Publications

2025

• Stochastic and deterministic approaches for studying telomere shortening and other cell dynamics
  
  • Olayé Jules
  , 2025. Telomeres are non-coding regions situated at the ends of chromosomes of eukaryotic cells, whose lengths vary during cell divisions through shortening and/or elongation. The shortening of telomeres is one of the main factors leading to replicative senescence, an irreversible state in which cells stop to divide. The study of telomeres has gained interest in recent years, notably due to their link with the emergence of cancer cells and with the aging of individuals. These studies have led to the development of mathematical models, allowing the description of the experiments conducted by biologists. Using these models often relies on assuming that a stationary profile of telomere lengths exists, or doing model approximations, for which theoretical results are not well-established. The main objective of this thesis is to provide theoretical results, through two axes of study.The first axis is the analysis of the long-time behaviour of the telomere lengths density in a telomere shortening model with elongation. The difficulties that we need to manage are the non-compact nature of the operator we study, and the semi-Markovian aspect of our model. The second axis is the study of an inverse problem, in which we aim to estimate an initial distribution of telomere lengths from measurements of senescence times. The main argument in solving this problem is to approximate our models by transport and transport-diffusion equations, on which estimators are easier to construct.In parallel with these works related to telomeres, two additional studies have been conducted in this thesis, still related to cell dynamics. In the first one, we propose a model for the neurogenesis phenomenon based on compound Poisson processes. In the second one, we perform a theoretical and numerical study of a method for estimating the division times distribution of bacteria, developed by a biologist during his thesis. (10.70675/e941b3aez5423z4d23zb2dfz9558c204420f)
  DOI : 10.70675/e941b3aez5423z4d23zb2dfz9558c204420f
• A quantitative comparison of high-order asymptotic-preserving and asymptotically-accurate IMEX methods for the Euler equations with non-ideal gases
  
  • Orlando Giuseppe
  • Boscarino Sebastiano
  • Russo Giovanni
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2025, 442, pp.118037. We present a quantitative comparison between two different Implicit-Explicit Runge-Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK approach involves an implicit coupling between the momentum and energy balance so as to avoid the acoustic CFL restriction, while the density can be treated in a fully explicit fashion. This approach leads to a mildly nonlinear equation for the pressure, which can be solved according to a fixed point procedure. An alternative strategy consists of employing a semi-implicit temporal integrator based on IMEX-RK methods (SI-IMEX-RK). The stiff dependence is carefully analyzed, so as to avoid the solution of a nonlinear equation for the pressure also for equations of state (EOS) of non-ideal gases. The spatial discretization is based on a Discontinuous Galerkin (DG) method, which naturally allows high-order accuracy. The asymptotic-preserving (AP) and the asymptotically-accurate (AA) properties of the two approaches are assessed on a number of classical benchmarks for ideal gases and on their extension to non-ideal gases. (10.1016/j.cma.2025.118037)
  DOI : 10.1016/j.cma.2025.118037
• Computer-assisted proofs for differential equations and dynamical systems
  
  • Breden Maxime
  , 2025.
• On random 3/2-stable maps
  
  • Kammerer Emmanuel
  , 2025. This thesis focuses on the asymptotic behaviour of random planar maps and random trees. In a first part, we study the geometry of large random planar maps with high degree vertices, also called stable maps, with a particular interest in the critical case: the case of 3/2-stable maps. We prove that these maps appear naturally in the study of random planar maps coupled with a loop O(n) model, a classical model of statistical mechanics, in the case n=2. We obtain the asymptotic behaviour of the distances between two uniform random vertices and we prove that the diameter is of the same order. A consequence of these results is that 3/2-stable maps do not satisfy scaling limits in the usual sense of Gromov-Hausdorff. However, we get the scaling limit of the distances between high degree vertices and the root. This scaling limit corresponds to a distance between the loops of a conformal loop ensemble and the boundary of the disc, measured using an independent Liouville quantum gravity, which is the Lamperti transform of the "quantum distance" to the boundary introduced by Aru, Holden, Powell and Sun. We then study the geodesics to the root for the first passage percolation distance on stable maps. We construct the scaling limit of the geodesics by means of a coalescing flow of pure jump diffusions.In a second part, we introduce a generalisation of the model of random recursive trees by adding a freezing mechanism. At some steps, a uniform random vertex is frozen and new vertices can no longer be attached to this vertex. The infection tree in an SIR model on the complete graph falls within this framework. We obtain local limits of these trees and scaling limits of the distances between the root and a typical vertex, of the distance between two uniform typical vertices and of the total height of the tree obtained after n steps. In the sub-linear case where the number of non-frozen vertices evolves as a given power of n, we identify a phase transition. Lastly, we consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalised converge. (10.70675/dfc08e5az605az4134z855dz6673559900bf)
  DOI : 10.70675/dfc08e5az605az4134z855dz6673559900bf
• Some mathematical models for flagellar activation mechanisms
  
