2023Activity reportProject-TeamTONUS

6.1.1 KOUGLOFV

• Name:
  Kinetic schemes On Unstructured Grids for Large Optimized Finite Volume simulations
• Keywords:
  Discontinuous Galerkin, Parallel numerical solvers
• Functional Description:
  This code, written with the RUST language, solves Maxwell's equations on a generic tetrahedral mesh, for applications in electromagnetism. The underlying numerical method is stable without a restrictive CFL condition on the time step, and the quasi-explicit resolution ensures a low computational cost. Thanks to these properties, the code is able to handle multi-scale aspects in the mesh. In addition, the code is enhanced with shared-memory parallelization.
• Contact:
  Victor Michel-Dansac

7.1.1 Practical and theoretical works around the kinetic and Lattice Boltzmann methods

Participants: Hubert Baty [Observatoire Astronomique de Strasbourg], Florence Drui [CEA, Saclay], Emmanuel Franck, Philippe Helluy, Romane Hélie, Clément Flint, Christian Klingenberg [Univ. Würzburg, Germany], Lukas Thanhäuser [Univ. Würzburg, Germany], Kevin Guillon [Univ. Bordeaux].

The work described in 3 is devoted to the simulation of magnetohydrodynamic (MHD) flows with a Lattice Boltzmann Method (LBM) that handles shock waves. The scheme is implemented on GPU using PyOpenCL and makes it possible to use very fine grids. The method is validated on complex resistive instabilities.

In 26 we develop a simple and efficient methodology for compressing data on the fly during LBM simulations. This approach makes it possible to handle simulations that would not enter the GPU memory. It is based on wavelet compression and presents a reasonable overhead.

In 29 we propose a rigorous entropy stability analysis of the LBM scheme. We also expose a new algorithm for performing an equivalent equation analysis of the kinetic scheme with over-relaxation.

In 30 we propose a simple general approach for applying boundary conditions in the LBM. The method is based on a correction that ensures entropy dissipation, while maintening scheme accuracy.

7.1.2 Extension of the hydrostatic reconstruction to moving steady solutions

Participants: Christophe Berthon [Nantes University], Victor Michel-Dansac.

In 17, we focused on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we paid close attention to steady solutions with nonzero velocity. The goal of this work was to derive a scheme that exactly preserves these stationary solutions, as well as the commonly preserved lake at rest steady solution, by proposing an extension of the well-known hydrostatic reconstruction 33. By appropriately defining the reconstructed states at the interfaces, any numerical flux function, combined with a relevant source term discretization, produces a well-balanced scheme that preserves both moving and non-moving steady solutions. This eliminates the need to construct specific numerical fluxes. Additionally, we proved that the resulting scheme is consistent with the homogeneous system on flat topographies, and that it reduces to the hydrostatic reconstruction when the velocity vanishes. To increase the accuracy of the simulations, we proposed a linear well-balanced high-order procedure.

7.1.3 Composition schemes for the guiding-center model

Participants: Michel Mehrenberger [Aix-Marseille Université], Laurent Navoret , Anh-Tuan Vu [Aix-Marseille Université].

In 31, we presented composition methods for solving non-linear transport equations, like the guiding-center model. By composing direct and adjoint transport steps on different well-chosen sub time steps, we were able to construct high-order in time numerical methods. The adjoint steps being implicit, they are replaced by explicit approximated adjoint steps using a given number of fixed point iterations. This does not modify the order of accuracy. Several numerical tests, using high-order semi-Lagrangian spatial discretization, assess the performance of the method. Despite the large number of substeps per iteration, the method can be interesting since it reduces the number of copies of the unknown.

7.1.4 Thermodynamically compatible discretization of a compressible two-fluid model with two entropy inequalities

Participants: Saray Busto [Universidade de Vigo, Spain], Michael Dumbser [Università degli Studi di Trento, Italy], Andrea Thomann .

In 8, we have introduced a new thermodynamically compatible finite volume scheme for the symmetric hyperbolic and thermodynamically compressible (SHTC) two-fluid model of Romenski et al. that is endowed with two entropy inequalities. The new method is able to discretize the two entropy inequalities directly and obtains total energy conservation as a mere consequence of the thermodynamically compatible discretization of all other equations. The thermodynamically compatible numerical flux is based on the seminal ideas of Abgrall, which was subsequently generalized and applied to SHTC systems. Compared to previous thermodynamically compatible finite volume schemes the new approach forwarded in this paper does not require the computation of any path integral but is totally general and can be applied to arbitrary overdetermined hyperbolic and thermodynamically compatible systems that admit an extra conservation law. The proposed HTC FV schemes satisfy two discrete entropy inequalities and are provably nonlinearly stable in the energy norm. We furthermore consider arbitrary high order accurate discontinuous Galerkin (DG) schemes applied to the vanishing viscosity limit of the overdetermined system. In this case, no particular care is taken to satisfy the additional conservation law exactly at the discrete level, apart from the mere resolution of all flow features. The numerical results clearly show that the schemes proposed in this project achieve their designed order of accuracy and that in the stiff relaxation limit the numerical solution tends to the asymptotically reduced Baer–Nunziato (BN) limit system with lift forces. The influence of the lift forces has been studied separately, showing that their presence in the BN limit is necessary to achieve a good agreement with the underlying SHTC system. This work was also the object of the short communication 9.

7.1.5 Hard congestion limit of the dissipative Aw-Rascle system

Participants: Nilasis Chaudhuri [Imperial College London], Laurent Navoret , Charlotte Perrin [CNRS & Aix-Marseille Université], Ewelina Zatorska [Imperial College London].

In 22, we analyse the famous Aw-Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the momentum equation which vanishes when the density is zero. The resulting system of PDEs can be used to model traffic or suspension flows in one dimension with the maximal packing constraint taken into account. After proving the global existence of smooth solutions, we study the so-called "hard congestion limit", and show the convergence of a subsequence of solutions towards a weak solution of an hybrid freecongested system. In the context of suspension flows, this limit can be seen as the transition from a suspension regime, driven by lubrication forces, towards a granular regime, driven by the contact between the grains.

