-size model taking into account several physical processes such
as non-hydrostatic 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 reduced-
size 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 methodolo-
gical 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 (multi-dimensional,
unstructured meshes, well-balanced, . . . ) 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 Navier-Stokes

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 multi-physics with strong couplings and nonlinearities.

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Inria Annual Report 2023

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 Navier-Stokes equations, but
relaxing the shallow water assumptions. The main purpose is then to obtain models well-adapted 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 Saint-Venant system from the Navier-Stokes equations is based

on two approximations (the so-called 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 Navier-Stokes equations.

On the other hand, many applications require the coupling with non-hydrodynamic equations, as in
the case of micro-algae production or erosion processes. These new equations comprise non-hyperbolic
features and a special analysis is needed.

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:

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5

• 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 represent-
ativeness 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.

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Inria Annual Report 2023

3.3 Numerical analysis

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,

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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/geo-chemistry 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 well-adapted to the modelling of geo-
physical 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 non-trivial 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
so-called 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 filling-up
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 non-hydrostatic terms have to be considered and an efficient numerical resolution
should be induced.

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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 micro-algae as a source of biofuel and as a technological solution for CO2 fixation
is the subject of intense academic and industrial research. Large-scale production of micro-algae has
potential for biofuel applications owing to the high productivity that can be attained in high-rate raceway
ponds. One of the key challenges in the production of micro-algae 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 depth-averaged 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 water-turbines, 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
water-turbines 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 real-life, 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.

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The simulation uncertainties can be reduced by the assimilation of fixed and mobile sensors. High-
quality 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 project-team. This evaluation, coordinated by Inria’s Eval-
uation 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 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

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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 tsuna-
mis. 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 assim-
ilation.

URL: http://cerea.enpc.fr/polyphemus/

Contact: Vivien Mallet

Participants: Sylvain Doré, Vivien Mallet

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7.1.5 Urban noise analysis

Keyword: Environment perception

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

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 New results

8.1 Numerical methods

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.

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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 fluctu-
ation 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 compon-
ents 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 conjec-
ture 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 Dif-
ferential 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

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stability issues. Drawing inspiration from the stability property of implicit numerical schemes, we intro-
duce 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 Modelling

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 compress-

ible Euler equation

Participants:

Juliette Dubois,
François Bouchut, Jacques Sainte-Marie.

Sébastien

Imperiale,

Anne Mangeney,

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Inria Annual Report 2023

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 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, 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

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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 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.

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 Sainte-Marie.

Jacques Sainte-Marie has a contract with Eaux de Paris about Hydraulic modeling, calibration and
diagnosis. (2020-2023, 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: 11.2020-10.2024

Local supervisor: Julien Salomon

Partners:

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Inria Annual Report 2023

• 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 model-

ling. In a first work, we consider Holocene dust transport simulation using PINN.

10.2 International research visitors

• May-June 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).

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10.3 National initiatives
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.

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Inria Annual Report 2023

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 optimiz-
ation 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)

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• 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).

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Inria Annual Report 2023

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 Par-
isot, 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, ava-

lanches, 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.

Project ANGE

21

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 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

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".

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Inria Annual Report 2023

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, Alle-

magne 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: Se‘minaire Analyse Nume‘rique 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-)

Project ANGE

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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 anti-discrimination 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’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

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Inria Annual Report 2023

•

•

•

•

•

•

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

Project ANGE

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•

•

•

•

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 approxima-
tion 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 uncertain-

ties in free surface flows models - Numerical analysis and implementation in Freshkiss3d

• EA, F. Benkhaldoun, PhD, Laila Baroukh, USPN, 2021-2024, Simulation numérique pour des écoule-

ments partiellement congestionnés avec rhéologie complexe

• BDM, Master, Dana Zilberberg, SU, Ecole des ponts, 2023, On the Caracterization of Hyberbolicity

of Free-Surface Euler Equations

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11.3.3 Juries

Inria Annual Report 2023

• 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 approxima-

tion 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 the‘orie cine‘tique collisionnelle

11.4 Popularization

• JSM organized Journée de la FSMP : "A l’eau les maths"

• JS co-organized a round-table discussion at the forum emploi-maths ("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- : 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

Project ANGE

27

– 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

12 Scientific production

12.1 Major publications

[1] E. Audusse, M.-O. Bristeau, M. Pelanti and J. Sainte-Marie. ‘Approximation of the hydrostatic
Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and
numerical validation’. In: J. Comput. Phys. 230 (2011), pp. 3453–3478. DOI: 10.1016/j.jcp.2011
.01.042. URL: http://dx.doi.org/10.1016/j.jcp.2011.01.042.

[2] E. Audusse, M.-O. Bristeau, B. Perthame and J. Sainte-Marie. ‘A multilayer Saint-Venant system
with mass exchanges for Shallow Water flows. Derivation and numerical validation’. In: ESAIM
Math. Model. Numer. Anal. 45 (2011), pp. 169–200. DOI: 10.1051/m2an/2010036. URL: http://dx
.doi.org/10.1051/m2an/2010036.

