2025Activity report​‌Project-TeamMACARON

3.1.1 Optimizing​ parts of numerical solvers​‌

High fidelity simulation of​​ compressible fluids still remains​​​‌ an important challenge, and​ we are convinced that​‌ solving it would benefit​​ from recent deep learning​​​‌ tools to optimize space​ and time discretizations, among​‌ which the Finite Volume,​​ Discontinuous Galerkin or Lattice​​​‌ Boltzmann methods. For nonlinear​ problems such as the​‌ Euler system or the​​ shallow water equations, theory​​​‌ has been developed to​ ensure that the numerical​‌ schemes capture the right​​ solution. However, this theoretical​​​‌ framework does not always​ indicate how to adapt​‌ the schemes, especially high-order​​ schemes that admit numerical​​​‌ instability problems, to increase​ accuracy or preserve certain​‌ physical properties. Choices are​​ then sometimes made in​​​‌ a heuristic way by​ tuning some parameters in​‌ the schemes:

• numerical Finite​​ Volumes flux corrections and​​​‌ slope limiters 84,​
• artificial viscosity for Discontinuous​‌ Galerkin schemes 52,​​
• relaxation matrix/equilibrium function for​​​‌ multi-scale relaxation schemes and​ the Lattice Boltzman Method​‌ 78,
• well-balanced corrections​​ 80, 57.​​​‌

These choices could be​ greatly improved using machine​‌ learning techniques. Our aim​​ is to design these​​​‌ key parameters automatically. This​ will simplify the use​‌ of these schemes (because​​ the parameters will no​​​‌ longer have to be​ chosen by the user)​‌ and increase the accuracy​​ of the methods (because​​​‌ the parameters will be​ chosen in a more​‌ optimal way). These strategies​​ are particularly well-suited to​​​‌ high-order schemes, where the​ extra precision is offset​‌ by lower stability, which​​ is often subject to​​​‌ correction. For that, we​ will consider numerical neural​‌ networks but also symbolic​​ regression methods which make​​​‌ it possible to obtain​ analytical formulas.

The team​‌ has specialised in schemes​​ based on relaxation approaches​​​‌ before avoiding or limiting​ the restriction of the​‌ CFL condition. These include​​ the kinetic relaxation approach​​​‌ 49, 53 and​ the Xin-Jin/Suliciu relaxation approaches​‌ for multiscale problems 99​​, 101. We​​​‌ will continue developing these​ approaches, in particular by​‌ extending them to more​​ difficult problems and increasing​​​‌ the order of accuracy.​ The numerical methods thus​‌ obtained are then to​​ be coupled with machine​​​‌ learning to make them​ more effective.

One of​‌ the main challenges is​​ to incorporate these data-driven​​​‌ functions into the schemes,​ while still preserving the​‌ classical properties of the​​ schemes: convergence, stability, entropy​​​‌ dissipation, positivity of the​ solutions, etc. To achieve​‌ this, the exact data-driven​​ function, as well as​​​‌ the training procedure, must​ be chosen carefully. More​‌ precisely, the choice of​​ the so-called loss function,​​​‌ which is optimized in​ the learning steps, is​‌ crucial. We will explore​​ supervised learning where loss​​​‌ functions compare the learned​ function to reference ones,​‌ as well as unsupervised​​ learning, where the loss​​ functions do not refer​​​‌ to any reference functions,‌ e.g., residual loss functions‌​‌ in PINNs (Physics-Informed Neural​​ Networks 88) or​​​‌ discriminative loss functions that‌ can detect defects in‌​‌ classical schemes (Generative Adversarial​​ Networks 60).

3.1.2 Meshless and‌​‌ neural approaches

3.1.3​​​‌ Optimizing the representation of​ the approximate solutions

3.1.4 Including data-driven predictions‌​‌ into numerical methods

3.2.1 Continual learning,​​​‌ sampling and likelihood

To​ obtain robust code that​‌ learns from the data​​ produced by the code,​​​‌ we need to use​ continuous learning methods (data​‌ that arrives regularly) and​​ to detect if the​​ code is going to​​​‌ be used in a‌ configuration where the neural‌​‌ network is not going​​ to work in order​​​‌ to de-activate the network,‌ for example. The second‌​‌ problem in learning is​​ the detection of out-of-distribution​​​‌ examples (OOD) 105.‌ We propose to study‌​‌ different methods for that​​ and apply them to​​​‌ our hybrid simulation codes.‌ We could use generative‌​‌ models (Variational auto-encoders 68​​, normalizing flows 69​​​‌, Denoising Diffusion Probabilistic‌ Model 65) in‌​‌ order to capture the​​ probabilistic distribution of the​​​‌ inputs data of the‌ code. This will allow‌​‌ us to test whether​​ a new input has​​​‌ been produced by the‌ distribution. If this is‌​‌ not the case, the​​ network is likely to​​​‌ fail. Another important problem‌ is to make the‌​‌ training continuous while a​​ given simulation code is​​​‌ used, in order to‌ become specialized to the‌​‌ data given by the​​ user. We can model​​​‌ the parameters and initial‌ state space $S_{\mathrm{0‌‌}}$ by a time-dependent probability​​ distribution where the evolution​​​‌ is assumed to be‌ smooth over time. The‌​‌ aim will be to​​ develop learning procedures that​​​‌ can capture $p_{\mathrm{t‌}}$ using a large training‌​‌ set at $t=0$ and smaller data​​​‌ sets at later times‌ $(t_1,‌‌...,t_n)$,​​​‌ in order to limit‌ data storage requirements. These‌​‌ small sets of continuously​​ arriving data correspond to​​​‌ the data produced each‌ time the code is‌​‌ used to produce a​​ simulation. This type of​​​‌ approaches are referred to‌ as continual learning or‌​‌ life-long learning in the​​ literature 66. Their​​​‌ use in the context‌ of PDEs has not‌​‌ been explored, to the​​ best of our knowledge.​​​‌ Continual learning could be‌ used on all the‌​‌ supervised models developed in​​ our project team, or​​​‌ specifically on generative models‌ that could in turn‌​‌ be used to train​​ other neural networks by​​​‌ means of generating examples‌ following the relevant distribution.‌​‌

3.2.2 Self-specialized numerical‌ methods

Combining the data-driven‌​‌ solvers from the first​​ axis with continual learning​​​‌ and Out-Of-Distribution Detection approaches,‌ we wish to design‌​‌ complete prototypes of self-specialized​​ codes. In practice, we​​​‌ would like to validate‌ this approach for two‌​‌ particular numerical methods in​​ simple configurations.

First use​​​‌ case: we construct‌ a 2D or 3D‌​‌ Lattice Boltzmann scheme code​​ for Euler, MHD or​​​‌ SHTC equations with some‌ guarantees on the stability‌​‌ of all regimes. We​​ will use a general​​​‌ relaxation matrix (multiple relaxation‌ time method). Using a‌​‌ reinforcement method or the​​ differentiable physical approach, we​​​‌ will learn the relaxation‌ matrix such that the‌​‌ discrete residue or the​​ error compared to a​​​‌ fine solution computed by‌ the user will be‌​‌ minimal. To obtain a​​ full prototype we must​​​‌ add a mechanism for‌ continual learning and a‌​‌ mechanism of OOD detection.​​ We must also include​​​‌ a safety mode of‌ the method in this‌​‌ case.

Second use case​​​‌: we write a​ hybrid finite element code​‌ for implicit time integration​​ for strongly nonlinear equations​​​‌ (nonlinear anisotropic diffusion, reduced​ MHD). The idea will​‌ be to construct a​​ first approximation of the​​​‌ solution using a parametric​ PINNs or a Neural​‌ operator (like Fourier Neural​​ Operator) and integrate this​​​‌ approximation inside the numerical​ methods. This approach will​‌ be used to enhance​​ the basis functions and​​​‌ accelerate the Newton convergence.​ One of the main​‌ questions is how to​​ construct the learning process​​​‌ with data which arrive​ step by step. We​‌ consider an implicit scheme​​ with a Newton method​​​‌ (neural networks which take​ data and previous time​‌ step input) with adaptive​​ time step. If the​​​‌ Newton convergence is fast,​ we increase the time​‌ step at the following​​ step. If there is​​​‌ no convergence, we recompute​ the time step with​‌ a smaller $\Delta \mathrm{t}$. The more we​​​‌ make simulations, the more​ we collect data to​‌ increase the accuracy of​​ the neural network for​​​‌ the prediction of Newton’s​ method.

3.3.1​​​‌ Reduced models in asymptotic​ regimes

In some previous​‌ and ongoing works (ANR​​ MILK), we have studied​​​‌ the construction of reduced​ models for kinetic equations​‌ in different asymptotic regimes​​ using neural networks. Such​​​‌ reduced models are very​ interesting since kinetic equations​‌ describe the evolution of​​ distribution in phase space​​​‌ (position-velocity), their full numerical​ resolution would require a​‌ lot of computing resources​​ and thus reduced models​​​‌ are much cheaper to​ simulate. We consider two​‌ different types of asymptotic​​ regimes.

The first asymptotic​​​‌ regime is the collisional​ regime. When the collision​‌ rate is high, the​​ velocity distribution function tends​​​‌ to be Gaussian and​ analytical reduced models are​‌ well known: these are​​ the Euler or Navier-Stokes​​​‌ systems. However, for weakly​ collisional regimes, there are​‌ no such analytical reduced​​ models and this is​​​‌ where neural network can​ help. We have started​‌ a work on the​​ non-local closure problem of​​​‌ the Euler equations for​ the Vlasov-Poisson dynamics 61​‌, 39 and we​​ would like to generalize​​​‌ it to more complex​ physical problems: complex collisional​‌ operator, two species coupling,​​ Vlasov-Maxwell dynamics with method​​​‌ able to be invariant​ to the spatial grid​‌ and potentially interpretable. We​​ can also consider generalized​​​‌ moment models 87,​ 62 and aim for​‌ a network to learn​​ the choice of moment​​​‌ and the local closure.​ In this context, we​‌ propose to ensure the​​ entropy stability of the​​ models obtained since local​​​‌ models are easier to‌ study. This type of‌​‌ method will also be​​ used to design macroscopic​​​‌ biological models using particle‌ simulations (ANR Mapeflu). The‌​‌ company AxesSim is very​​ interested in Vlasov-Maxwell simulations​​​‌ and has optimized codes‌ for hyperbolic equations. The‌​‌ construction of reduced models​​ within this framework would​​​‌ be an important axis‌ of collaboration.

The second‌​‌ asymptotic regime is the​​ strong magnetic field regime.​​​‌ Indeed, in this regime,‌ the charged particles will‌​‌ rotate rapidly around a​​ slow trajectory. Since following​​​‌ the highly oscillating trajectories‌ would be very computationally‌​‌ demanding, we would like​​ a model for the​​​‌ slow trajectory only. In‌ sophisticated physical configurations (e.g.,‌​‌ for non-periodic magnetic fields),​​ deriving an analytical solution​​​‌ is difficult if not‌ impossible. Using neural networks,‌​‌ we would like to​​ filter the fast oscillating​​​‌ dynamics and then devise‌ a reduced model. In‌​‌ addition, separately reconstructing the​​ fast rotation dynamics would​​​‌ make it possible to‌ add relevant corrections to‌​‌ the slow dynamics model.​​ This would allow us​​​‌ to construct valid schemes‌ in different magnetic field‌​‌ magnitude regimes 50.​​

3.3.2‌​‌ Continuous Reduced Order Modeling​​ (CROM) for strongly nonlinear​​​‌ PDEs and kinetic equations‌