7.1.6 Implicit-explicit solver for a two-fluid single-temperature model

Participants: Maria Lukáčová-Medviďová [JGU Mainz, Germany], Ilya Peshkov [Università degli Studi di Trento, Italy], Andrea Thomann .

In 7, we have derived an analyzed a new implicit-explicit finite volume (RS-IMEX FV) scheme for a single-temperature SHTC model. We note that the two-fluid model allows two velocities and pressures. Further, it includes two dissipative mechanisms: phase pressure and velocity relaxations. In the proposed scheme these processes are treated differently. The relative velocity relaxation term is linear and is resolved as a part of the implicit sub-system, whereas the pressure relaxation is strongly nonlinear and therefore is treated separately by the Newton method. Our RS-IMEX FV method is constructed in such a way that acoustic-type waves are linearized around a suitably chosen reference state (RS) and approximated implicitly in time and by means of central finite differences in space. The remaining advective-type waves are approximated explicitly in time and by means of the Rusanov FV method. The RS-IMEX FV scheme is suitable for all Mach number flows, but in particular it is asymptotic preserving in the low Mach number flow regimes. Many multi-phase flows, such as granular or sediment transport flows, can be modeled within the single-temperature approximation. In turn, many of these flows are weakly compressible and therefore impose severe time step restrictions if solved with a time-explicit numerical scheme. Therefore, the proposed RS-IMEX FV scheme is suitable to model various environmental flows. The proposed method was tested on a number of test cases for low and moderately high Mach number flows demonstrating the capability of the scheme to properly capture both regimes. The theoretical second order accuracy of the scheme was confirmed on a stationary vortex test case. We compared the second order scheme against its first order variant which showed that the second order scheme yields more accurate approximations of discontinuities. Finally, the theoretically proven asymptotic preserving property was verified numerically.

7.1.7 Two-Dimensional Linear Implicit Relaxed Scheme for Hyperbolic Conservation Laws

Participants: Angelo Iollo [Université de Bordeaux & Inria MEMPHIS, France], Gabriella Puppo [Sapienza – Università di Roma, Italy], Andrea Thomann .

In 10, we present a two-dimensional extension to the linear implicit all-speed finite volume scheme for hyperbolic conservation laws based on Jin-Xin relaxation recently forwarded in 44. It is based on stiffly accurate SDIRK (Singly-Diagonal Implicit Runge-Kutta) methods in time and a convex combination of Rusanov and centered fluxes in space making it asymptotically consistent in the low Mach number regime and allows an accurate capturing of material waves under large time steps. The scheme is numerically tested on the Euler equations and a non-linear model for elasticity in the compressible and low Mach number regime.

7.2.1 Enrichment of Discontinuous Galerkin bases with Physics-Informed Neural Networks

Participants: Emmanuel Franck, Victor Michel Dansac, Laurent Navoret.

In 28, we proposed to enrich Discontinuous Galerkin (DG) bases, so that the resulting scheme provides a much better approximation of steady solutions to hyperbolic systems of balance laws. The basis enrichment leverages a prior – an approximation of the steady solution – which we computed using a Physics-Informed Neural Network (PINN). We proved convergence results and error estimates, showing that the basis with prior does not change the order of convergence, and that the error constant is improved. To construct the prior, parametric PINNs were used. Numerical experiments on 1D and 2D hyperbolic systems show that the DG scheme with prior is much more accurate on steady solutions than the DG scheme without prior, while retaining the same approximation quality on unsteady solutions.

7.2.2 An optimal control framework for adaptive neural ordinary differential equations

Participants: Joubine Aghili , Olga Mula [TU Eindhoven].

In 16, we proposed an iterative adaptive algorithm where we progressively refined the time discretization (i.e. increasing the number of layers). Provided that certain tolerances are met across the iterations, we prove that the strategy converges to the underlying continuous problem. One salient advantage of such a shallow-to-deep approach is that it helps to benefit in practice from the higher approximation properties of deep networks by mitigating over-parametrization issues.

7.2.3 Deep optimal control to design hybrid numerical schemes

Participants: Emmanuel Franck, Léo Bois, Laurent Navoret, Vincent Vigon.

In 19, we propose a method for constructing a neural network viscosity in order to reduce the non-physical oscillations generated by high-order Discontiuous Galerkin (DG) methods. To this end, the problem is reformulated as an optimal control problem for which the control is the viscosity function and the cost function involves comparison with a reference solution after several compositions of the scheme. The learning process is strongly based on a time propagation method which uses the ML framework to compute the gradient of the full scheme with respect to the parameters of the network at many time steps.

7.2.4 Modelling solar coronal magnetic fields with physics-informed neural networks

Participants: Hubert Baty [Observatoire Astronomique de Strasbourg], Vincent Vigon .

In 4, we present a novel numerical approach aiming at computing equilibria and dynamics structures of magnetized plasmas in coronal environments. A technique based on the use of neural networks that integrates the partial differential equations of the model, and called physics-informed neural networks (PINNs), is introduced. The functionality of PINNs is explored via calculation of different magnetohydrodynamic (MHD) equilibrium configurations, and also the derivation of exact two-dimensional steady-state magnetic reconnection solutions. The advantages and drawbacks of PINNs compared to traditional numerical codes are discussed in order to propose future improvements. Interestingly, PINNs are a meshfree method in which the obtained solution and associated different order derivatives are quasi-instantaneously generated at any point of the spatial domain. We believe that our results can help to pave the way for future developments of time dependent MHD codes based on PINNs.

7.3.1 Hamiltonian reduced model for wave equations

Participants: Emmanuel Franck, Guillaume Steimer, Laurent Navoret, Vincent Vigon, Raphaël Côte [Unistra].

In the paper 24 we propose a non-linear reduction method for models coming from the spatial discretization of partial differential equations: it is based on convolutional auto-encoders and Hamiltonian neural networks. Their training is coupled in order to simultaneously learn the encoder-decoder operators and the reduced dynamics. Several test cases on non-linear wave dynamics show that the method has better reduction properties than standard linear Hamiltonian reduction methods.