  • Alouges François
  • Anello Irene
  • Desimone Antonio
  • Lefebvre-Lepot Aline
  • Levillain Jessie
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2025, 35 (11), pp.2395-2424. This paper focuses on studying a model for molecular motors responsible for the bending of the axoneme in the flagella of microorganisms. The model is a coupled system of partial differential equations inspired by Jülicher et al. or Camalet, incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution is proved, together with the presence of a supercritical Hopf bifurcation. Additionally, numerical simulations are provided to illustrate the theoretical results. A brief study on the generalization to N-rows is also included. (10.1142/S0218202525500423)
  DOI : 10.1142/S0218202525500423
• Effects of a mutation on the fitness of a bacterium : theoretical estimation and numerical implementation
  
  • Garnier Guillaume
  , 2025. This thesis presents a mathematical study of genetic mutations and their effects on the fitness of individuals, a central concept in evolutionary biology. A mutation is a spontaneous or induced alteration of DNA, which can be deleterious, neutral, or beneficial. These mutations affect the fitness of individuals, i.e., their ability to survive and reproduce. The main question addressed is the estimation of the Density of Fitness Effects (DFE), which describes the distribution of the effects of mutations on fitness. Understanding the shape of the DFE is essential for predicting population evolution, genetic diversity, and the consequences of conservation programs. The starting point of this work is an experimental protocol developed by Lydia Robert et al. (2018), which allows real-time observation of mutation events in E. coli. These new data open up opportunities for improved estimation of the DFE, but also raise statistical challenges due to experimental noise .In the first part of this manuscript, we consider a stochastic model from [77] that describes the evolution of a bacterial population under mutation pressure. We develop a nonparametric estimation method based on Fourier estimators to recover the DFE, and establish convergence results for our estimator. The second part introduces two deterministic models for the evolution of fitness in a population structured by growth rate. These models allow us to study the asymptotic behavior of the population and provide mathematical insight into the dynamics of mutation accumulation observed in experiments. Finally, the third part applies various statistical methods to the experimental data, aiming to reconstruct the DFE from its empirical moments and to assess whether it is unimodal or multimodal. This work builds a bridge between experimental biology and the mathematical modeling of mutation effects. (10.70675/410665dbzd24ez44cdza752z2d8061d239a3)
  DOI : 10.70675/410665dbzd24ez44cdza752z2d8061d239a3
• Robust calibration of an air-carbon ablation model employing Plasmatron and molecular beam data
  
  • Piro Vittorio
  • Capriati Michele
  • Bariselli Federico
  • Congedo Pietro Marco
  • Magin Thierry E.
  , 2025. Understanding and accurately predicting gas-surface interaction phenomena during a vehicle's re-entry phase is critical for the design of thermal protection materials. In this work, we aim to improve the robustness of an air-carbon ablation model by calibrating its reaction rates using both low-pressure molecular beam data and high-pressure Plasmatron data, as well as numerical models, following a Bayesian approach. Firstly, the subset of nitrogen chemical reactions is inferred, resulting in a finite-rate nitrogen model successfully calibrated and validated at both low-and highpressure. A surrogate-based Bayesian framework is employed, comparing artificial neural network and Kriging approaches to mimic the nitrogen model predictions at high-pressure and accelerate posterior sampling. Then, for the first time, atomic oxygen reaction rates are also included in the calibration, along with low-pressure oxygen observations. Since the experimental data used for calibration do not include high-pressure conditions, the oxygen reaction rates for accuracy at high pressure could not be fully characterised. Nevertheless, the resulting models demonstrated superior performance compared to the state-of-the-art model under low-pressure conditions.
• Bayesian model updating of rotating wind turbines
  