The Reduced Order Modeling‌​‌ (ROM) and reduced basis​​ methods 64 have demonstrated​​​‌ their powerful capabilities for‌ many problems. They are‌​‌ based on a “projection"​​ of the model onto​​​‌ a reduced basis obtained‌ by singular value decomposition‌​‌ of snapshots of the​​ solutions 45. However,​​​‌ they have difficulties in‌ reducing hyperbolic PDE dynamics‌​‌ and highly nonlinear problems.​​ Since some years the​​​‌ main alternative is based‌ on auto-encoder neural networks‌​‌ 79, 70.​​ Imposing a symplectic structure​​​‌ in these methods is‌ part of the ANR‌​‌ project MILK, where we​​ investigate reduction with manifold​​​‌ learning or auto-encoder approaches.‌ In this project, we‌​‌ propose to focus on​​ a very recent approach​​​‌ called Continuous ROM47‌, 46, 106‌​‌, which is based​​ on the implicit neural​​​‌ representation paradigm. The‌ classical ROM approach discretizes‌​‌ the PDE to obtain​​ a large dimensional ODE​​​‌ and compresses this ODE‌ with a Convolutional Auto-encoder‌​‌ or POD. Here, the​​ idea to represent the​​​‌ solution (decoder) using a‌ MLP coordinate based network‌​‌ which depends also on​​ latent variables which are​​​‌ obtained by an auto-encoder.‌ As in the ROM‌​‌ approach, the aim is​​ to write the dynamics​​​‌ on the latent variable.‌ All the works on‌​‌ physics-informed neural networks will​​ be used for the​​​‌ decoder. For the encoder‌ process, we will investigate‌​‌ some permutation-invariant neural networks​​ or greedy approaches. Here,​​​‌ we propose to study‌ multiple strategies to learn‌​‌ the reduced model (Reduced​​ Galerkin projection, differentiable physics​​​‌ learning, classical supervised methods).‌ We will also study‌​‌ how to incorporate the​​ properties of the PDE​​​‌ in these reduced models‌ (asymptotic limits, well-balancing, symplectic‌​‌ properties, Poisson brackets 63​​ or entropy dissipation, which​​​‌ is essential for stability).‌ We will mainly apply‌​‌ these news approaches on​​​‌ nonlinear conservation laws, wave​ equations and kinetic models.​‌ These approaches could also​​ be interesting to compute​​​‌ a reduced basis only​ in the velocity space​‌ for kinetic equations. To​​ obtain explicable and easy​​​‌ to disseminate reduced models,​ we will couple these​‌ methodologies with symbolic regression​​ methods (see e.g. 98​​​‌, 44) which​ allows to learn analytic​‌ formula. Comparing to the​​ classical approaches, the reduced​​​‌ models obtained with CROM​ approach can be used​‌ on any meshes and​​ consequently coupled with any​​​‌ code without additional interpolation​ step and can be​‌ used with symbolic approaches.​​ Obtaining analytical models is​​​‌ not possible with traditional​ ROM approaches.

3.4.1 Reinforcement​​ Learning methods for PDEs​​​‌ and high dimensional action​ spaces

In the last​‌ decade, many RL algorithms​​ have been written by​​​‌ the machine learning community.​ This approach allows constructing​‌ feedback loops that are​​ essential for real-time control.​​​‌ Some of these methods​ can handle a continuous​‌ action (control) space. However​​ these methods are more​​​‌ difficult to use in​ large-dimensional action spaces and​‌ for long time problem.​​ Indeed, depending on the​​​‌ application, there may be​ problems with exploration (we​‌ do not know the​​ action space correctly) or​​​‌ with precision and regularity​ (it is more difficult​‌ to obtain precise control​​ compared to classical gradient​​​‌ approaches). For such problems,​ the control is a​‌ spatial function (discretized in​​ general) so the dimension​​​‌ is large. In this​ case we are not​‌ able to correctly define​​ an admissible/realistic action and​​​‌ sample the action space.​ For this reason, these​‌ algorithms generally make use​​ of a basic parametrization​​​‌ of the action function​ which is very restrictive.​‌ We propose to use​​ generative models/operators to construct​​​‌ probabilistic policies able to​ explore large-dimensional structured actions,​‌ and to couple this​​ with gradient methods (adjoint​​​‌ approach, PINNs) to guide​ the exploration towards interesting​‌ areas. These methods will​​ be an alternative to​​​‌ differential physics to train​ large networks (which is​‌ a very costly, and​​ sometimes unstable, approach) present​​​‌ in numerical schemes or​ physical model taking into​‌ account of the long​​ time stability.

3.4.2 Optimal control​​ and physics-informed ML

Recent​​​‌ work, such as 82​ have used PINNs to​‌ solve open loop optimal​​ control problems. These methods​​​‌ could be very interesting​ for solving high dimensional​‌ problems, closed loop problems,​​ or shape optimization, which​​​‌ is equivalent to a​ neural implicit representation. Indeed,​‌ for closed loop problems,​​ standard approaches based on​​​‌ the Hamilton Jacobi Bellman​ equation are very cumbersome​‌ to implement. We will​​ study these methods from​​ a theoretical point of​​​‌ view on simple cases‌ and their practical improvement.‌​‌ We will also investigate​​ the extension of these​​​‌ approaches with physics-informed neural‌ operators, which seem to‌​‌ have a greater approximation​​ capacity than PINNs and​​​‌ could be efficient to‌ treat inverse problems in‌​‌ high dimension. Another strategy​​ we propose is to​​​‌ use generative models. Generative‌ models, like diffusion models,‌​‌ make it possible to​​ sample high-dimensional probability distributions.​​​‌ Recently, a new approach‌ to robot control has‌​‌ been proposed. It consists​​ in training a diffusion​​​‌ model to build an‌ efficient control from a‌​‌ random control. This amounts​​ to concentrating a probability​​​‌ law of controls on‌ the most optimal control‌​‌ using physics-informed loss. We​​ propose to couple this​​​‌ with Neural encoder approaches‌ and apply it to‌​‌ control PDEs and inverse​​ problems.

3.4.3 Accelerated open loop​​ optimal control by ML​​​‌

Optimal control methods that‌ are based on the‌​‌ Pontryagin maximum principle and​​ gradient-based methods are very​​​‌ computationally intensive. Reducing the‌ computational cost of these‌​‌ methods is an important​​ issue, that could be​​​‌ solved using machine learning.‌ In a similar way‌​‌ to the case of​​ Newton's method, Neural operator/PINNs​​​‌ approaches can be used‌ to obtain an approximate‌​‌ solution of the control​​ problem which will be​​​‌ used as an initial‌ guess to accelerate the‌​‌ convergence of the iterative​​ methods. We will also​​​‌ study another approach which‌ consists of using reduced‌​‌ modeling to accelerate each​​ step of the gradient​​​‌ method. We have recently‌ constructed a method where‌​‌ we control a complex​​ problem by constructing a​​​‌ reduced model which is‌ checked and corrected according‌​‌ to the effect of​​ the control obtained on​​​‌ the full model. We‌ wish to focus on‌​‌ correcting the reduced model​​ (which may be invalid​​​‌ in some areas) as‌ the control algorithm proceeds.‌​‌ These approaches could be​​ viewed as model-based Reinforcement​​​‌ learning and will use‌ our work on reduced‌​‌ modeling in Section 3.3​​. This project is​​​‌ a lower priority than‌ the other optimal control‌​‌ projects.

3.4.4 Inverse‌ problem and super-resolution

We‌​‌ consider the following inverse​​ problem: given a discrete-time​​​‌ measurement of the propagation‌ of a sound impulse‌​‌ from a pointwise, omnidirectional​​ source to a microphone​​​‌ array (called RIR or‌ Room Impulse Response), can‌​‌ we estimate the geometry​​ of the room? As​​​‌ part of Tom Sprunck's‌ PhD, (01/11/2021 – 17/12/2024),‌​‌ this question has been​​ partially addressed theoretically and​​​‌ numerically, in the case‌ of cuboid rooms. To‌​‌ formalize this problem and​​ deal with numerical aspects,​​​‌ we are investigating the‌ use of the so-called‌​‌ image source method, that​​ allows replacing the boundary​​​‌ of the room to‌ be reconstructed by a‌​‌ constellation of image sources​​ corresponding to iteratively reflected​​​‌ copies of the original‌ sound source with respect‌​‌ to the walls of​​ the room. The question​​​‌ can then be formulated‌ as an optimization problem‌​‌ which consists of identifying​​​‌ the positions of a​ linear combination of Dirac​‌ masses in space —​​ the image sources —​​​‌ from discrete time observations​ of the solution of​‌ the wave equation at​​ the microphones (the RIRs),​​​‌ which are imaged by​ a linear operator. Knowing​‌ the positions of the​​ image sources up to​​​‌ order 1 is then​ sufficient to reconstruct the​‌ geometry of the room.​​ This problem is thus​​​‌ part of the recent​ framework of super-resolution, which​‌ aims at reconstructing the​​ positions and amplitudes of​​​‌ the peaks of a​ sparse measurement from linear​‌ observations. We consider here​​ a convex relaxation of​​​‌ the problem by extending​ it to the set​‌ of Radon measurements (BLASSO).​​ We are currently considering​​​‌ the implementation of efficient​ numerical methods exploiting this​‌ relaxation. To make the​​ method applicable to real​​​‌ world data that feature​ complex frequency- and angle-dependent​‌ responses of sources, microphones​​ and reflecting surfaces inside​​​‌ the room, we intend​ to hybridize these methods​‌ with data driven techniques.​​ These could be achieved​​​‌ by training generative models​ on real databases of​‌ source, microphone and wall​​ responses, or by using​​​‌ deep unrolling on parts​ of the optimization scheme,​‌ in order to optimize​​ them end-to-end on real​​​‌ or realistically simulated data.​

7.1.1 acoustic-sfw

• Name:​‌
  Hearing the Shape of​​ a Shoebox Room
• Keywords:​​​‌
  Acoustic Model, Acoustics, Inverse​ problem, Super-resolution
• Functional Description:​‌

  1) An adaptation of​​ the Sliding Frank-Wolfe algorithm​​​‌ for the gridless 3D​ recovery of image sources​‌ from room impulse responses​​ recorded with a compact​​​‌ microphone array. The algorithm​ is described in details​‌ in this article: [1]​​ Sprunck, T., Deleforge, A.,​​​‌ Privat, Y., & Foy,​ C. (2022). Gridless 3d​‌ recovery of image sources​​ from room impulse responses.​​​‌ IEEE Signal Processing Letters,​ 29, 2427-2431. HAL: https://inria.hal.science/hal-03763838/​‌

  2) An algorithms that​​ recovers the 18 input​​​‌ parameters of the shoebox​ image source method from​‌ given such an estimated​​ image source point cloud,​​​‌ namely: - The room's​ width, depth and height​‌ - The 6 DoF​​ room translation and rotation​​​‌ in the array's coordinate​ frames - The 3D​‌ source position - One​​ absorption coefficient for each​​​‌ of the room boundary.​

  The algorithm is described​‌ in details in this​​ article: [2] Sprunck, T.,​​​‌ Deleforge, A., Privat, Y.,​ & Foy, C. (2025).​‌ Fully reversing the shoebox​​ image source method: From​​​‌ impulse responses to room​ parameters. IEEE Transactions on​‌ Audio, Speech and Language​​ Processing. HAL: https://inria.hal.science/hal-04567514/

• Release​​​‌ Contributions:
  First version.
• URL:​
  https://­github.­com/­Sprunckt/­acoustic-sfw
• Contact:
  Antoine Deleforge​‌

7.1.2 opla

• Name:
  One​​ Page Layout Automator
• Keywords:​​​‌
  Python, Web
• Functional Description:​
  - Generate a professional​‌ webpage from a single​​ markdown file - Handle​​​‌ publication lists coming from​ HAL database or from​‌ a bibtex file -​​ Highly customizable thanks to​​​‌ the use of jinja​ templates, shortcodes and custom​‌ styles
• Contact:
  Matthieu Boileau​​

7.1.3 LLG3D

• Name:
  LLG3D​​​‌
• Keywords:
  3D, Python, MPI,​ Micromagnetism, Landau-Lifshitz-Gilbert equation
• Functional​‌ Description:
  LLG3D is a​​ solver for the stochastic​​​‌ Landau-Lifshitz-Gilbert equation in 3D.​ It is written in​‌ Python and utilizes the​​ MPI and OpenCL libraries​​​‌ to parallelize computations.
• URL:​
  https://­llg3d.­pages.­math.­unistra.­fr/­llg3d/
• Contact:
  Matthieu Boileau​‌
• Partner:
  IPCMS

7.1.4 Scimba​​

• Name:
  SCIentific Machine learning​​​‌ liBrary
• Keywords:
  Scientific computing,​ Machine learning
• Functional Description:​‌
  Scimba is a library,​​ based on Pytorch, which​​​‌ implements a number of​ physically informed learning methods​‌ for PDEs. It is​​ a research library, the​​​‌ list of implemented methods​ will evolve with our​‌ research. The main tools​​ implemented currently or in​​​‌ the future are PINNs​ and Neural Galerkine methods,​‌ neural operators and generative​​ models.
• URL:
  https://­www.­scimba.­org/
• Contact:​​​‌
  Emmanuel Franck
• Partners:
  Inria,​ CEA

8.1.1 Well-balanced schemes​‌

Participants: Victor Michel-Dansac,​​ Andrea Thomann.