7.3.2 Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision

Participants: Emmanuel Franck, Ibtissem Lannabi [Univ Pau], Laurent Navoret, Youssouf Nasseri, Giuseppe Parasiliti [INRIA Ange], Guillaume Steimer.

The paper 27 proposes a reduced model to simulate the one-dimensional Vlasov-Poisson equation. The model provides the space-time dynamics of a few macroscopic quantities constructed following the Reduced Order Method (ROM) in the velocity variable: the compression is thus applied to the semi-discretization of the Vlasov equation. To gain efficiency, a Discrete Empirical Interpolation Method (DEIM) is applied to the compressed non-linear Fokker-Planck operator. Furthermore, we propose a correction to the reduced collision operator which ensures that the reduced moments satisfy an Euler-type system. Numerical simulations of the reduced model show that the model can capture the plasma dynamics in different collisional regimes and initial conditions at a low cost.

7.4.1 Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers

Participants: Clémentine Courtès , Matthieu Boileau , Raphaël Côte [Université de Strasbourg], Paul-Antoine Hervieux [Université de Strasbourg], Giovanni Manfredi [Université de Strasbourg].

In 25, we solved the Landau-Lifshitz-Gilbert equation in the finite-temperature regime, where thermal fluctuations are modeled by a random magnetic field whose variance is proportional to the temperature. We obtained Curie temperatures $T_C$ that are in line with the experimental values for cobalt, iron and nickel and for finite-sized objects such as nanowires (1D) and nanolayers (2D), we study the variances of the Curie temperature with respect to the smallest size of the system. Moreover, optimization and parallelization of the python code solving the Landau-Lifshitz-Gilbert equation in the finite-temperature regime led to a 100-time acceleration of the code. We were therefore able to study the effect of the size of the material on the magnetization, in particular the value of the Curie temperature.

7.4.2 Minimal time of magnetization switching in small ferromagnetic ellipsoidal samples

Participants: Raphaël Côte [Université de Strasbourg], Clémentine Courtès , Guillaume Ferrière [Inria Lille], Yannick Privat .

Considering a ferromagnetic material of ellipsoidal shape, the associated magnetic moment then has two asymptotically stable opposite equilibria, of the form $\pm \overline{m}$. In order to use these materials for memory storage purposes, it is necessary to know how to control the magnetic moment. In 23, we use as a control variable a spatially uniform external magnetic field and consider the question of flipping the magnetic moment, i.e., changing it from the $+\overline{m}$ configuration to the $-\overline{m}$ one, in minimal time. Of course, it is necessary to impose restrictions on the external magnetic field used. We therefore include a constraint on the $L^{\infty }$ norm of the controls, assumed to be less than a threshold value $U$. We show that, generically with respect to the dimensions of the ellipsoid, there is a minimal value of $U$ for this problem to have a solution. We then characterize it precisely. Finally, we investigate some particular configurations associated to geometries enjoying symmetry properties and show that in this case the magnetic moment can be controlled in minimal time without imposing a threshold condition on $U$. This type of phenomenon (existence of a minimum time only if the control is powerful enough and non-controllability otherwise) seems new and leads to interesting extensions for more complex systems.

7.4.3 Reduced modeling and optimal control of epidemiological individual-based models with contact heterogeneity

Participants: Clémentine Courtès, Emmanuel Franck, Killian Lutz, Laurent Navoret, Yannick Privat.

Modeling epidemics using classical population-based models suffers from shortcomings that so-called individual-based models are able to overcome. They are able to take into account heterogeneity features, such as super-spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are expensive to simulate and difficult to optimize, both in theory and in practice. By combining the reinforcement learning philosophy with reduced models, we propose in 5 a numerical approach to determine optimal health policies for a stochastic individual-based model taking into account heterogeneity in the population. More precisely, we introduce a deterministic reduced population-based model involving a neural network, designed to faithfully mimic the local dynamics of the more complex individual-based model. Then the optimal control is determined by sequentially training the network until an optimal strategy for the population-based model succeeds in also containing the epidemic when simulated on the individual-based model. After describing the practical implementation of the method, several numerical tests are proposed to demonstrate its ability to determine controls for models with contact heterogeneity.

7.4.4 Numerical analysis of a shape optimization algorithm

Participants: Antonin Chambolle [CEREMADE & Inria MOKAPLAN, Paris, France], Idriss Mazari-Fouquer [CEREMADE, Paris, France], Yannick Privat .

In 20, 21, we prove a new result in shape optimization: the convergence of the fixed-point (also called thresholding) algorithm in three optimal control problems under large volume constraints. This algorithm was introduced by Céa, Gioan and Michel, and is of constant use in the simulation of $L^{\infty }-L^1$ optimal control problems. In this paper we consider the optimisation of the Dirichlet energy, of Dirichlet eigenvalues and of certain non-energetic problems. Our proofs rely on new diagonalisation procedure for shape Hessian matrices in optimal control problems, which leads to local stability estimates.

7.4.5 Optimal scenario for road evacuation in an urban environment

Participants: Emmanuel Franck , Laurent Navoret , Mickael Bestard, Yannick Privat .

How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow, for example, emergency vehicles to pass? In 18, we are interested in this question which we reformulate as an optimal control problem. We consider a macroscopic road traffic model on networks, semi-discretized in space and decide to give ourselves the possibility to control the flow at junctions. Our target is to smooth the traffic along a given path within a fixed time. A sparsity constraint is imposed on the controls, in order to ensure that the optimal strategies are feasible in practice. We perform an analysis of the resulting optimal control problem, proving the existence of an optimal control and deriving optimality conditions, which we rewrite as a single functional equation. We then use this formulation to derive a new mixed algorithm interpreting it as a mix between two methods: a descent method combined with a fixed point method allowing global perturbations. We verify with numerical experiments the efficiency of this method on examples of graphs, first simple, then more complex. We highlight the efficiency of our approach by comparing it to standard methods. We propose an open source code implementing this approach in the Julia language.