[3] M.-O. Bristeau, A. Mangeney, J. Sainte-Marie and N. Seguin. ‘An energy-consistent depth-averaged
Euler system: derivation and properties’. In: Discrete and Continuous Dynamical Systems - Series B
20.4 (2015), p. 28.

[4]

[5]

J. Ledoux, S. Riffo and J. Salomon. ‘Analysis of the Blade Element Momentum Theory’. working
paper or preprint. Apr. 2020. URL: https://hal.archives-ouvertes.fr/hal-02550763.

J. Sainte-Marie. ‘Vertically averaged models for the free surface Euler system. Derivation and
kinetic interpretation’. In: Math. Models Methods Appl. Sci. (M3AS) 21.3 (2011), pp. 459–490. DOI:
10.1142/S0218202511005118. URL: http://dx.doi.org/10.1142/S0218202511005118.

12.2 Publications of the year

International journals

[6] E. Basquin, A. El Baz, J. Sainte-Marie, A. Rabaute, M. Thomas, S. Lafuerza, A. El M’Rini, D. Mercier,
E. D’acremont, M.-O. Bristeau and A. Creach. ‘Evaluation of tsunami inundation in the plain of
Martil (north Morocco): Comparison of four inundation estimation methods’. In: Natural Hazards
Research (June 2023). DOI: 10.1016/j.nhres.2023.06.002. URL: https://hal.science/hal-
04134599.

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Inria Annual Report 2023

[7] A. Belgodere, F. Allaire, J.-B. Filippi, V. Mallet and F. Guéniot. ‘On the Marginal Cost of the Duration of
a Wildfire’. In: Journal of Forest Economics 38.3 (2023), pp. 265–292. DOI: 10.1561/112.00000565.
URL: https://hal.science/hal-04256909.

[8] O. Bernard, L.-d. Lu and J. Salomon. ‘Optimal periodic resource allocation in reactive dynamical
systems: Application to microalgal production’. In: International Journal of Robust and Nonlinear
Control 33.9 (June 2023), pp. 4989–5010. DOI: 10.1002/rnc.6171. URL: https://hal.science
/hal-03170481.

[9] L. Boittin, M.-O. Bristeau, F. Bouchut, A. Mangeney, J. Sainte-Marie and F. Souillé. ‘Low-Mach type
approximation of the Navier-Stokes system with temperature and salinity for free surface flows’. In:
Communications in Mathematical Sciences 21.1 (Jan. 2023), pp. 151–172. DOI: 10.4310/CMS.2023
.v21.n1.a7. URL: https://inria.hal.science/hal-02510711.

[10] P.-M. Boulvard and E. Mémin. ‘Diagnostic of the Lévy area for geophysical flow models in view
of defining high order stochastic discrete-time schemes’. In: Foundations of Data Science (2023),
pp. 1–25. DOI: 10.3934/fods.2023011. URL: https://inria.hal.science/hal-04241686.

[11]

J. Dubois, S. Imperiale, A. Mangeney, F. Bouchut and J. Sainte-Marie. ‘Acoustic and gravity waves in
the ocean: a new derivation of a linear model from the compressible Euler equation’. In: Journal of
Fluid Mechanics 970 (Sept. 2023), A28. DOI: 10.1017/jfm.2023.595. URL: https://hal.scienc
e/hal-03880423.

[12] L. Grigori, S. A. Hirstoaga and J. Salomon. ‘A Parareal algorithm for a highly oscillating Vlasov-
Poisson system with reduced models for the coarse solving’. In: Computers & Mathematics with
Applications 130 (2023), pp. 137–148. URL: https://hal.science/hal-03903280.

[13]

J. Guillod and V. Šverák. ‘Numerical Investigations of Non-uniqueness for the Navier–Stokes Initial
Value Problem in Borderline Spaces’. In: Journal of Mathematical Fluid Mechanics 25.3 (Aug. 2023),
p. 46. DOI: 10.1007/s00021-023-00789-5. URL: https://hal.science/hal-04112126.

Conferences without proceedings

[14] L. Migus, J. Salomon and P. Gallinari. ‘Stability of implicit neural networks for long-term forecasting
in dynamical systems’. In: ICLR 2023 Workshop on Physics for Machine Learning. Kigali, Rwanda,
1st May 2023. URL: https://hal.science/hal-04132587.

[15] L. Serrano, L. Migus, Y. Yin, J. A. Mazari and P. Gallinari. ‘INFINITY: Neural Field Modeling for
Reynolds-Averaged Navier-Stokes Equations’. In: Workshop on Synergy of Scientific and Machine
Learning Modeling (ICML 2023). Honolulu, HI, United States, 28th July 2023. URL: https://hal.s
cience/hal-04171439.

Doctoral dissertations and habilitation theses

[16] N. 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 ANGE, 2022. URL:
https://hal.science/tel-03990996.