In​​​‌ 6, we presented​ a high-order finite volume​‌ framework for the numerical​​ simulation of shallow water​​ flows. The method is​​​‌ designed to accurately capture‌ complex dynamics inherent in‌​‌ shallow water systems, and​​ it is particularly suited​​​‌ for real applications such‌ as tsunami simulations. The‌​‌ arbitrarily high-order framework ensures​​ accurate representation of flow​​​‌ behavior, crucial for simulating‌ phenomena characterized by rapid‌​‌ changes and fine-scale features.​​ Thanks to an ad-hoc​​​‌ reformulation in terms of‌ production-destruction terms, the time‌​‌ integration ensures positivity preservation​​ without any time-step restrictions,​​​‌ a vital attribute for‌ physical consistency, especially in‌​‌ scenarios where negative water​​ depth reconstructions could lead​​​‌ to unrealistic results. In‌ order to introduce the‌​‌ preservation of general steady​​ equilibria dictated by the​​​‌ underlying balance law, the‌ technique from previous MACARON‌​‌ work 38 was used.​​ Indeed, we blended the​​​‌ high-order reconstruction and the‌ numerical flux through a‌​‌ convex combination with a​​ well-balanced approximation, which is​​​‌ able to provide exact‌ preservation of both stationary‌​‌ and moving equilibria for​​ pseudo-monodimensional states as well​​​‌ as for general 2D‌ water at rest solutions.‌​‌

Concerning compressible fluid dynamics,​​ in 5, we​​​‌ derived a numerical scheme‌ to approximate weak solutions‌​‌ of the Euler equations​​ with a gravitational source​​​‌ term. The designed scheme‌ is proved to be‌​‌ fully well-balanced since it​​ is able to exactly​​​‌ preserve all moving equilibrium‌ solutions, as well as‌​‌ the corresponding steady solutions​​ at rest obtained when​​​‌ the velocity vanishes. Moreover,‌ the proposed scheme is‌​‌ entropy-preserving since it satisfies​​ all fully discrete entropy​​​‌ inequalities. In addition, in‌ order to satisfy the‌​‌ required admissibility of the​​ approximate solutions, the positivity​​​‌ of both approximate density‌ and pressure is established.‌​‌ An extension to two-dimensional​​ problems is given, applying​​​‌ the one-dimensional framework direction‌ by direction on Cartesian‌​‌ grids. Since the previous​​ work was devoted to​​​‌ ideal gases, we constructed‌ an extension to non-ideal‌​‌ gases in 16,​​ in which we extended​​​‌ all properties, and also‌ proposed a second-order extension.‌​‌ Validation experiments were carried​​ out on six different​​​‌ equations of state as‌ examples, four analytic and‌​‌ two tabulated ones.

8.1.2​​ Fourth-order entropy-stable lattice Boltzmann​​​‌ schemes for hyperbolic systems‌

Participants: Thomas Bellotti,‌​‌ Philippe Helluy, Laurent​​ Navoret.

In 4​​​‌, we have developed‌ a novel framework for‌​‌ constructing fourth-order entropy-stable lattice​​ Boltzmann schemes tailored to​​​‌ multidimensional nonlinear systems of‌ conservation laws. These schemes‌​‌ maintain fourth-order accuracy for​​ smooth solutions while ensuring​​​‌ entropy stability through a‌ local relaxation process.

8.1.3‌​‌ A stochastic front tracking​​ method for compressible flow​​​‌ with interfaces

Participants: Philippe‌ Helluy.

In 31‌​‌, we propose a​​ front tracking method to​​​‌ deal with compressible flows‌ involving sharp interfaces. This‌​‌ method relies on a​​ first-order finite-volumes scheme of​​​‌ Lagrange-Projection type with a‌ pseudo-random sampling technique, allowing‌​‌ to reduce numerical diffusion​​ and keep interfaces sharp.​​​‌

8.1.4 Simulations of Richtmyer-Meshkov‌ instabilities using a stochastic‌​‌ front tracking method

Participants:​​ Philippe Helluy.

In​​​‌ 15, we apply‌ a stochastic front tracking‌​‌ method to simulate Richtmyer-Meshkov​​ instabilities. This approach demonstrates​​​‌ significantly better agreement with‌ experimentally measured growth rates‌​‌ compared to non-tracking computations.​​​‌

8.1.5 Convergence of a​ hyperbolic thermodynamically compatible finite​‌ volume scheme for the​​ Euler equations

Participants: Andrea​​​‌ Thomann.

In 10​, we study the​‌ convergence of a novel​​ family of thermodynamically compatible​​​‌ schemes for hyperbolic systems​ (HTC schemes) in the​‌ framework of dissipative weak​​ solutions applied to the​​​‌ Euler equations of compressible​ gas dynamics. The results​‌ are obtained under a​​ physically-reasonable assumption that a​​​‌ fluid is out of​ vacuum and has a​‌ bounded energy. Two key​​ novelties of our method​​​‌ are i) entropy is​ treated as one of​‌ the main field quantities​​ and ii) the total​​​‌ energy conservation is a​ consequence of compatible discretization​‌ and application of the​​ Abgrall flux.

8.1.6 Semi-implicit​​​‌ schemes for hyperbolic multi-scale​ systems of continuum mechanics​‌

Participants: Andrea Thomann.​​

In 18 a new​​​‌ semi-implicit relaxation scheme for​ the simulation of multi-scale​‌ hyperbolic conservation laws based​​ on a Jin-Xin relaxation​​​‌ approach is presented and​ is an extension of​‌ the previous work 100​​. It is based​​​‌ on the splitting of​ the flux function into​‌ two or more subsystems​​ separating the different scales​​​‌ of the considered model​ whose stiff components are​‌ relaxed thus yielding a​​ linear structure of the​​​‌ resulting relaxation model on​ the relaxation variables. This​‌ allows the construction of​​ a linearly implicit numerical​​​‌ scheme, where convective processes​ are discretized explicitly. Thanks​‌ to this linearity, the​​ discrete scheme can be​​​‌ reformulated in linear decoupled​ wave-type equations resulting in​‌ the same number of​​ evolved variables as in​​​‌ the original system. To​ obtain a scale independent​‌ numerical diffusion, centred fluxes​​ are applied on the​​​‌ implicitly treated terms, whereas​ classical upwind schemes are​‌ applied on the explicit​​ parts. The numerical scheme​​​‌ is validated by applying​ it on the Toro​‌ & Vázquez-Cendón splitting of​​ the Euler equations 103​​​‌ and the Fambri splitting​ of the ideal MHD​‌ equations 54 where the​​ flux is split in​​​‌ two, respectively three sub-systems.​

A similar approach has​‌ been applied in 29​​, where we introduce​​​‌ a novel structure-preserving vertex-staggered​ semi-implicit four-split discretization of​‌ a unified first order​​ hyperbolic formulation of continuum​​​‌ mechanics that is able​ to describe at the​‌ same time fluid and​​ solid materials in one​​​‌ and the same mathematical​ model. The governing PDE​‌ system goes back to​​ pioneering work of Godunov,​​​‌ Romenski, Peshkov and collaborators,​ see 86. Previous​‌ structure-preserving discretizations of this​​ system allowed to respect​​​‌ the curl-free properties of​ the distortion field and​‌ of the specific thermal​​ impulse in the absence​​​‌ of source terms and​ were also able to​‌ properly deal with the​​ low Mach number limit​​​‌ with respect to the​ adiabatic sound speed. However,​‌ the evolution of the​​ thermal impulse and the​​​‌ distortion field were still​ discretized explicitly, thus requiring​‌ a rather severe CFL​​ stability restriction on the​​​‌ time step based on​ the shear sound speed​‌ and on the finite,​​ but potentially large, speed​​​‌ of heat waves. Instead,​ the new four-split semi-implicit​‌ scheme presented in this​​ paper has a CFL​​ time step restriction based​​​‌ only on the magnitude‌ of the velocity field‌​‌ of the continuum. For​​ this purpose, the governing​​​‌ PDE system is split‌ into four subsystems: i)‌​‌ a convective subsystem, which​​ is the only one​​​‌ that is treated explicitly;‌ ii) a heat subsystem;‌​‌ iii) a subsystem containing​​ momentum, distortion field and​​​‌ specific thermal impulse; iv)‌ a pressure subsystem. The‌​‌ last three subsystems ii)-iv)​​ are all discretized implicitly,​​​‌ hence the time step‌ is only limited by‌​‌ a rather mild CFL​​ condition based on the​​​‌ magnitude of the velocity‌ field. The method is‌​‌ consistent with the low​​ Mach number limit of​​​‌ the equations, with the‌ stiff relaxation limits and‌​‌ it maintains an exactly​​ curl-free distortion field and​​​‌ thermal impulse in the‌ case of linear source‌​‌ terms or in their​​ absence. We show several​​​‌ numerical results for classical‌ benchmark problems that allow‌​‌ to assess the performance​​ of the scheme in​​​‌ different asymptotic limits of‌ the governing equations, including‌​‌ the fluid and solid​​ limit.

8.1.7 Phi-FD: A​​​‌ well-conditioned finite difference method‌ inspired by phi-FEM for‌​‌ general geometries on elliptic​​ PDEs

Participants: Vincent Vigon​​​‌.

The paper 11‌ introduces phi-FD, a new‌​‌ finite difference method for​​ elliptic PDEs on general​​​‌ geometries, inspired by phi-FEM.‌ It operates on simple‌​‌ Cartesian grids while handling​​ complex domains via a​​​‌ level-set description, yielding a‌ flexible scheme whose system‌​‌ matrix remains well-conditioned, unlike​​ earlier non-rectangular finite difference​​​‌ methods. The authors prove‌ quasi-optimal convergence rates in‌​‌ several norms and demonstrate​​ good conditioning of the​​​‌ discrete system. They also‌ incorporate multigrid techniques to‌​‌ speed up solution of​​ the linear systems. Numerical​​​‌ experiments in 2D and‌ 3D confirm the theoretical‌​‌ results and show that​​ phi-FD performs competitively with​​​‌ standard finite element methods‌ and the Shortley-Weller scheme.‌​‌

8.2.1 Analysis‌ and Optimization of a‌​‌ Liquid-vapor Thermohydraulic Model

Participants:​​ Philippe Helluy.

In​​​‌ 14, we perform‌ a mathematical analysis and‌​‌ optimization of the drift-flux​​ model used in industrial​​​‌ thermal-hydraulic codes. The optimization‌ is based on a‌​‌ data-driven approach using a​​ neural network to predict​​​‌ the stationnary solutions of‌ the model. This allow‌​‌ to accelerate the convergence​​ of the code.

8.2.2​​​‌ Acceleration of the Convergence‌ of a Core Thermal‌​‌ Hydraulic Code Using Initialization​​ from a Neural Network​​​‌

Participants: Philippe Helluy.‌

In 21, we‌​‌ investigate the use of​​ neural networks to predict​​​‌ steady-state solutions for the‌ THYC-coeur code. This method‌​‌ achieves significant acceleration (exceeding​​ 60%) for nuclear reactor​​​‌ core simulations by providing‌ better initializations.

8.2.3 Enriched‌​‌ Finite element with neural​​ network

Participants: Victor Michel-Dansac​​​‌, Emmanuel Franck.‌

This work 24 is‌​‌ concerned with the enrichment​​ of finite element approximation​​​‌ spaces in order to‌ improve the accuracy of‌​‌ numerical solutions for elliptic​​ partial differential equations. The​​​‌ proposed approach aims at‌ enhancing the approximation of‌​‌ steady solutions without modifying​​​‌ the underlying finite element​ scheme or its convergence​‌ properties. The enrichment strategy​​ relies on the introduction​​​‌ of a prior, defined​ as an approximate solution​‌ of the elliptic problem,​​ which is computed using​​​‌ a Physics-Informed Neural Network​ (PINN). After recalling the​‌ standard finite element formulation,​​ we present a systematic​​​‌ procedure to enrich the​ finite element space with​‌ this prior. We then​​ establish rigorous a priori​​​‌ error estimates, showing that​ the enriched finite element​‌ method preserves the original​​ order of convergence, while​​​‌ improving the associated error​ constants. Particular attention is​‌ paid to the treatment​​ of boundary conditions, which​​​‌ plays a crucial role​ in the theoretical analysis​‌ and in the practical​​ construction of the enriched​​​‌ space. We show how​ the prior must be​‌ incorporated in order to​​ ensure consistency of the​​​‌ method and to avoid​ spurious boundary effects. Several​‌ numerical experiments are finally​​ presented to validate the​​​‌ theoretical results. These tests​ demonstrate that the enriched​‌ finite element method provides​​ a significantly improved accuracy​​​‌ compared to the standard​ finite element approach, while​‌ retaining the same convergence​​ behavior.