7.4.6 Spontaneous rotations in epithelia as an interplay between cell polarity and RhoA activity at boundaries

Participants: Simon Lo Vecchio [IGBMC, Strasbourg], Olivier Pertz [Cellular Dynamics lab, Berne], Marcela Szopos [MAP5, Paris], Laurent Navoret, Daniel Riveline [IGBMC, Strasbourg].

Directed flows of cells in vivo are essential in morphogenesis. They shape living matter in phenomena involving cell mechanics and regulations of the acto-myosin cytoskeleton. However the onset of coherent motion during collective cell migration is still poorly understood. In 6 we show that coherence is set by spontaneous alignments of cell polarity by designing cellular rings of controlled dimensions. A tug-of-war between opposite polarities dictates the onset of coherence, as assessed by tracking live cellular shapes and motions in various experimental conditions. In addition, we identify an internally driven constraint by cellular acto-myosin cables at boundaries as essential to ensure coherence. Moreover, active force is generated as evaluated by the high RhoA activity. Its contribution is required to trigger coherence as shown by our numerical simulations based on a novel Vicsek-type model including free active boundaries. Altogether, spontaneous coherent motion results from basic interplay between cell orientations and active cables at boundaries.

9.1.1 Visits of international scientists

9.1.2 Visits to international teams

9.2.1 Other european programs/initiatives

• Machine Learning for Kinetic equations
  • Acronym: ANR-DFG MILK
  • Duration: 01/2022 – 12/2024
  • Coordinator: E. Franck, Inria Antenna in Strasbourg & E. Sonnendrücker, Technische Universität München (TUM)
  • Partners: Inria Antenna in Strasbourg & TUM
  • Participants: Clémentine Courtès , Emmanuel Franck , Laurent Navoret
  • Abstract: Kinetic models are accurate descriptions of interacting particle systems in physics. However, their numerical resolution is often too demanding, as they are defined in the large-dimensional position/velocity phase space and involve multi-scale dynamics. For this reason, reduced models have been developed that represent optimal trade-offs between numerical cost and modeling completeness. In general, this reduction is carried out in two ways. The first is based on asymptotic models that filter out fast dynamics and are obtained when a small parameter tends towards zero (collision/oscillation limit). The second, called reduced order modeling, consists in finding a smaller representation of the problem able to describe the dynamics (POD). The main objective of this project is to design new reduced order models that are more efficient than classical ones, based on machine learning techniques applied to kinetic data. Ensuring the stability of the obtained models will be a key point of these studies.

9.3.1 National projects

• MOdeling and SImulation of COmplex Ferromagnetic systems:
  • Acronym: ANR MOSICOF
  • Duration: 10/2021 – 10/2025
  • Coordinator: S. Labbé, Sorbonne Université
  • Partners: Sorbonne université, Université de Pau et des Pays de l'Adour, Université de Strasbourg
  • Participants: Clémentine Courtès , Yannick Privat
  • Abstract: During the last decade, promising applications of ferromagnetic materials have emerged in the domains of nanoelectronics (spintronic) and data storage: complex ferromagnetic systems are increasingly used for digital data recording and logic devices. They reduce the energy storage cost while improving the performance of the devices. The goal of this proposal is to bring together mathematicians and physicists around the understanding of the properties of ferromagnetism. One of the main objectives is to highlight and treat new multi-physics models, allowing for optimization and control of the magnetizations, and to simulate the phenomena in a more efficient and less expensive way. We wish to develop approaches leading to mathematically justified and physically relevant solutions for the analysis and optimization of these materials, and which could ultimately lead to implementation on devices.
• Modelling the effect of Apoptosis on Epithelium FLUidity
  • Acronym: ANR MAPEFLU
  • Duration: 03/2023 – 02/2027
  • Coordinator: Laurent Navoret
  • Partners: Institut Pasteur, Université Paris Université de Strasbourg (IRMA, IGBMC)
  • Participants: Laurent Navoret , Roxana Sublet
  • Abstract: Epithelia have a viscoelastic behaviour: they respond as solids over short times and as fluids over large times. This fluidity plays an essential role in morphogenesis and tissue deformation. At the cellular scale, fluidity is achieved by the remodelling of junctions between cells due to their interactions but also by cell division and death. However, the contribution of apoptosis to fluidity has been little studied and remains unclear since cell death is also associated with local elastic constraints. Our project first aims at developing a novel particle model, describing cell cycles and the polarities interactions (Vicsek-like model), to assess the impact of cell death rate on tissue fluidity. The construction of this model will be strongly guided by comparisons with in vitro (MDCK cells) and in vivo (Drosophila pupa) experiments. From this particle model, a hydrodynamic model will be rigorously derived and simulations based on this new macroscopic description will be utilized to improve the understanding of tissue dynamics. The present study will thus provide a generic model, consistent with the experimental data and allowing one of the first systematic assessments of the role of apoptosis in tissues.
• PEPR IA: PC IA-EDP:
  • Acronym: PEPR IA/ PC IA-EDP
  • Duration: 01/09/2023 – 31/08/2027
  • Coordinator: Antonin Chambolle
  • Partners: Univ. Paris-Dauphine (PSL), Univ. Paris-Cité, Sorbonne Univ., Univ. Paris-Saclay, Univ. Toulouse, Univ. Lyon (CNRS), Univ. Bordeaux, Univ. Côte d’Azur, CREST (ENSAE/Institut Polytechnique de Paris) and Univ. Strasbourg
  • Participants: Emmanuel Franck , Clémentine Courtès , Vincent Vigon , Victor Michel-Dansac , Joubine Aghili , Philippe Helluy , Laurent Navoret
  • Abstract: The PEPR IA is a large national project on IA. The PC IA-PDE is a project funded by the ANR, which gathers ten major French institutions involved in developing the mathematical analysis of AI, the study of optimization in machine learning, as well as in developing machine learning for numerical analysis and scientific computing. We will study the link between modern IA methods and optimal control, optimal transport, PDE and numerical analysis. The team is involved in the optimal control aspect.
• PEPR Numpex: PC Exa-MA:
  • Acronym: PEPR Numpex/ PC Exama
  • Duration: 01/09/2023 – 31/08/2027
  • Coordinator: Christophe Prud'Homme et Hélène Barucq
  • Partners: Unistra, INRIA, Sorbonne University, Polytechnique, CEA
  • Participants: Emmanuel Franck , Clémentine Courtès , Vincent Vigon , Victor Michel-Dansac , Joubine Aghili , Philippe Helluy , Laurent Navoret
  • Abstract: The Exa-MA project focuses on the Exascale aspects of digital methods, guaranteeing their adaptability to existing and future hardware. It is also a cross-disciplinary project, proposing methods and tools in which modelling, data and AI, through algorithms, are central. The team is mainly involved in the WP2 on reduced modeling and ML technics but also in the WP1 on numerical methods.