[17] C. El Hassanieh. ‘Analysis and numerical approximation of some mathematical models of free-
surface flows’. Sorbonne Université; Université Libanaise; Inria Paris, Équipe ANGE, 7th Dec. 2023.
URL: https://theses.hal.science/tel-04356497.

[18] A. Leblond. ‘Well-posedness and long-time behaviour of the Stokes-transport equation’. Sorbonne

Université, 10th Nov. 2023. URL: https://theses.hal.science/tel-04356556.

[19] L. Migus. ‘Deep neural networks and partial differential equations’. Sorbonne Université, 1st Dec.

2023. URL: https://theses.hal.science/tel-04336969.

Reports & preprints

[20] E. Audusse, V. Dubos, N. Gaveau and Y. Penel. Energy stable and linearly well-balanced numerical
schemes for the non-linear Shallow Water equations with Coriolis force. 29th July 2023. URL: https:
//hal.science/hal-03509990.

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[21] N. Ayi and N. Pouradier Duteil. Graph Limit for Interacting Particle Systems on Weighted Random

Graphs. 18th July 2023. URL: https://hal.science/hal-04164951.

[22] A.-L. Dalibard, J. Guillod and A. Leblond. Long-time behavior of the Stokes-transport system in a

channel. 1st June 2023. URL: https://hal.science/hal-04114516.

[23] B. Di Martino, C. El Hassanieh, E. Godlewski, J. Guillod and J. Sainte-Marie. Hyperbolicity of a
semi-Lagrangian formulation of the hydrostatic free-surface Euler system. 29th Aug. 2023. URL:
https://hal.science/hal-04190892.

[24] C. El Hassanieh, S. Israwi, H. Kalisch, D. Mitsotakis and A. Senthilkumar. Mechanical balance laws
for two-dimensional Boussinesq systems. 22nd Jan. 2024. URL: https://hal.science/hal-0430
7057.

[25] C. El Hassanieh, M. Rigal and J. Sainte-Marie. Implicit kinetic schemes for the Saint-Venant system.

28th Mar. 2023. URL: https://hal.science/hal-04048832.

[26] E. Franck, I. Lannabi, Y. Nasseri, L. Navoret, G. Parasiliti and G. Steimer. Hyperbolic reduced model
for Vlasov-Poisson equation with Fokker-Planck collision. 4th Apr. 2023. URL: https://hal.scien
ce/hal-04099697.

[27] F. Hecht, S.-M. Kaber, L. Perrin, A. Plagne and J. Salomon. Parallel approximation of the exponential

of Hermitian matrices. 28th June 2023. URL: https://hal.science/hal-03948509.

12.3 Cited publications

[28] E. Audusse. ‘A multilayer Saint-Venant model : Derivation and numerical validation’. In: Discrete

Contin. Dyn. Syst. Ser. B 5.2 (2005), pp. 189–214.

[29] E. Audusse, M.-O. Bristeau, M. Pelanti and J. Sainte-Marie. ‘Approximation of the hydrostatic
Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and
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<scratchpad>
- Main topic: Research Centre ANGE (Inria Paris Centre at Sorbonne University) - numerical analysis, geophysics, and environment
- Key points: 
  - Focus on gravity-driven flows in various situations (hazardous flows, sustainable energies, risk management)
  - Development of efficient, robust, and validated models and numerical tools
  - Coupling with non-hydrodynamic equations (micro-algae production, erosion processes)
  - Importance of data assimilation and uncertainty quantification
  - Applications in geophysics, hydrology, biology, and sustainable energy
- Structure: 
  - Introduction to the project-team and research activities
  - Overview of the research program and objectives
  - Description of the numerical analysis and modeling efforts
  - Discussion of application domains and potential artifacts to ignore
- Potential artifacts to ignore: 
  - Links, HTML tags, and other web-related elements
</scratchpad>

<final_summary>
The ANGE research centre, located at Inria Paris Centre at Sorbonne University, focuses on numerical analysis, geophysics, and environment. The team aims to develop efficient, robust, and validated models and numerical tools for gravity-driven flows in various situations, including hazardous flows, sustainable energies, and risk management. The research program involves coupling with non-hydrodynamic equations, such as those related to micro-algae production and erosion processes. Data assimilation and uncertainty quantification are also crucial aspects of the research. The team's work has applications in geophysics, hydrology, biology, and sustainable energy, making significant contributions to our understanding of complex systems and their interactions.
The ANGE research centre, located at Inria Paris Centre at Sorbonne University, focuses on numerical analysis, geophysics, and environment. The team aims to develop efficient, robust, and validated models and numerical tools for gravity-driven flows in various situations, including hazardous flows, sustainable energies, and risk management. The research program involves coupling with non-hydrodynamic equations, such as those related to micro-algae production and erosion processes. Data assimilation and uncertainty quantification are also crucial aspects of the research. The team's work has applications in geophysics, hydrology, biology, and sustainable energy, making significant contributions to our understanding of complex systems and their interactions.