8.3.1 Domain decomposition​ of neural networks applied​‌ to wave problems

Participants:​​ Victor Michel-Dansac.

Accurately​​​‌ simulating wave propagation is​ crucial in fields such​‌ as acoustics, electromagnetism, and​​ seismic analysis. Traditional numerical​​​‌ methods, like finite difference​ and finite element approaches,​‌ are widely used to​​ solve governing partial differential​​​‌ equations (PDEs) such as​ the Helmholtz equation. However,​‌ these methods face significant​​ computational challenges when applied​​​‌ to high-frequency wave problems​ in complex two-dimensional domains.​‌ In 28, we​​ investigated Finite Basis Physics-Informed​​​‌ Neural Networks (FBPINNs) and​ their multilevel extensions as​‌ a promising alternative. These​​ methods leverage domain decomposition,​​​‌ partitioning the computational domain​ into overlapping sub-domains, each​‌ governed by a local​​ neural network. We assess​​​‌ their accuracy and computational​ efficiency in solving the​‌ Helmholtz equation for the​​ homogeneous case, demonstrating their​​​‌ potential to mitigate the​ limitations of traditional approaches.​‌

8.3.2 Neural Semi Lagrangian​​ solver for convection diffusion​​​‌ methods

Participants: Victor Michel-Dansac​, Emmanuel Franck,​‌ Laurent Navoret, Vincent​​ Vigon.

The classical​​​‌ methods are not able​ to treat with a​‌ good accuracy the convection​​ diffusion problems which appears​​​‌ in plasma or astrophysics.​ We propose a new​‌ sequential in time neural​​ network based method which​​​‌ coupling the PINNS approaches​ with the semi-Lagrangian method​‌ which allows to overcome​​ the stability issue. It​​​‌ relies on projecting the​ initial condition onto a​‌ finite-dimensional neural space, and​​ then solving an optimization​​​‌ problem, involving the backwards​ characteristic equation, at each​‌ time step. It is​​ particularly well-suited for implementation​​​‌ on GPUs, as it​ is fully parallelizable and​‌ does not require a​​ mesh. We provide rough​​​‌ error estimates, present several​ high-dimensional numerical experiments to​‌ assess the performance of​​ our approach, and compare​​​‌ it to other classical​ and neural methods. At​‌ the end the approach​​ is validated on plasma​​ dynmanic problem like the​​​‌ Vlasov equations 13.‌

8.3.3 Phi-FEM-FNO: A new‌​‌ approach to train a​​ Neural Operator as a​​​‌ fast PDE solver for‌ variable geometries

Participants: Vincent‌​‌ Vigon.

The paper​​ 12 introduces a method​​​‌ for solving PDEs on‌ varying geometries by combining‌​‌ the phi-FEM finite element​​ approach with the Fourier​​​‌ Neural Operator (FNO). FNO‌ is used as a‌​‌ learned operator that maps​​ problem data to solutions,​​​‌ while phi-FEM represents complex,‌ changing domains via level-set‌​‌ functions. The method is​​ applied to Poisson-Dirichlet and​​​‌ nonlinear elasticity equations, and‌ its performance is demonstrated‌​‌ through three numerical test​​ cases. The final test​​​‌ case also presents a‌ new phi-FEM-based numerical scheme‌​‌ for hyperelastic materials, providing​​ numerical evidence of the​​​‌ effectiveness of the combined‌ phi-FEM-FNO approach.

8.3.4 A‌​‌ neural network for predicting​​ with the diffusion equation:​​​‌ a case study of‌ long rooms

Participants: Antoine‌​‌ Deleforge.

The paper​​ 19 presents a method​​​‌ for estimating the spatially‌ dependent diffusion coefficient of‌​‌ the diffusion equation model​​ using an artificial neural​​​‌ network, for the case‌ study of acoustic modeling‌​‌ in long rooms. The​​ network is trained to​​​‌ relate the dimensions of‌ the room, the absorption‌​‌ coefficients of the surfaces​​ and the 3D source​​​‌ and receiver positions to‌ the corresponding diffusion coefficient‌​‌ using supervised learning on​​ data generated by an​​​‌ available solver. Results show‌ that the trained model‌​‌ can quickly recover the​​ space-varying diffusion coefficients over​​​‌ the room based only‌ on the model’s inputs.‌​‌ When the predicted diffusion​​ coefficients of the neural​​​‌ network are used in‌ the diffusion equation, the‌​‌ sound pressure level and​​ reverberation time of the​​​‌ room can be accurately‌ predicted. This paper received‌​‌ a best student paper​​ award.

8.4.1 Reduction of Hamiltonian‌​‌ particle dynamics

Participants: Emmanuel​​ Franck, Laurent Navoret​​​‌, Guillaume Steimer,‌ Vincent Vigon.

Hamiltonian‌​‌ particle-based simulations of plasma​​ dynamics are inherently computationally​​​‌ intensive, primarily due to‌ the large number of‌​‌ particles required to obtain​​ accurate solutions. This challenge​​​‌ becomes even more acute‌ in many-query contexts, where‌​‌ numerous simulations must be​​ conducted across a range​​​‌ of time and parameter‌ values. Consequently, it is‌​‌ essential to construct reduced​​ order models from such​​​‌ discretizations to significantly lower‌ computational costs while ensuring‌​‌ validity across the specified​​ time and parameter domains.​​​‌ Preserving the Hamiltonian structure‌ in these reduced models‌​‌ is also crucial, as​​ it helps maintain long-term​​​‌ stability.

In 30,‌ we introduce a nonlinear‌​‌ non-intrusive, data-driven model order​​ reduction method for the​​​‌ 1D-1V Vlasov-Poisson system, discretized‌ using a Hamiltonian Particle-In-Cell‌​‌ scheme. Our approach relies​​ on a two-step projection​​​‌ framework: an initial linear‌ projection based on the‌​‌ Proper Symplectic Decomposition, followed​​ by a nonlinear projection​​​‌ learned via an autoencoder‌ neural network. The reduced‌​‌ dynamics are then modeled​​ using a Hamiltonian neural​​​‌ network. The offline phase‌ of the method is‌​‌ split into two stages:​​​‌ first, constructing the linear​ projection using full-order model​‌ snapshots; second, jointly training​​ the autoencoder and the​​​‌ Hamiltonian neural network to​ simultaneously learn the encoder-decoder​‌ mappings and the reduced​​ dynamics. We validate the​​​‌ proposed method on several​ benchmarks, including Landau damping​‌ and two-stream instability.

8.4.2​​ Learning non-canonical Hamiltonian dynamics​​​‌

Participants: Clémentine Courtès,​ Emmanuel Franck, Laurent​‌ Navoret, Léopold Trémant​​.

This contribution focuses​​​‌ on learning non-canonical Hamiltonian​ dynamics from data, where​‌ long-term predictions require the​​ preservation of structure both​​​‌ in the learned model​ and in numerical schemes.​‌ Previous research focused on​​ either facet, respectively with​​​‌ a potential-based architecture and​ with degenerate variational integrators,​‌ but new issues arise​​ when combining both. In​​​‌ experiments, the learnt model​ is some- times numerically​‌ unstable due to the​​ gauge dependency of the​​​‌ scheme, rendering long-time simulations​ impossible. In 27,​‌ we identify this problem​​ and propose two different​​​‌ training strategies to address​ it, either by directly​‌ learning the vector field​​ or by learning a​​​‌ time-discrete dynamics through the​ scheme. Several numerical test​‌ cases assess the ability​​ of the methods to​​​‌ learn complex physical dynamics,​ like the guiding center​‌ from gyrokinetic plasma physics.​​

8.5.1 Minimal time​ control of underdamped parametric​‌ oscillators

Participants: Killian Lutz​​.

Controlling a damped​​​‌ oscillator is crucial in​ various technological and scientific​‌ fields, such as structural​​ engineering, aerospace, and noise​​​‌ reduction device design. This​ paper deals with a​‌ classical underdamped harmonic oscillator,​​ focusing on its minimal-time​​​‌ control by modulating its​ time-dependent frequency. The goal​‌ is to connect in​​ minimal time two states​​​‌ with zero kinetic energy​ but different displacements. We​‌ provide a detailled description​​ of the set of​​​‌ reachable states and of​ the structure of optimal​‌ trajectories, which we precisely​​ describe in phase space.​​​‌ This analysis paves the​ way for linking optimal​‌ control to parametric resonance​​ in mechanical systems 32​​​‌.

8.5.2 Time optimal​ synthesis of gates for​‌ Markovian open qudits

Participants:​​ Killian Lutz.

Coherent​​​‌ control protocols enabling fast​ and accurate implementations of​‌ logical gates is a​​ key issue in quantum​​​‌ computing. This work deals​ with the optimal implementation​‌ of quantum gates subject​​ to experimental constraints on​​​‌ the multi-chromatic electromagnetic control​ pulses. Our assumptions encapsulate​‌ qudits of arbitrary finite​​ dimension subject to decoherence​​​‌ modelled by the GSK-Linblad​ equation. Given a unitary​‌ gate we show the​​ existence of a time-minimal​​​‌ protocol minimizing the error.​ We derive universal and​‌ easily computable a priori​​ lower and upper bounds​​​‌ on both the minimal​ time and minimal error.​‌ The wide applicability of​​ these estimates helps in​​​‌ quantifying a posteriori the​ distance to optimality of​‌ numerically calculated control protocols​​ 33.

8.5.3 Data-driven​​​‌ optimal control and inverse​ problems: Ferromagnetic modelisation

Participants:​‌ Clémentine Courtès.

In​​ 7, we investigate​​​‌ a simple model of​ notched ferromagnetic nanowires by​‌ focusing on the case​​ of a single unimodal​​ notch. We establish the​​​‌ existence and uniqueness of‌ the critical point of‌​‌ the energy, through a​​ lifting argument, which reduces​​​‌ the problem to a‌ generalized Sturm-Liouville equation, and‌​‌ the Mountain-Pass theorem. Finally,​​ we show that the​​​‌ solution corresponds to a‌ system of magnetic spins‌​‌ characterized by a single​​ domain wall localized in​​​‌ the vicinity of the‌ notch.

In 26,‌​‌ we study from a​​ mathematical point of view​​​‌ the nanoparticle model of‌ a magnetic colloid. Our‌​‌ objective is to obtain​​ properties of stable stationary​​​‌ structures that arise in‌ the long-time limit for‌​‌ the magnetic nanoparticles dynamics​​ following this model. More​​​‌ precisely, we present a‌ detailed study of two‌​‌ specific structures using techniques​​ from the calculus of​​​‌ variations. The first, called‌ the spear, consists of‌​‌ a chain of aligned​​ particles interacting via a​​​‌ Lennard-Jones potential. We establish‌ existence and uniqueness results,‌​‌ derive bounds on the​​ distances between neighboring particles,​​​‌ and provide a sharp‌ asymptotic description as the‌​‌ number of particles tends​​ to infinity. The second​​​‌ structure, the ring, features‌ particles uniformly distributed along‌​‌ a circle. We prove​​ its existence and uniqueness​​​‌ and derive an explicit‌ formula for its radius.‌​‌

8.5.4 Hearing the Shape​​ of a Cuboid Room​​​‌ Using Sparse Measure Recovery‌

Participants: Antoine Deleforge.‌​‌

In the companion papers​​ 9 and 17,​​​‌ a variant of Kac's‌ famous problem, ‘‘Can one‌​‌ hear the shape of​​ a drum?” is explored​​​‌ by addressing a geometric‌ inverse problem in acoustics.‌​‌ The objective is to​​ reconstruct the shape of​​​‌ a cuboid room using‌ acoustic signals measured by‌​‌ microphones placed within the​​ room. This geometric problem​​​‌ is reduced to locating‌ a finite set of‌​‌ acoustic point sources, known​​ as image sources. We​​​‌ propose a solution algorithm‌ inspired by super-resolution optimization‌​‌ techniques. This involves a​​ convex relaxation of the​​​‌ finite-dimensional problem to an‌ infinite-dimensional subspace of Radon‌​‌ measures. Analytical insights into​​ this problem are provided,​​​‌ and the efficiency of‌ the algorithm is demonstrated‌​‌ through multiple numerical examples.​​

The broader theme of​​​‌ "hearing the walls of‌ a room" and related‌​‌ inverse problems in room​​ acoustics is the central​​​‌ theme of A. Deleforge's‌ HDR thesis 23.‌​‌

8.6.1 Analysis​​ and simulations of a​​​‌ particle model for collective‌ cell dynamics

Participants: Laurent‌​‌ Navoret, Roxana Sublet​​.