10.1.1 Scientific events: organisation

10.1.2 Journal

10.1.3 Talks

• 12/2023: Colloquium “Physique et Mathématique”, Strasbourg, France (Laurent Navoret )
• 12/2023: AIAE'23: 3rd International Workshop on Artificial Intelligence and Augmented Engineering, Orsay, France (Victor Michel-Dansac )
• 12/2023: Group seminar of Prof. Christiane Helzel, Heinrich-Heine Universität Düsseldorf, Germany (Andrea Thomann )
• 11/2023: Journées Mathrice, Paris, France (Matthieu Boileau )
• 11/2023: Finite Volumes for Complex Applications, FVCA10, Strasbourg, France (Andrea Thomann )
• 10/2023: International Conference on Applied Mathematics and Mechanics (ICAMM 2023), Indore, Madhya Pradesh, India (online) (Victor Michel-Dansac )
• 09/2023: 3rd Inria-DFKI European Summer School on AI (IDESSAI 2023), Sophia-Antipolis, France (Victor Michel-Dansac )
• 08/2023: Kolloquium der Mechanik, TU Darmstadt, Germany (Andrea Thomann )
• 06/2023: Workshop "Around numerical analysis of lattice Boltzmann methods, Palaiseau, France (Philippe Helluy )
• 06/2023: "22ème Journée Calcul Scientifique et Modélisation Mathématique d'Amiens", Amiens, France (Philippe Helluy )
• 06/2023: NumHyp 2023, Bordeaux, France (Victor Michel-Dansac )
• 06/2023: Séminaire X/Stra, Strasbourg, France (Vincent Vigon )
• 04/2023: Lebesgue Doctoral Meeting, Nantes, France (Clémentine Courtès )
• 03/2023: Seminar, univ. Dijon, France (Yannick Privat )
• 03/2023: Univ. Lisbon, Portugal (Yannick Privat )
• 01/2023: PDE Masterclass, Nancy, France (Clémentine Courtès )
• through 2023: many talks in the Machine Learning workgroup (Matthieu Boileau , Clémentine Courtès , Emmanuel Franck , Laurent Navoret , Victor Michel-Dansac , Yannick Privat , Vincent Vigon )

10.1.4 Leadership within the scientific community

• Member of the IEEE Technical Committee on Audio and Acoustic Signal Processing (Antoine Deleforge )

10.1.5 Research administration

• Board member of “GDR Calcul” (Matthieu Boileau )
• Commission régionale d'interclassement des ingénieurs et techniciens CNRS (Matthieu Boileau )
• Member of the CdT (commission locale de Développement Technologique) Inria Research Center at Université de Lorraine (Matthieu Boileau )
• Member of the Conseil Scientifique de l'Ecole Doctorale MS2I, Université de Strasbourg (Matthieu Boileau )
• Member of the Conseil Scientifique de l'ITI IRMIA++ (Matthieu Boileau )
• Committee for an associate professor (section 26), University of Strasbourg (Clémentine Courtès )
• 09/2023 – now: Organization of the internal Seminar at Strasbourg University (G. Ancona, Clémentine Courtès , Y. le Floch, X. Zeng)
• 09/2021 – now: Organization of the PDE Seminar at Strasbourg University (Joubine Aghili , Clémentine Courtès and Victor Michel-Dansac )
• Elected member of the "commission des mathématiciens", University of Strasbourg (Clémentine Courtès , Laurent Navoret )
• 04/2021 – now: nominated member of the Inria Research Center at Université de Lorraine “comité de centre” (Clémentine Courtès )
• Referent for research data, Inria Research Center at Université de Lorraine (Antoine Deleforge )
• 01/2021 – now: Organization of the Machine Learning working group at Strasbourg University (Emmanuel Franck )
• Member of the board of “GDR Calcul” (Emmanuel Franck )
• 11/2023 – now: Member of CNU Section 26 (Emmanuel Franck )
• Co-responsable du GT IA du PEPR NumPex (Emmanuel Franck )
• Comex Inria Nancy-Grand-Est (Philippe Helluy )
• Elected member of the “Commission de la Recherche” of the University of Strasbourg (Philippe Helluy )
• 09/2018 – 09/2023: Head of the CNRS Lab IRMA “Institut de Recherche Mathématique Avancée”, UMR 7501 (Philippe Helluy )
• Elected member of the experts committee, UFR Math-Info, Université de Strasbourg (Laurent Navoret )
• Responsable formation, Institut Thématique Interdisciplinaire IRMIA++, Université de Strasbourg (Laurent Navoret )
• Member of the jury for the AMIES company thesis prize (Yannick Privat )
• 11/2019 – now: Member of CNU Section 26 (Yannick Privat )
• 04/2019 – 09/2023: Member of the IRMA expert committee (Yannick Privat )
• Jan. 2023-Aug. 2023: Head of the “Modeling and Control” team at IRMA (Yannick Privat )
• 2023-2027: Local leader (University of Strasbourg) of the PEPR Numerical analysis, optimal control and optimal transport for AI (Yannick Privat )
• Committee for an full professor (section 26), univ. Clermont Auvergne (Yannick Privat )