The goal of​​​‌ this contribution is to‌ propose an agent-based model‌​‌ that originally combines classical​​ Vicsek-like polarity alignments and​​​‌ contact forces. The description‌ additionally incorporates velocity feedback‌​‌ on polarity and soft​​ attraction-repulsion interactions. In 34​​​‌, we carefully study‌ the well posedness of‌​‌ the model, we introduce​​ a suitable discretization and​​​‌ perform an extensive range‌ of numerical experiments to‌​‌ assess the impact of​​ different modeling ingredients. The​​​‌ dynamical system is capable‌ of recovering the order-disorder‌​‌ phase transition of the​​ flock, as well as​​​‌ the jamming effect in‌ high density regimes. As‌​‌ such, the developed framework​​ can be seen as​​​‌ a promising theoretical tool‌ that could contribute to‌​‌ improving the understanding of​​​‌ complex collective cell dynamics​ and emerging tissue flows.​‌

8.6.2 Towards Interpretable Time​​ Series Foundation Models

Participants:​​​‌ Matthieu Boileau, Philippe​ Helluy.

In 20​‌, we investigate the​​ distillation of time series​​​‌ reasoning capabilities into small,​ instruction-tuned language models (Qwen).​‌ This work aims to​​ establish a foundation for​​​‌ building interpretable time series​ foundation models that can​‌ explain temporal patterns.

8.6.3​​ Minimal time of magnetization​​​‌ switching in small ferromagnetic​ ellipsoidal samples

Participants: Clémentine​‌ Courtès.

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 magentic moment.​‌ In 8, 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 $+\stackrel{¯‌}{m}$ to the $-\overline{\mathrm{m}}$ 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 $L^{\mathrm{\infty ‌}}$ norm of the controls,​​ assumed to be less​​​‌ than a threshold value​ $U$. We show​‌ that, generally 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.

8.6.4 Structural​‌ schemes for Hamiltonian systems​​

Participants: Victor Michel-Dansac,​​​‌ Emmanuel Franck.

In​ the work 25 we​‌ propose to use new​​ structural methods to design​​​‌ scheme for Hamiltonian ODE.​ After the construction of​‌ 4, 6 and 8​​ order schemes we propose​​​‌ some analysis to compare​ to classical approaches. We​‌ also study the modified​​ equation for a simpler​​​‌ pendulum problem. The schemes​ are validated on a​‌ large set of tests​​ case and show strong​​​‌ accuracy in long time​ limit.

8.6.5 Modeling in​‌ radiative transfer for astrophysics​​ applications

Participants: Emmanuel Franck​​​‌.

In current cosmological​ simulations, the radiative transfer​‌ modules generally rely on​​ the M1 approximation which​​​‌ provides non physical behavior.​ The spherical harmonics model​‌ of order $n$ (called​​ $P_n$) may​​​‌ correct these issues. In​ 35 we present a​‌ comparative and highly detailed​​ study between the M1​​​‌ and PN models for​ academic or more realistic​‌ test cases derived from​​ reionization problems. The shortcomings​​​‌ and strengths of each​ approach are discussed in​‌ detail. The results show​​ that a transition to​​​‌ PN improves reionization simulations.​

9.1.1 CIFRE EDF: Acceleration​​​‌ of thermal-hydraulic codes

Participants:‌ Philippe Helluy, Gauthier‌​‌ Lazare.

This project​​ (Gauthier Lazare's thesis) focuses​​​‌ on the “Development of‌ an efficient numerical method‌​‌ for solving a partially​​ non-equilibrium homogeneous two-phase model​​​‌ in a heterogeneous porous‌ medium”'. It aims to‌​‌ accelerate the THYC-coeur thermal-hydraulic​​ code using AI techniques​​​‌ and improved numerical schemes.‌

9.1.2 CIFRE Axessim: AI‌​‌ for test results documentation​​

Participants: Philippe Helluy,​​​‌ Jérémy Pawlus.

This‌ project (Jérémy Pawlus's thesis)‌​‌ is titled “Refinement of​​ large models for the​​​‌ documentation and prediction of‌ test results”. It involves‌​‌ using Large Language Models​​ (LLMs) to analyze and​​​‌ predict results from industrial‌ test data series.

10.1.1 Inria​​​‌ associate team not involved‌ in an IIL or‌​‌ an international program

Participants:​​ Clementine Courtes.

Coordinator:​​​‌ A. de Laire (Université‌ de Lille)

Topic: Study‌​‌ of dispersive PDE systems​​ for wave propagation

10.2.1‌ Visits of international scientists‌​‌

10.2.2‌​‌ Visits to international teams​​

10.3.1‌ ANR MOSICOF (MOdeling and‌​‌ SImulation of COmplex Ferromagnetic​​ systems)

Participants: Clémentine Courtès​​​‌.

Dates: 10/2021 –‌ 10/2025.

Coordinator: S. Labbé,‌​‌ Sorbonne Université.

Partners: Sorbonne​​ Université, Université de Pau​​​‌ et des Pays de‌ l'Adour, Université de Strasbourg‌​‌

Decription: 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.

10.3.2​​​‌ ANR JCJC SMEAGOL (Méthode​ structurelle – Application à​‌ des systèmes hyperboliques généraux)​​

Participants: Victor Michel-Dansac.​​​‌

Dates: 11/2024 – 10/2028.​

Funding: 283 k€

Coordinator:​‌ Victor Michel-Dansac

Decription: The​​ structural method, introduced over​​​‌ the last two years,​ develops high-order numerical schemes​‌ for solving PDEs on​​ compact stencils. This finite​​​‌ difference approach is unique​ in that it approximates​‌ both the solution and​​ its derivatives with the​​​‌ same order of accuracy​ by defining two independent​‌ sets of discrete equations:​​ the physical equations (PEs)​​​‌ and the structural equations​ (SEs). The PEs represent​‌ the problem's physics, while​​ SEs ensure the accuracy​​​‌ of the discretization. This​ separation provides a high​‌ degree of flexibility, allowing​​ for the modification of​​​‌ PEs to include specific​ constraints (e.g., ensuring a​‌ vector field is divergence-free)​​ and the adjustment of​​​‌ SEs to handle non-smooth​ solutions or enhance stability.​‌ The ANR project SMEAGOL​​ seeks to extend this​​​‌ method to hyperbolic systems​ of balance laws in​‌ multiple spatial dimensions, where​​ continuous initial conditions often​​​‌ lead to non-smooth solutions​ and multiscale regime changes.​‌ This makes the method​​ particularly suitable for complex​​​‌ problems in fluid mechanics​ or electromagnetism. The separation​‌ between physical and structural​​ equations in this framework​​​‌ allows for the dynamic​ adaptation of the scheme​‌ to the local problem,​​ switching PEs or SEs​​​‌ on or off as​ needed. SMEAGOL's goals include​‌ both constructing and adapting​​ the structural method to​​​‌ these advanced applications, to​ develop well-balanced, asymptotic-preserving and​‌ robust schemes.

10.3.3 ANR​​ MAPEFLU (Modelling the effect​​​‌ of Apoptosis on Epithelium​ FLUidity)

Participants: Laurent Navoret​‌.

Dates: 03/2023–02/2027

Coordinator:​​ Laurent Navoret

Partners: Institut​​​‌ Pasteur, Université Paris Université​ de Strasbourg (IRMA, IGBMC)​‌

Decription: 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.

10.3.4 ANR PHI-FEM‌ (Développement d'une méthode aux‌​‌ éléments finis pour la​​ conception de jumeaux numériques​​​‌ temps réel en chirurgie)‌

Participants: Vincent Vigon.‌​‌

Dates: 12/2022 - 11/2026​​

Grant: 324 k€

Coordinator:​​​‌ Michel Duprez

Partners: Inria‌ teams MACARON and MIMESIS.‌​‌

Decription: Phi-FEM is a​​ recently proposed finite element​​​‌ method for the efficient‌ numerical solution of partial‌​‌ differential equations in domains​​ defined by level-set functions.​​​‌ The main objective of‌ this project is to‌​‌ develop Phi-FEM into an​​ efficient, patient-specific, and real-time​​​‌ simulation tool for human‌ organs. To achieve this‌​‌ goal, we will adapt​​ Phi-FEM to equations relevant​​​‌ to biomechanics, provide an‌ efficient implementation allowing the‌​‌ use of real organ​​ geometries, and finally combine​​​‌ it with convolutional neural‌ networks to make it‌​‌ real-time after training.

10.3.5​​ ANR SIMBADNESTICOST (Simulation based​​​‌ network structure inference constrained‌ by observed spike trains)‌​‌

Participants: Vincent Vigon,​​ Emmanuel Franck.

Dates:​​​‌ 01/2023 - 12/2026

Grant:‌ 159 k€

Coordinator: Christophe‌​‌ Pouzat (IRMA, Strasbourg University)​​

Partners: Inria, IRMA

Decription:​​​‌ Neurophysiologists are nowadays able‌ to record from a‌​‌ large number of extracellular​​ electrodes and to extract,​​​‌ from the raw data,‌ the sequences of action‌​‌ potentials or spikes generated​​ by many neurons. Unfortunately​​​‌ these "many neurons" still‌ represent only a tiny‌​‌ fraction of the neuronal​​ population which constitutes the​​​‌ network. Using association statistics‌ such as the estimation‌​‌ of the cross-correlation functions,​​ they are trying to​​​‌ infer the structure of‌ the network formed by‌​‌ the recorded neurons. But​​ this inference is compromised​​​‌ by the tremendous under-sampling‌ of the neuronal population‌​‌ and by the errors​​ made during the sequences​​​‌ reconstruction. This yields a‌ "network picture" usually called‌​‌ a "functional network" whose​​ features depend strongly on​​​‌ the recording conditions (such‌ as the presence/absence of‌​‌ a stimulation). We consider​​ that reconstructing the network​​​‌ formed by the recorded‌ neurons is an ill-posed‌​‌ problem. We propose to​​ focus instead on the​​​‌ "generative probability distribution" of‌ the network: what is‌​‌ the probability to have​​ a connection from a​​​‌ type A neuron to‌ a type B neuron?‌​‌ Is the probability to​​ have a connection from​​​‌ neuron Y of type‌ B to neuron X‌​‌ of type A dependent​​ on the presence of​​​‌ a connection from X‌ to Y? We propose‌​‌ to simulate first the​​ whole network using a​​​‌ simplified neuronal dynamics and‌ different (parametrized) generative probability‌​‌ distributions. We will then​​ compare the association statistics​​​‌ between the simulated and‌ the experimentally observed cases.‌​‌ This type of approach​​ is now commonly used​​​‌ in several fields under‌ different names like "Approximate‌​‌ Bayesian Computation" or "Simulation​​ based Inference". We will​​​‌ then be able to‌ asses if there is‌​‌ an "over representation of​​ reciprocal connections" using data​​​‌ from the first olfactory‌ relay of an insect.‌​‌

10.3.6 PEPR IA/PC IA-EDP​​

Participants: Philippe Helluy,​​​‌ Joubine Aghili, Clémentine‌ Courtès, Emmanuel Franck‌​‌, Victor Michel-Dansac,​​ Vincent Vigon, Laurent​​​‌ Navoret.

Dates: 01/09/2023‌ – 31/08/2027

Coordinator: A.‌​‌ Chambolle (Univ. Paris-Dauphine)

Decription:​​​‌ The PEPR IA is​ a large national project​‌ on artificial intelligence (AI).​​ 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 AI​​​‌ methods and optimal control,​ optimal transport, PDE and​‌ numerical analysis. The team​​ is involved in the​​​‌ optimal control aspect.

10.3.7​ PEPR Numpex/PC Exa-MA

Participants:​‌ Philippe Helluy, Joubine​​ Aghili, Clémentine Courtès​​​‌, Emmanuel Franck,​ Victor Michel-Dansac, Vincent​‌ Vigon, Laurent Navoret​​.

Dates: 10/2021 –​​​‌ 10/2025.

Coordinator: Christophe Prud'homme​

Decription: 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.

10.3.8 ANR​ PRC JNL-G (Jumeau Numérique​‌ du Laboratoire National des​​ Champs Magnétiques Intenses-Grenoble)

Participants:​​​‌ Joubine Aghili.