10.2.1 Teaching

• Licence 1, “Maths pour les sciences 2”, 64h lectures + problem sessions, Strasbourg University, France (Joubine Aghili )
• Licence 1, “Mathematics for biology”, 12h lectures + 23h exercise sessions, Strasbourg University, France (Michaël Gutnic )
• Licence 1, “Mathematics for health studies”, 36h, Strasbourg University, France (Michaël Gutnic )
• Licence 2, “Applied numerical analysis”, 18h, Strasbourg University, France (Clémentine Courtès )
• Licence 2, “Object-Oriented Programming in Python”, 16h lectures (Emmanuel Franck , Victor Michel-Dansac ) + 16h computer labs (Victor Michel-Dansac ), Strasbourg University, France
• Licence 2, “Scientific computing”, 20h lectures + 17h computer labs, Strasbourg University, France (Michaël Gutnic )
• Licence 2 Sciences et Société, “Introduction à l'apprentissage automatique ”, 12.5h, Strasbourg University, France (Laurent Navoret )
• Licence 2, “Numerical resolution techniques”, 16h computer labs, Strasbourg University, France (Andrea Thomann )
• “Probability and Statistics”, 30h, CNAM, France (Michaël Gutnic )
• Licence 3, “Calcul scientifique et analyse numérique”, 56h lectures + computer labs, Strasbourg University, France (Joubine Aghili )
• Licence 3, “Numerical analysis techniques 1”, 32h lectures + problem sessions + computer labs, Strasbourg University, France (Clémentine Courtès )
• Licence 3, “Scientific computing”, 65h lectures + exercise sessions, Strasbourg University, France (Clémentine Courtès )
• Licence 3, “Nonlinear Optimization”, 61h lectures + exercise sessions, Strasbourg University, France (Clémentine Courtès )
• Licence 3, “Advanced C++”, 20h lectures (Emmanuel Franck ) + 34h computer labs (Emmanuel Franck ), Strasbourg University, France
• Licence 3, “Numerical analysis techniques 2”, 34h, Strasbourg University, France (Philippe Helluy )
• Licence 3, “Introduction to C++”, 34h, Strasbourg University, France (Philippe Helluy )
• Master 1, “Projet”, 7h supervision, Strasbourg University, France (Joubine Aghili )
• Master 1, “Méthodes Numériques”, 8h computer labs, Strasbourg University, France (Joubine Aghili )
• Master 1, “Calcul scientifique 2”, 28h lectures, Strasbourg University, France (Joubine Aghili )
• Master 1, “Parallel Computing”, 20h, Strasbourg University, France (Matthieu Boileau )
• Master 1, “Artificial Intelligence, Machine Learning, Deep Learning”, 24h, Télécom Physique Strasbourg, France (Antoine Deleforge )
• Master 1, “Machine Learning”, 4h lectures + 4h computer labs, Strasbourg University, France (Emmanuel Franck )
• Master 1 Pure Mathematics, “Scientific computing”, 13h lectures (Philippe Helluy ) + 14h computer labs (Philippe Helluy & Victor Michel-Dansac ), Strasbourg University, France
• Master 1 Applied Mathematics, “Scientific computing”, 35h, Strasbourg University, France (Laurent Navoret )
• Master 1, “Optimization”, 6h computer labs, Strasbourg University, France (Clémentine Courtès )
• Master 1, “Optimization”, 62.5h, Strasbourg University, France (Laurent Navoret )
• Master 1 Applied Mathematics, “Random models”, 35h, Strasbourg University, France (Vincent Vigon )
• Master 1 Applied Mathematics, “Data mining”, 35h, Strasbourg University, France (Vincent Vigon )
• Master 1 Applied Mathematics, “Signal processing”, 35h, Strasbourg University, France (Vincent Vigon )
• Master 1 DUAS, “Data science”, 50h, Strasbourg University, France (Vincent Vigon )
• Master 1 & 2, “Initiation to Machine Learning”, 24h, Télécom Physique Strasbourg, France (Antoine Deleforge )
• Master 2, “Projet”, 7h supervision, Strasbourg University, France (Joubine Aghili )
• Master 2 Agrégation, “Calcul scientifique”, 10h lectures, Strasbourg University, France (Joubine Aghili )
• Master 2 Cell Physics, “Basics in mathematics”, 24h, Strasbourg University, France (Laurent Navoret )
• Master 2 Cell Physics, “Math for living matter”, 6h, Strasbourg University, France (Laurent Navoret )
• Master 2 Agrégation, “Scientific computing”, 28h, Strasbourg University, France (Philippe Helluy )
• Master 2 Agrégation, “Scientific computing”, 38h, Strasbourg University, France (Laurent Navoret )
• Master 2 Agrégation, “Probability”, 50h, Strasbourg University, France (Vincent Vigon )
• Master 2 Pure Mathematics, “Nonlinear evolution PDEs”, 30h, Strasbourg University, France (Clémentine Courtès )
• Master 2 Pure Mathematics, “Hydrodynamic limits of system of interacting particles”, 32h, Strasbourg University, France (Laurent Navoret )
• Master 2 Applied Mathematics, “Numerical methods for hyperbolic PDEs”, 35h, Strasbourg University, France (Laurent Navoret )
• Master 2, “Data Science”, 20h, Strasbourg University, France (Matthieu Boileau )
• Master 2, “Numerical methods for hyperbolic PDEs”, 35h, Strasbourg University, France (Philippe Helluy )
• Master 2, “Structure-preserving methods for Hamiltonian ODEs”, 14h, Strasbourg University, France (Victor Michel-Dansac )
• Master 2, “Variational Analysis and Planification”, 30h, Strasbourg University, France (Yannick Privat )
• Master 2, “Optimal control”, 70h, Strasbourg University, France (Yannick Privat )
• Master 2 Applied Mathematics, “Signal processing and deep learning”, 35h, Strasbourg University, France (Vincent Vigon )
• Master 2 Applied Mathematics, “Graphs and applications”, 35h, Strasbourg University, France (Vincent Vigon )
• Diplôme d'université, “Interdisciplinary seminars”, 8h, Strasbourg University, France (Laurent Navoret )
• Training Course, “Basics for scientific python”, 28h, Urfist (Unité Régionale de Formation à l'Information Scientifique et Technique), France (Matthieu Boileau )