Dates:​ 12/2025 - 12/2027

Coordinator:​‌ Christophe Trophime

Partners: LNCMI​​ (Grenoble), Cemosis (Strasbourg)

Decription:​​​‌ This project is centered​ on improving how magnets​‌ are designed and operated​​ at the LNCMI-G. The​​​‌ main aim is to​ create a digital twin​‌ (DT) — a detailed​​ virtual model — that​​​‌ mirrors the complex systems​ of LNCMI-G's 30 MW​‌ magnet installation and cooling​​ systems (300 l/s, 25​​​‌ bars)- similar to those​ of a nuclear power​‌ plant. This DT is​​ expected to find better​​​‌ ways to optimize and​ run the magnets, breaking​‌ through current limitations. The​​ DT focuses on the​​​‌ LNCMI-G as an instrument.​ The DT seeks to​‌ improve the control over​​ the magnets and their​​​‌ energy consumption, enhancing user​ service delivery and operational​‌ control.

10.3.9 ANR PRCI​​ DFG-ANR (Machine learning for​​​‌ reduced kinetic models)

Participants:​ Emmanuel Franck, Laurent​‌ Navoret, Vincent Vigon​​, Clémentine Courtès.​​​‌

Dates: 01/2022 - 12/2025.​

Coordinator: E. Franck

Partners:​‌ TUM (Munich)

Description: 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​​ modelling 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 modelling, 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 models‌ obtained will be a‌​‌ key point studied.

10.3.10​​ USIAS grant

Participants: Vincent​​​‌ Vigon.

Dates: 01/2025‌ - 12/2027.

Coordinator: V.‌​‌ Vigon

Partners: University of​​ Strabsourg institute for advanced​​​‌ study

Description: This project‌ aims to map neuronal‌​‌ methylome turnover at single-cell​​ resolution. The study challenges​​​‌ the long-held view that‌ DNA methylation is static‌​‌ in post-mitotic neurons, suggesting​​ instead a dynamic plasticity​​​‌ linked to aging and‌ disease. Using long-read sequencing‌​‌ (Nanopore) and machine learning​​ tools, the team plans​​​‌ to analyze methylation kinetics‌ in mice. The objective‌​‌ is to identify genomic​​ regions undergoing rapid turnover​​​‌ and to understand the‌ role of the Tet3‌​‌ enzyme in this process.​​ The research focuses on​​​‌ neurons in the prefrontal‌ cortex, a key area‌​‌ for higher cognitive functions.​​ This work could reveal​​​‌ new epigenetic mechanisms fundamental‌ to brain plasticity. The‌​‌ results will help determine​​ whether methylation turnover is​​​‌ a central player in‌ neuronal identity and function.‌​‌

11.1.1 Scientific​​​‌ events: organisation

11.1.2 Journal

11.1.3 Invited talks​‌

11.1.4 Scientific expertise

• Reviewer​​ for a CEFIPRA (Indo​​​‌ French Centre for the‌ Promotion of Advanced Research)‌​‌ grant (Victor Michel-Dansac​​ )
• Reviewer for the​​​‌ DataAI Chair, AI cluster‌ Paris-Saclay (Laurent Navoret‌​‌ )
• Reviewer for a​​ ANR project (Laurent​​​‌ Navoret )
• Reviewer for‌ IDEX Attractivités grants at‌​‌ Unistra (Joubine Aghili​​ )
• Member of HCERES​​​‌ comity evaluation of DTIS,‌ ONERA (Emmanuel Franck‌​‌ )
• Member of COMPIPERS​​ for Phd/Post doc/délégation (​​​‌Emmanuel Franck )
• CIFRE‌ expertise (Antoine Deleforge‌​‌ )

11.1.5 Research administration​​

• Training coordinator, Interdisciplinary Thematic​​​‌ Institute IRMIA++, University of‌ Strasbourg (Laurent Navoret‌​‌ )
• Elected member of​​ the mathematicians’ committee, Faculty​​​‌ of Mathematics and Computer‌ Science (UFR Maths-Info), University‌​‌ of Strasbourg (Clémentine​​ Courtès , Laurent Navoret​​​‌ )
• Elected member of‌ the expert committee, Faculty‌​‌ of Mathematics and Computer​​ Science (UFR Maths-Info), University​​​‌ of Strasbourg (Joubine‌ Aghili , Laurent Navoret‌​‌ )
• Nominated member of​​ the IRMA Laboratory Council,​​​‌ University of Strasbourg (‌Clémentine Courtès )
• Parity‌​‌ referent, co-coordinator and member​​ for INSMI, the Faculty​​​‌ of Mathematics and Computer‌ Science (UFR Maths-Info), and‌​‌ IRMA (Clémentine Courtès​​ )
• Nominated referent of​​​‌ the Inria research data‌ committee for the University‌​‌ of Lorraine and Strasbourg​​ centers (Antoine Deleforge​​​‌ )
• Member of the‌ Research Commission (Commission de‌​‌ la Recherche) of the​​ University of Strasbourg (​​​‌Philippe Helluy )
• Referent‌ for the Quantitative Imaging‌​‌ Platform (PIQ) at the​​ University of Strasbourg (​​​‌Philippe Helluy )
• Head‌ of the MOCO (Modeling‌​‌ and Control) team at​​ IRMA, University of Strasbourg​​​‌ (Philippe Helluy )‌
• Member of the Scientific‌​‌ Committee of the “GDR​​ Calcul”, INSMI, (Emmanuel​​​‌ Franck )
• Head of‌ the AI for Scientific‌​‌ Computing Working Group of​​ the GDR CP4 (INSII),​​​‌ currently being created (‌Emmanuel Franck )

11.2.1 Teaching‌

• 14h of CM and‌​‌ 14h of TP in​​ Intro to Object-Oriented Programming​​​‌ in L2 informatique at‌ UFR Maths-Info, Strasbourg University‌​‌ (Victor Michel-Dansac )​​
• 14h of TP in​​​‌ Scientific Computing in M1‌ CSMI at UFR Maths-Info,‌​‌ Strasbourg University (Victor​​​‌ Michel-Dansac )
• 16 hours​ of CM in Basics​‌ in mathematics in Master​​ 2 Cell Physics at,​​​‌ Strasbourg University, France (Laurent​ Navoret)
• 8 hours of​‌ CM in Math for​​ living matter in Master​​​‌ 2 Cell Physics at​ Strasbourg University, France (Laurent​‌ Navoret)
• 20 hours of​​ CM in Scientific computing​​​‌ in Master 2 Agrégation​ at Strasbourg University, France​‌ (Laurent Navoret)
• 20 hours​​ of TD in Scientific​​​‌ computing in Master 2​ Agrégation at Strasbourg University,​‌ France (Laurent Navoret)
• 28​​ hours of CI in​​​‌ Scientific machine learning in​ Master 1 Scientific Computing​‌ at Strasbourg University, France​​ (Laurent Navoret)
• 16 hours​​​‌ of TD-TP in Analysis​ in Licence 2 Computer​‌ Science at Strasbourg University,​​ France (Laurent Navoret)
• 6​​​‌ hours of TD in​ Interdisciplinary seminars in Diplôme​‌ d'université at Strasbourg University,​​ France (Laurent Navoret)
• 30h​​​‌ of CM/TD in python​ programming for mathematics in​‌ L1 MPA at UFR​​ Maths-Info, Strasbourg University, France​​​‌ (Clémentine Courtès )​
• 15h of CM in​‌ numerical analysis in L2​​ computer science at UFR​​​‌ Maths-Info, Strasbourg University, France​ (Clémentine Courtès )​‌
• 8h of TD in​​ numerical analysis in L2​​​‌ computer science at UFR​ Maths-Info, Strasbourg University, France​‌ (Clémentine Courtès )​​
• 6h of TP in​​​‌ numerical analysis in L2​ computer science at UFR​‌ Maths-Info, Strasbourg University, France​​ (Clémentine Courtès )​​​‌
• 22h of TD in​ nonlinear optimization in L3​‌ maths-eco and actuarial sciences​​ at UFR Maths-Info, Strasbourg​​​‌ University, France (Clémentine​ Courtès )
• 37h of​‌ CM in scientific computing​​ in L3 magistère at​​​‌ UFR Maths-Info, Strasbourg University,​ France (Clémentine Courtès​‌ )
• 28h of TD​​ in scientific computing in​​​‌ L3 magistère at UFR​ Maths-Info, Strasbourg University, France​‌ (Clémentine Courtès )​​
• 15h of CM in​​​‌ numerical analysis in L3​ mathematics at UFR Maths-Info,​‌ Strasbourg University, France (​​Clémentine Courtès )
• 18h​​​‌ of TD in numerical​ analysis in L3 mathematics​‌ at UFR Maths-Info, Strasbourg​​ University, France (Clémentine​​​‌ Courtès )
• 16h of​ TP on computer assisted​‌ proof in M1 CSMI​​ at UFR Maths-Info, Strasbourg​​​‌ University (Philippe Helluy​ )
• 20h of CM​‌ in C++ in L3​​ informatique, UFR Maths-Info, Strasbourg​​​‌ University (Philippe Helluy​ )
• 28h of CI​‌ in scientific computing in​​ M1 CSMI, UFR Maths-Info,​​​‌ Strasbourg University (Philippe​ Helluy )
• 28h of​‌ CI in numerical methods​​ for partial differential equations​​​‌ in M2 CSMI at​ UFR Maths-Info, Strasbourg University​‌ (Andrea Thomann )​​
• 28h of CI in​​​‌ scientific machine learning in​ M2 CSMI at UFR​‌ Maths-Info, Strasbourg University (​​Emmanuel Franck )
• 12h​​​‌ of CI in advances​ numerical methods and ML​‌ in M1 physics, Strasbourg​​ University (Emmanuel Franck​​​‌ )
• 28h of CI​ in Calcul scientifique 2​‌ in M1 CSMI at​​ UFR Maths-Info, Strasbourg University​​​‌ (Joubine Aghili )​
• 64h of CI in​‌ Maths pour les sciences​​ 1, L1 magistère, Strasbourg​​​‌ University (Joubine Aghili​ )
• 7h Project 3​‌ in M1 CSMI at​​ UFR Maths-Info, Strasbourg University​​​‌ (Joubine Aghili )​
• 12h CM and 8h​‌ TP in Numerical resolution​​ techniques in M1 physics,​​ Strasbourg University (Joubine​​​‌ Aghili )
• 60h CI‌ in Modelisation Probabiliste in‌​‌ M2 Agregation at UFR​​ Maths-Info, Strasbourg University (​​​‌Vincent Vigon )
• 35h‌ CI in Traitement et‌​‌ exploitation des données in​​ M1 CSMI at UFR​​​‌ Maths-Info, Strasbourg University (‌Vincent Vigon )
• 35h‌​‌ CI in Traitement du​​ signal et des images​​​‌ 1 in M1 CSMI‌ at UFR Maths-Info, Strasbourg‌​‌ University (Vincent Vigon​​ )
• 35h CI in​​​‌ Traitement du signal et‌ des images 2 in‌​‌ M2 CSMI at UFR​​ Maths-Info, Strasbourg University (​​​‌Vincent Vigon )
• 45h‌ CI in Science des‌​‌ données pour l'actuariat in​​ M2 Actuariat at UFR​​​‌ Maths-Info, Strasbourg University (‌Vincent Vigon )
• 20h‌​‌ CI in Logiciel pour​​ la statistique in M1​​​‌ Actuariat at UFR Maths-Info,‌ Strasbourg University (Vincent‌​‌ Vigon )
• 17,5h CM​​ in Artificial Intelligence, Machine​​​‌ Learning and Deep Learning‌ at Télécom Physique Strasbourg‌​‌ (Antoine Deleforge )​​
• 12h TP in Deep​​​‌ Learning at Télécom Physique‌ Strasbourg (Antoine Deleforge‌​‌ )