10.2.2 Supervision

• 09/2022 – now: Dean of the Mathematics and Computer Science faculty (Directeur de l'UFR Mathématique et Informatique) in Strasbourg university (Michaël Gutnic )
• PhD completed in April 2023 15: R. Hélie, “Relaxation methods for kinetic models in plasma physics.”. Matthieu Boileau , Emmanuel Franck , Philippe Helluy and Laurent Navoret .
• PhD completed in December 2023: M. Bestard, “Optimal control for numerical simulation in physics plasma.”. Emmanuel Franck , Laurent Navoret and Yannick Privat .
• PhD completed in December 2023: L. Bois, “Machine learning for numerical methods. Application in plasma physics.”. Philippe Helluy , Emmanuel Franck , Laurent Navoret and Vincent Vigon .
• PhD in progress: C. Flint, “Efficient data compression for high-performance PDE solvers.”. Beginning: October 2020. Philippe Helluy and S. Genaud (Inria CAMUS).
• PhD in progress: T. Sprunck, “Can one hear the shape of a room?”. Beginning: September 2021. Antoine Deleforge and Yannick Privat .
• PhD in progress: N. Victorion, “Numerical methods assisted by deep learning for wave problems”. Beginning: September 2021. H. Barucq (Inria MAKUTU) and Emmanuel Franck .
• PhD in progress: G. Steimer, “Model reduction using deep learning for plasma physics”. Beginning: October 2021. R. Côte, Emmanuel Franck and Laurent Navoret
• PhD in progress: M. Pallanque, “Radiative transfer models for astrophysical code”. Beginning: September 2022. P. Ocvirk (Strasbourg Observatory) and Emmanuel Franck
• PhD in progress: G. Lazare, “Simulations performantes en thermo-hydraulique des cœurs avec THYC”. Beginning: November 2022. Philippe Helluy and EDF Chatou.
• PhD in progress: A. Bélières–Frendo, “Shape optimization through learning”. Beginning: December 2023. C. Prud'homme (Strasbourg University), C. Dapogny (CNRS & Grenoble University) and Victor Michel-Dansac
• PhD in progress: K. Lutz, “Optimal control of Lindblad equations”. Beginning: September 2023. Emmanuel Franck & Yannick Privat
• PhD in progress: C. Schnoebelen, “Geometric methods for wave equations”. Beginning: October 2023. Emmanuel Franck & Laurent Navoret & E. Ophstein (IRMA)
• PhD in progress: R. Sublet, “Mathematical models for collective cell dynamics”. Beginning: October 2023. Laurent Navoret & M. Szopos (Univ. Paris Cité)
• PhD in progress: R. San Roman, “Self supervised disentangled representation learning of audio data for compression and generation”. Beginning: June 2022. Y. M. Adi (Meta AI), Antoine Deleforge , R. Serizel (MULTISPEECH) and G. Synnaeve (Meta AI)
• PhD in progress: S. Dilungana, “New Algorithms for Automated Room Acoustic Diagnosis”. Beginning: October 2020. Antoine Deleforge , C. Foy (CEREMA) and S. Faisan (Université de Strasbourg)

10.2.3 Juries

• Examiner in the PhD jury of Mouna Kassan, Université de Pau et des Pays de l'Adour (Clémentine Courtès )
• Examiner in the PhD jury of Xiaoyu Bie, Université de Grenoble (Antoine Deleforge )
• Reviewer for the PhD thesis of Jai Kumar “Machine learning for numerical processing and analysis of kinetic and fluid simulations of fusion plasmas”, Université Aix-Marseille CEA-Cadarache (Emmanuel Franck )
• Reviewer for the PhD thesis of A. Al Kheir “Étude de quelques problèmes d'optimisation de forme spectrale”, univ. Pau et des pays de l'Adour, June 2023 (Yannick Privat )
• Examiner, reviewer or president of the following PhD juries: T. Bellotti, Palaiseau, June 2023; S. Maazioui, July 2023, Paris XIII; G. Joméee, Marseille, November 2023; K. Guillon, Bordeaux,November 2023; Axel Maupoux, Toulouse, December 2023; Lucas Tallois, December 2023, Bordeaux; M. Bestard, December 2023, Strasbourg (Philippe Helluy )
• Examiner of the following HDR Jury: E. Franck, Strasbourg, January 2023; A. Charguéraud, Strasbourg, February 2023 (Philippe Helluy )

10.3.1 Education

• stage d'observation de 3e : L. Avon, 12/2023 (Matthieu Boileau )

10.3.2 Interventions

• Conference in a 4th grade class as part of the "Semaine des mathématiques », Sébastien Brant college, Eschau (Matthieu Boileau )
• Conference in front of parents of students as part of Ose La Recherche., Le Vaisseau, Strasbourg (Matthieu Boileau )
• 06/2023 : scientific workshop for the "MathC2+" week, for high school students (Clémentine Courtès )
• 05-06/2023 : research talks aimed at high school students (Clémentine Courtès )
• 02/2023 : talk aimed at PhD students on scientific careers (Clémentine Courtès )
• since 08/2022 : organization of the mathematics and computing week "Les Cigognes" for high school girls (Clémentine Courtès , M. Duflot-Kremer, A. de Roton, P. Py, S. Tapie)
• "Comment fonctionnent les modèles de language (ChatGPT, etc.)". Talk in front of colleagues from other fields (medecine, literature). July 2023, April 2023 (Philippe Helluy )