11.2.2 Supervision

• PostDoc​​ Florian Salin, 2025-, "Greedy​​​‌ neural approaches for transport‌ PDEs and optimal control"‌​‌ (Emmanuel Franck ,​​ Laurent Navoret , Victor​​​‌ Michel-Dansac )
• PostDoc Yanfei‌ Xiang, 2025-, "Generative modeling‌​‌ and optimal control" (​​Antoine Deleforge , Emmanuel​​​‌ Franck , Laurent Navoret‌ , Victor Michel-Dansac )‌​‌
• PostDoc Dinh Hung Truong,​​ 2023 -2025, "Design of​​​‌ Neural Operators based on‌ PINNs; applications to wave‌​‌ propagation and fluid dynamics"​​ (Victor Michel-Dansac ,​​​‌ Emmanuel Franck )
• PhD‌ Thesis Vincent Italiano (Univ.‌​‌ Strasbourg), 2025-, "Efficient neural​​ operators for forward and​​​‌ inverse wave propagation problems"‌ (Antoine Deleforge ,‌​‌ Laurent Navoret )
• PhD​​ Thesis Virgile Bertrand (Univ.​​​‌ Strasbourg), 2024-, "Constructing the‌ structural method for hyperbolic‌​‌ partial differential equations" (33%​​ Emmanuel Franck , 33%​​​‌ Victor Michel-Dansac )
• PhD‌ Thesis Daria Hrebenshchykova (Univ.‌​‌ Côte d'Azur), 2024-, "Building​​ physics-based multilevel surrogate models​​​‌ from neural networks. Application‌ to electromagnetic wave propagation"‌​‌ (33% Victor Michel-Dansac )​​
• PhD Thesis Nicolas Pailliez​​​‌ (Univ. Strasbourg), 2024-, "Implicit‌ neural representation and opertator‌​‌ learning for multi-scale physical​​ problems" (Victor Michel-Dansac​​​‌ , Emmanuel Franck ,‌ Laurent Navoret )
• PhD‌​‌ Thesis Amaury Bélières-Frendo. (Univ.​​ Strasbourg), 2023-, "Shape optimization​​​‌ through learning" (25% Victor‌ Michel-Dansac )
• PhD Thesis‌​‌ Claire Schnoebelen (Univ. Strasbourg),​​ 2023-, "Structure preserving ML​​​‌ methods for Hamiltonian PDEs"‌ (33% Emmanuel Franck ,‌​‌ 33% Laurent Navoret )​​
• PhD Thesis Frédérique Lecourtier​​​‌ (Univ. Strasbourg), 2023-, "Hybrid‌ finite elements for digital‌​‌ twins" (33% Emmanuel Franck​​ )
• PhD Thesis Killian​​​‌ Lutz (Univ. Strasbourg), 2023-,‌ "Optimal control for Linblad‌​‌ equation" (50% Emmanuel Franck​​ )
• PhD Thesis Mei​​​‌ Pallanque (Univ. Strasbourg), 2022-2025,‌ "New radiative transfer methods‌​‌ in numerical simulation of​​ the epoch of reionisation​​​‌ " (20% Emmanuel Franck‌ )
• PhD Thesis Guillaume‌​‌ Steimer (Univ. Strasbourg), 2022-2025,​​ "Model order reduction method​​​‌ for Hamiltonian dynamics using‌ deep learning" (25% Emmanuel‌​‌ Franck , 25% Vincent​​ Vigon , 25% Laurent​​​‌ Navoret )
• PhD Thesis‌ Amaury Bélières-Frendo. (Univ. Strasbourg),‌​‌ 2023-, "Shape optimization through​​ learning" (25% Victor Michel-Dansac​​​‌ )
• PhD Thesis Roxana‌ Sublet (Univ. Strasbourg), 2023-,‌​‌ "Models for collective cell​​​‌ dynamics" (50% Laurent Navoret​ )
• PhD Thesis Hassan​‌ Ballout (Univ. Strasbourg), 2024-,​​ "Nonlinear model reduction" (33%​​​‌ Joubine Aghili )
• PhD​ Thesis Ghauthier Lazare (EDF),​‌ 2022-2025 (50% Philippe Helluy​​ )
• PhD Thesis Robin​​​‌ San Roman (META, Inria),​ 2022-2025 (33% Antoine Deleforge​‌ )
• PhD Thesis Jean-Daniel​​ Pascal (CEREMA, Inria), 2024-​​​‌ (50% Antoine Deleforge )​
• PhD Thesis Lauriane Turelier,​‌ "Ferromagnetism and domain walls​​ in nanowires", 2023- (50%​​​‌ Clémentine Courtès )
• Master​ thesis (M2) Oussama Bouhenniche,​‌ “Asymptotic-preserving and well-balanced high-order​​ scheme for the Euler​​​‌ equations with gravity” (​Andrea Thomann , Victor​‌ Michel-Dansac )
• Master thesis​​ (M2) Marie Sengler, “Study​​​‌ and improvement of PINNs​ for magnetic field simulations​‌ ” (Emmanuel Franck​​ , F. Molenda (Thales),​​​‌ Victor Michel-Dansac , J.​ Tryoen (Thales))
• Master thesis​‌ (M1) Franck Jacquard, “Introduction​​ to the hydrostatic reconstruction”​​​‌ (Victor Michel-Dansac )​
• Master Thesis (M2) A.​‌ Wade, funded by PEPR​​ Math-Vives (Joubine Aghili​​​‌ )
• Master Thesis (M1)​ A. Sow, funded by​‌ PEPR (Joubine Aghili​​ )
• Master Thesis (M1)​​​‌ R. Vivant, "Sindy methods​ for Generic systems" (​‌Emmanuel Franck , Andrea​​ Thomann )
• Master Thesis​​​‌ (M2), M. Gressier, "Sequential​ in time neural network​‌ for radiative transfer" funded​​ by astrophysics lab (​​​‌Emmanuel Franck , Joubine​ Aghili )
• Master Thesis​‌ (M1), S. Hachem, "transformers​​ for neural operators" founded​​​‌ by INRIA (Emmanuel​ Franck )
• Bachelor Thesis​‌ (L3) Arif Yildirim, “Study​​ of a well-balanced scheme​​​‌ for the shallow water​ equations” (Victor Michel-Dansac​‌ , Laurent Navoret )​​
• Interdisciplinary project (Math and​​​‌ interaction University Diploma), Abakar​ Youssouf, Hans Zeballos Rivera,​‌ France (Victor Michel-Dansac​​ , Laurent Navoret )​​​‌
• Bachelor Thesis (L3) J.​ Kieffer, funded by PEPR​‌ Maths-Vives (Joubine Aghili​​ )

11.2.3 Juries

• 12/2025:​​​‌ Reviewer in the PhD​ committee for Nilo Schwencke,​‌ Paris-Saclay University (Emmanuel​​ Franck )
• 12/2025: Reviewer​​​‌ in the PhD committee​ for Nicolas Lepage, CNAM​‌ (Emmanuel Franck )​​
• 12/2025: Reviewer in the​​​‌ PhD committee for Lola​ Chabat, University of Pau​‌ (Emmanuel Franck )​​
• 12/2025: Reviewer in the​​​‌ PhD committee for Abbas​ Kabalan, ENPC (Emmanuel​‌ Franck )
• 12/2025: Member​​ of the PhD committee​​​‌ for Killian Vuillemot, University​ of Montpellier (Emmanuel​‌ Franck )
• 06/2025: Member​​ of the PhD committee​​​‌ for Julien Besset, University​ of Pau (Emmanuel​‌ Franck )
• 09/2025: Member​​ of the PhD committee​​​‌ for Alex Podgorny, University​ of Strasbourg (Emmanuel​‌ Franck )
• 09/2025: Reviewer​​ in the PhD committee​​​‌ for Gonzague Radureau, University​ of Nice (Emmanuel​‌ Franck )
• 02/2025: Reviewer​​ in the PhD committee​​​‌ for Kalinja Naffer-Chevassier, UTC​ (Emmanuel Franck )​‌
• 02/2025: Reviewer in the​​ PhD committee of Jean-Marie​​​‌ Lemercier, University of Hamburg​ (Antoine Deleforge )​‌
• 12/2025: Member of the​​ PhD committee for Nilo​​​‌ Schwencke, Paris-Saclay University (​Victor Michel-Dansac )
• 11/2025:​‌ Member of the PhD​​ committee for Guillaume du​​​‌ Pont de Romémont, Arts​ et Métiers ParisTech (​‌Victor Michel-Dansac )
• 03/2025:​​ Member of the PhD​​​‌ committee for Yen Chung​ Hung, University Savoie Mont​‌ Blanc (Victor Michel-Dansac​​ )
• Member of Selection​​ committee for researchers CRCN/ISFP,​​​‌ Inria Center at University‌ Côte d'Azur (Clémentine‌​‌ Courtès )
• Member of​​ Selection committee for MCF,​​​‌ CNU 26, University of‌ Bordeaux (Emmanuel Franck‌​‌ )
• Member of Selection​​ committee for MCF, CNU​​​‌ 26, University of Nantes‌ (Emmanuel Franck )‌​‌
• Member of Selection committee​​ for MCF, CNU 26,​​​‌ University of Toulouse (‌Clémentine Courtès )
• Jury‌​‌ member of the external​​ aggregation of mathematics (​​​‌Clémentine Courtès , Emmanuel‌ Franck )
• Jury member‌​‌ of the mathematics olympiade​​ of 1ère (Clémentine​​​‌ Courtès )
• Jury member‌ for the recruitement of‌​‌ a permanent lecturer (PRAG),​​ Strasbourg University (Joubine​​​‌ Aghili )
• Jury member‌ for the recruitement of‌​‌ temporary lecturers (ATER and​​ PRAG contractuel), Strasbourg University​​​‌ (Joubine Aghili )‌
• Jury member for the‌​‌ recruitement of Chargés de​​ Recherche for the Inria​​​‌ center of the University‌ of Lorraine (Antoine‌​‌ Deleforge )

11.2.4 Educational​​ and pedagogical outreach

Clémentine​​​‌ Courtès was in charge‌ of the option "mathematics‌​‌ and statistics to prepare​​ for administrative competitions" of​​​‌ the Bachelor in public‌ administration which is a‌​‌ joint program between the​​ UFR Mathematics-Informatics and IPAG.​​​‌

Furthermore, Clémentine Courtès held‌ research talks aimed at‌​‌ high school students:

• Charleville​​ Mézières, November
• Les Voivres,​​​‌ October
• RJMI Strasbourg, April‌

Furthermore she participated in‌​‌ the events

• Co-organization of​​ the mathematics and computing​​​‌ week "Les Cigognes" for‌ high school girls, October‌​‌
• Scientific workshop "modelling a​​ chocolate cake" for high​​​‌ school students, May
• Talk‌ on "Events to encourage‌​‌ high school girls to​​ take up science", at​​​‌ the IREM-mathematics laboratories, April,‌ Strasbourg University

Antoine Deleforge‌​‌ gave 1 hour each​​ of science outreach presentations​​​‌ for 6 classes in‌ 5 schools across Alsace:‌​‌

• Lycée polyvalent Marguerite Yourcenar​​ (Erstein, 2nd)
• Jebsheim (CM1-CM2),​​​‌ Horbourg-Wihr (CE1-CE2)
• Brant (Colmar,‌ CM2)
• Lycée Fustel de‌​‌ Coulanges (Strasbourg, 2nd) for​​ the fête des sciences​​​‌ and the CHICHE-SNT program.‌

Deep Learning and applications‌​‌ 2025

In association with​​ the MACARON team, a​​​‌ practical session for the‌ Summer School "Deep Learning‌​‌ and applications" taking place​​ in Strasbourg in Aug​​​‌ 25-29 was organized by‌ Philippe Helluy . The‌​‌ title of the lecture​​ was "Time series reasoning​​​‌ with language models" by‌ Svitlana Vyetrenko, Source Files‌​‌, Event Link.​​

11.3.1 Specific​​​‌ official responsibilities in science‌ outreach structures

Joubine Aghili‌​‌ is a member of​​ the committee "Science Ouverte"​​​‌ at Strasbourg University since‌ 2025.

11.3.2 Productions (articles,‌​‌ videos, podcasts, serious games,​​ ...)

Clémentine Courtès appeared​​​‌ on an episode of‌ the podcast "Tête-à-tête chercheuse(s)"‌​‌ which was moderated by​​ Nathalie Ayi.