International journals

• 3 articleH.Hubert Baty, F.Florence Drui, P.Philippe Helluy, E.Emmanuel Franck, C.Christian Klingenberg and L.Lukas Thanhäuser. A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations..Applied Mathematics and Computation440March 2023, 127667HALDOIback to text
• 4 articleH.Hubert Baty and V.Vincent Vigon. Modelling solar coronal magnetic fields with physics-informed neural networks.Monthly Notices of the Royal Astronomical Society5272024, 2575-2584HALDOIback to text
• 5 articleC.Clémentine Courtès, E.Emmanuel Franck, K.Killian Lutz, L.Laurent Navoret and Y.Yannick Privat. Reduced modelling and optimal control of epidemiological individual-based models with contact heterogeneity.Optimal Control Applications and Methods2023HALDOIback to text
• 6 articleS.Simon Lo Vecchio, O.Olivier Pertz, M.Marcela Szopos, L.Laurent Navoret and D.Daniel Riveline. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries.Nature PhysicsJanuary 2024HALDOIback to text
• 7 articleM.Mária Lukáčová-Medvid'ová, I.Ilya Peshkov and A.Andrea Thomann. An implicit-explicit solver for a two-fluid single-temperature model.Journal of Computational Physics498February 2024, 112696HALDOIback to text
• 8 articleA.Andrea Thomann and M.Michael Dumbser. Thermodynamically compatible discretization of a compressible two-fluid model with two entropy inequalities.Journal of Scientific Computing971August 2023, 9HALDOIback to text

Conferences without proceedings

• 9 inproceedingsM.Michael Dumbser, S.Saray Busto and A.Andrea Thomann. On Thermodynamically Compatible Finite Volume Schemes for Overdetermined Hyperbolic Systems.FVCA10433Springer Proceedings in Mathematics & StatisticsStrasbourg, FranceOctober 2023, 103-110HALDOIback to text
• 10 inproceedingsA.Angelo Iollo, G.Gabriella Puppo and A.Andrea Thomann. Two-Dimensional Linear Implicit Relaxed Scheme for Hyperbolic Conservation Laws.FVCA 2023433Springer Proceedings in Mathematics & StatisticsStrasbourg, FranceSpringer Nature SwitzerlandOctober 2023, 171-179HALDOIback to text
• 11 inproceedingsN.Nicolas Victorion, H.Hélène Barucq, H.Henri Calandra, F.Florian Faucher and E.Emmanuel Franck. Optimized Finite Differences methods and Machine Learning to reduce numerical dispersion for the wave equation.Journées Ondes Sud-Ouest (JOSO)Toulouse, FranceMarch 2023HAL
• 12 inproceedingsN.Nicolas Victorion, H.Hélène Barucq, H.Henri Calandra, E.Emmanuel Franck and F.Florian Faucher. Improving the efficiency of acoustic wave solver with optimized FD andby coupling FEM with Machine Learning.Rencontre Ondes et et leurs Applications (ROA)PAU, FranceJune 2023HAL

Scientific book chapters

• 13 inbookE.Emmanuel Franck, J.Jürgen Fuhrmann, V.Victor Michel-Dansac and L.Laurent Navoret. Preface.432Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic ProblemsSpringer Proceedings in Mathematics & StatisticsSpringer Nature SwitzerlandSeptember 2023HALDOIback to text
• 14 inbookE.Emmanuel Franck, J.Jürgen Fuhrmann, V.Victor Michel-Dansac and L.Laurent Navoret. Preface.433Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related ProblemsSpringer Proceedings in Mathematics & StatisticsSpringer Nature SwitzerlandOctober 2023HALDOIback to text

Doctoral dissertations and habilitation theses

• 15 thesisR.Romane Hélie. Relaxation scheme for the simulation of plasmas in tokamaks.Université de StrasbourgMarch 2023HALback to text

Reports & preprints

• 16 miscJ.Joubine Aghili and O.Olga Mula. An optimal control framework for adaptive neural ODEs.April 2023HALback to text
• 17 miscC.Christophe Berthon and V.Victor Michel-Dansac. A fully well-balanced hydrodynamic reconstruction.April 2023HALback to text
• 18 miscM.Mickael Bestard, E.Emmanuel Franck, L.Laurent Navoret and Y.Yannick Privat. Optimal scenario for road evacuation in an urban environment.October 2023HALback to text
• 19 miscL.Léo Bois, E.Emmanuel Franck, L.Laurent Navoret and V.Vincent Vigon. An optimal control deep learning method to design artificial viscosities for Discontinuous Galerkin schemes.September 2023HALback to text
• 20 miscA.Antonin Chambolle, I.Idriss Mazari-Fouquer and Y.Yannick Privat. Stability of optimal shapes and convergence of thresholding algorithms in linear and spectral optimal control problems.June 2023HALback to text
• 21 miscA.Antonin Chambolle, I.Idriss Mazari-Fouquer and Y.Yannick Privat. Stability of optimal shapes and convergence of thresholding algorithms in linear and spectral optimal control problems: Supplementary material.June 2023HALback to text
• 22 miscN.Nilasis Chaudhuri, L.Laurent Navoret, C.Charlotte Perrin and E.Ewelina Zatorska. Hard congestion limit of the dissipative Aw-Rascle system.June 2023HALback to text
• 23 miscR.Raphaël Côte, C.Clémentine Courtès, G.Guillaume Ferriere and Y.Yannick Privat. Minimal time of magnetization switching in small ferromagnetic ellipsoidal samples.January 2023HALback to text
• 24 miscR.Raphaël Côte, E.Emmanuel Franck, L.Laurent Navoret, G.Guillaume Steimer and V.Vincent Vigon. Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network.November 2023HALback to text
• 25 miscC.Clémentine Courtès, M.Matthieu Boileau, R.Raphaël Côte, P. A.Paul Antoine Hervieux and G.Giovanni Manfredi. Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers.December 2023HALback to text
• 26 miscC.Clément Flint and P.Philippe Helluy. Reducing the memory usage of Lattice-Boltzmann schemes with a DWT-based compression.February 2023HALback to text
• 27 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 2023HALback to text
• 28 miscE.Emmanuel Franck, V.Victor Michel-Dansac and L.Laurent Navoret. Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks.October 2023HALback to text
• 29 miscK.Kévin Guillon, R.Romane Hélie and P.Philippe Helluy. Stability analysis of the vectorial lattice-Boltzmann method.February 2023HALback to text
• 30 miscR.Romane Hélie and P.Philippe Helluy. Stable second order boundary conditions for kinetic approximations.June 2023HALback to text
• 31 miscM.Michel Mehrenberger, L.Laurent Navoret and A.-T.Anh-Tuan Vu. Composition schemes for the guiding-center model.March 2023HALback to text