11.3.3 Others​​​‌ science outreach relevant activities‌

Clémentine Courtès participated in‌​‌ the Journées des Universités​​ et des formations post-bac,​​​‌ présentation des filières à‌ l'UFR maths-info which took‌​‌ place in January 2025.​​

International journals

• 2 article​‌J.Joubine Aghili,​​ R.Romain Hild,​​​‌ V.Victor Michel-Dansac,​ V.Vincent Vigon and​‌ E.Emmanuel Franck.​​ Accelerating the convergence of​​​‌ Newton's method for nonlinear​ elliptic PDEs using Fourier​‌ neural operators.Communications​​ in Nonlinear Science and​​​‌ Numerical Simulation1402​January 2025, 108434​‌HALDOI
• 3 article​​A.Amaury Bélières--Frendo,​​​‌ E.Emmanuel Franck,​ V.Victor Michel-Dansac and​‌ Y.Yannick Privat.​​ Volume-Preserving Geometric Shape Optimization​​​‌ of the Dirichlet Energy​ Using Variational Neural Networks​‌.Neural Networks184​​April 2025, 106957​​​‌HALDOI
• 4 article​T.Thomas Bellotti,​‌ P.Philippe Helluy and​​ L.Laurent Navoret.​​​‌ Fourth-order entropy-stable lattice Boltzmann​ schemes for hyperbolic systems​‌.SIAM Journal on​​ Scientific Computing471​​​‌February 2025, A586-A611​HALDOIback to​‌ text
• 5 articleC.​​Christophe Berthon, V.​​​‌Victor Michel-Dansac and A.​Andrea Thomann. Towards​‌ a fully well-balanced and​​ entropy-stable scheme for the​​​‌ Euler equations with gravity:​ preserving isentropic steady solutions​‌.Mathematics of Computation​​April 2025HALDOI​​​‌back to text
• 6​ articleM.Mirco Ciallella​‌, L.Lorenzo Micalizzi​​, V.Victor Michel-Dansac​​​‌, P.Philipp Öffner​ and D.Davide Torlo​‌. A high-order, fully​​ well-balanced, unconditionally positivity-preserving finite​​​‌ volume framework for flood​ simulations.GEM -​‌ International Journal on Geomathematics​​166February 2025​​​‌HALDOIback to​ text
• 7 articleR.​‌Raphaël Côte, C.​​Clémentine Courtès, G.​​​‌Guillaume Ferriere, L.​Ludovic Godard-Cadillac and Y.​‌Yannick Privat. Existence​​ and uniqueness of domain​​​‌ walls for notched ferromagnetic​ nanowires.ESAIM: Control,​‌ Optimisation and Calculus of​​ Variations312025,​​​‌ 60HALDOIback​ to text
• 8 article​‌R.Raphaël Côte,​​ C.Clémentine Courtès,​​​‌ G.Guillaume Ferriere and​ Y.Yannick Privat.​‌ Minimal time of magnetization​​ switching in small ferromagnetic​​​‌ ellipsoidal samples.Journal​ de l'École polytechnique —​‌ MathématiquesTome 12January​​ 2025, 147-184HAL​​​‌DOIback to text​
• 9 articleA.Antoine​‌ Deleforge, C.Cédric​​ Foy, Y.Yannick​​​‌ Privat and T.Tom​ Sprunck. Hearing the​‌ Shape of a Cuboid​​ Room Using Sparse Measure​​​‌ Recovery.Inverse Problems​419September 2025​‌, 095002HALDOI​​back to text
• 10​​​‌ articleM.Michael Dumbser​, M.Mária Lukáčová-Medvid'ová​‌ and A.Andrea Thomann​​. Convergence of a​​​‌ Hyperbolic Thermodynamically Compatible Finite​ Volume scheme for the​‌ Euler equations.Numerische​​ MathematikDecember 2025HAL​​​‌DOIback to text​
• 11 articleM.Michel​‌ Duprez, V.Vanessa​​ Lleras, A.Alexei​​​‌ Lozinski, V.Vincent​ Vigon and K.Killian​‌ Vuillemot. Phi-FD :​​ A well-conditioned finite difference​​​‌ method inspired by phi-FEM​ for general geometries on​‌ elliptic PDEs.Journal​​ of Scientific Computing104​​​‌23May 2025HAL​DOIback to text​‌
• 12 articleM.Michel​​ Duprez, V.Vanessa​​​‌ Lleras, A.Alexei​ Lozinski, V.Vincent​‌ Vigon and K.Killian​​ Vuillemot. Phi-FEM-FNO: a​​ new approach to train​​​‌ a Neural Operator as‌ a fast PDE solver‌​‌ for variable geometries.​​Communications in Nonlinear Science​​​‌ and Numerical Simulation152‌January 2026, 109131‌​‌HALDOIback to​​ text
• 13 articleE.​​​‌Emmanuel Franck, V.‌Victor Michel-Dansac, L.‌​‌Laurent Navoret and V.​​Vincent Vigon. Neural​​​‌ semi-Lagrangian method for high-dimensional‌ advection-diffusion problems.Computer‌​‌ Methods in Applied Mechanics​​ and Engineering448B​​​‌January 2026, 118481‌HALDOIback to‌​‌ text
• 14 articleP.​​Philippe Helluy and G.​​​‌Gauthier Lazare. Analysis‌ and Optimization of a‌​‌ Liquid-vapor Thermohydraulic Model.​​ESAIM: Proceedings and Surveys​​​‌81October 2025,‌ 77-103HALback to‌​‌ text
• 15 articleO.​​Olivier Hurisse, J.​​​‌James Glimm and P.‌Philippe Helluy. Simulations‌​‌ of Richtmyer-Meshkov instabilities using​​ a stochastic front tracking​​​‌ method.Physica D:‌ Nonlinear PhenomenaOctober 2025‌​‌HALback to text​​
• 16 articleV.Victor​​​‌ Michel-Dansac and A.Andrea‌ Thomann. Towards a‌​‌ fully well-balanced and entropy-stable​​ scheme for the Euler​​​‌ equations with gravity: General‌ equations of state.‌​‌Computers and Fluids303​​December 2025, 106853​​​‌HALDOIback to‌ text
• 17 articleT.‌​‌Tom Sprunck, A.​​Antoine Deleforge, Y.​​​‌Yannick Privat and C.‌Cédric Foy. Fully‌​‌ Reversing the Shoebox Image​​ Source Method: From Impulse​​​‌ Responses to Room Parameters‌.IEEE transactions on‌​‌ acoustics, speech, and signal​​ processing33January 2025​​​‌, 1022-1033HALDOI‌back to text
• 18‌​‌ articleA.Andrea Thomann​​. Semi-implicit relaxed finite​​​‌ volume schemes for hyperbolic‌ multi-scale systems of conservation‌​‌ laws.Journal of​​ Computational Physics539October​​​‌ 2025, 114263HAL‌DOIback to text‌​‌

International peer-reviewed conferences

• 19​​ inproceedingsI.Ilaria Fichera​​​‌, A.Antoine Deleforge‌, C.Cédric Foy‌​‌, J.-D.Jean-Daniel Pascal​​, C.Christian Prax​​​‌, M.Marceau Tonelli‌, C.Cédric van‌​‌ Hoorickx and M.Maarten​​ Hornikx. A neural​​​‌ network for predicting with‌ the diffusion equation: a‌​‌ case study of long​​ rooms.EuroNoise 2025​​​‌ - 11th EAA Annual‌ European Conference on Acoustics‌​‌ and Noise Control Engineering​​Málaga, FranceEuropean Acoustics​​​‌ AssociationJune 2025,‌ 4171-4178HALDOIback‌​‌ to textback to​​ text

Conferences without proceedings​​​‌

• 20 inproceedingsM.Matthieu‌ Boileau, P.Philippe‌​‌ Helluy, J.Jeremy​​ Pawlus and S.Svitlana​​​‌ Vyetrenko. Towards Interpretable‌ Time Series Foundation Models‌​‌.1st ICML Workshop​​ on Foundation Models for​​​‌ Structured DataVancouver, Canada‌arXivJuly 2025HAL‌​‌DOIback to text​​
• 21 inproceedingsG.Gauthier​​​‌ Lazare, C.Corentin‌ Coudroy, P.Philippe‌​‌ Helluy, E.Erwan​​ Le Coupanec, Q.​​​‌Qingqing Feng, F.‌Frank Hulsemann, S.‌​‌Stéphane Pujet and P.​​Pauline Rotach. Acceleration​​​‌ of the Convergence of‌ a Core Thermal Hydraulic‌​‌ Code Using Initialization from​​ a Neural Network.​​​‌21st International Topical Meeting‌ on Nuclear Reactor Thermal‌​‌ HydraulicsBusan, South Korea​​August 2025HALback​​​‌ to text

Edition (books,‌ proceedings, special issue of‌​‌ a journal)

• 22 periodical​​​‌P.Philippe Helluy,​ J.-M.Jean-Marc Hérard and​‌ N.Nicolas Seguin,​​ eds. Sixth Workshop on​​​‌ Compressible Multiphase Flows -​ Derivation, Closure laws, Thermodynamics​‌.ESAIM: Proceedings and​​ Surveys78December 2025​​​‌, 1-1HALDOI​back to text

Doctoral​‌ dissertations and habilitation theses​​

• 23 thesisA.Antoine​​​‌ Deleforge. Can One​ Hear the Walls of​‌ a Room? Physics- and​​ Data-Driven Inverse Methods for​​​‌ Acoustic Signal Processing.​Université de StrasbourgNovember​‌ 2025HALback to​​ text

Reports & preprints​​​‌

• 24 miscH.Hélène​ Barucq, M.Michel​‌ Duprez, F.Florian​​ Faucher, E.Emmanuel​​​‌ Franck, F.Frédérique​ Lecourtier, V.Vanessa​‌ Lleras, V.Victor​​ Michel-Dansac and N.Nicolas​​​‌ Victorion. Enriching continuous​ Lagrange finite element approximation​‌ spaces using neural networks​​.February 2025HAL​​​‌back to text
• 25​ miscS.Stéphane Clain​‌, E.Emmanuel Franck​​ and V.Victor Michel-Dansac​​​‌. Structural schemes for​ Hamiltonian systems.January​‌ 2025HALback to​​ text
• 26 miscR.​​​‌Raphaël Côte, C.​Clémentine Courtès, G.​‌Guillaume Ferriere, L.​​Ludovic Godard-Cadillac and Y.​​​‌Yannick Privat. The​ Spear and the Ring:​‌ Emergent Structures in Magnetic​​ Colloidal Suspensions.April​​​‌ 2025HALback to​ text
• 27 miscC.​‌Clémentine Courtès, E.​​Emmanuel Franck, M.​​​‌Michael Kraus, L.​Laurent Navoret and L.​‌Léopold Trémant. Neural​​ non-canonical Hamiltonian dynamics for​​​‌ long-time simulations.September​ 2025HALback to​‌ text
• 28 miscV.​​Victorita Dolean, D.​​​‌Daria Hrebenshchykova, S.​Stéphane Lanteri and V.​‌Victor Michel-Dansac. Neural​​ network-driven domain decomposition for​​​‌ efficient solutions to the​ Helmholtz equation.October​‌ 2025HALback to​​ text
• 29 miscM.​​​‌Michael Dumbser, A.​Andrea Thomann, M.​‌Maurizio Tavelli and W.​​W Boscheri. A​​​‌ structure-preserving semi-implicit four-split scheme​ for continuum mechanics.​‌November 2025HALback​​ to text
• 30 misc​​​‌E.Emmanuel Franck,​ L.Laurent Navoret,​‌ V.Vincent Vigon,​​ R.Raphaël Côte and​​​‌ G.Guillaume Steimer.​ Reduced Particle in Cell​‌ method for the Vlasov-Poisson​​ system using auto-encoder and​​​‌ Hamiltonian neural.June​ 2025HALback to​‌ text
• 31 miscP.​​Philippe Helluy and O.​​​‌Olivier Hurisse. A​ stochastic front tracking method​‌ for compressible flow with​​ interfaces.October 2025​​​‌HALback to text​
• 32 miscK.Killian​‌ Lutz and Y.Yannick​​ Privat. Minimal Time​​​‌ Control of Underdamped Parametric​ Oscillators.April 2025​‌HALback to text​​
• 33 miscK.Killian​​​‌ Lutz and Y.Yannick​ Privat. Time Optimal​‌ Synthesis of Gates for​​ Markovian Open Qudits.​​​‌July 2025HALback​ to text
• 34 misc​‌L.Laurent Navoret,​​ R.Roxana Sublet and​​​‌ M.Marcela Szopos.​ From flocking to jamming​‌ in collective cell dynamics:​​ a Vicsek-like model including​​​‌ contact forces.December​ 2025HALback to​‌ text
• 35 miscM.​​Mei Palanque, P.​​​‌Pierre Ocvirk, E.​Emmanuel Franck, P.​‌Pierre Gerhard, D.​​Dominique Aubert and O.​​Olivier Marchal. Higher​​​‌ order methods for Radiative‌ Transfer in Astrophysical simulations:‌​‌ Pn vs M1.​​July 2025HALDOI​​​‌back to text