  • Delette Nina
  • Pfister Jean-Lou
  • Denimal Goy Enora
  • El Amri Mohamed Reda
  • Mevel Laurent
  , 2025, pp.1-3.
• Energy estimate of a Discrete Duality Finite Volume scheme for a phase-field model with surfactants
  
  • Castellano Margherita
  • Goudenège Ludovic
  • Nabet Flore
  , 2025. In this work we establish a discrete energy estimate for a phase-field model describing a ternary mixture of two immiscible fluids (air and water) and surfactants, firstly introduced by [3]. We mainly rely on the phase-field formulation presented in [5], where the authors include a stabilization term to the model analyzed in [4]. The stabilization term ensures that the free energy remains bounded from below, which is essential for deriving the discrete energy estimate. This will later guarantee the existence of an approximate solution and the convergence of the numerical scheme (which will be covered in a forthcoming paper). We propose a spatial discretization using the Discrete Duality Finite Volume (DDFV) method, which is particularly wellsuited for the simulation of non-linear diffusive problems. This method can handle very general (possibly non-conforming or anisotropic) meshes, while preserving key structural properties of the continuous problem at the discrete level.
• A sequential variational Bayesian approach to Gaussian process quantile regression for optimization
  
  • Nicolas Hugo
  • Le Maître Olivier
  • Congedo Pietro Marco
  , 2025. Quantile regression [1] extends the classical least-squares regression to the estimation of the conditional quantiles of a random variable. In the frequentist approach, one casts the quantile regression into the problem of minimizing a loss function, possibly completed with regularization terms. The Bayesian counterpart, first proposed in [2], formulates the problem as a posterior inference over a function space. Bayesian inference can rely on Markov chain Monte Carlo (MCMC) methods to sample the posterior distribution. Variation Bayesian inference techniques alleviate some of the computational burdens of MCMC by introducing latent variables and providing an analytical approximation of their posterior distribution.
• On measure-valued solutions for a structured population model with transfers
  
  • Magal Pierre
  • Raoul Gaël
  , 2025, pp.76. We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to population having singular distributions in trait. We extend the definition of the transfer operator to non-negative measures with a finite second moment, and we discuss the regularity of the fixed distributions of that transfer operator. Finally, we consider a dynamic transfer model where an initial population distribution is affected by a transfer operator: we prove the existence and uniqueness of mild measure-valued solutions for that Cauchy problem.
• Long-time behaviors of dynamics with mean field interactions
  
  • Wang Songbo
  , 2025. This thesis is devoted to the study of the long-time behaviors of dynamics with mean field interactions and their associated particle systems. For most cases treated in the thesis, the structural condition for the long-time behaviors is the flat convexity of the mean field energy functional, which is different from the displacement convexity studied in the classical works of optimal transport and gradient flow. The thesis is comprised of three parts. In the first part, we study the overdamped and underdamped mean field Langevin dynamics, which are gradient dynamics associated to a mean field free energy functional, and show their time-uniform propagation of chaos properties by exploiting their gradient structures and a uniform logarithmic Sobolev inequality. In the second part, we first develop some technical results on logarithmic Sobolev inequalities and apply them to get the time-uniform propagation of chaos for various McKean-Vlasov diffusions. Specifically, for the 2D viscous vortex model, we develop strong regularity bounds on its mean field limit on the whole space and show its propagation of chaos by the Jabin-Wang method; we also study its size of chaos problem using the entropy approach of Lacker and obtain time-uniform sharp bounds in the high viscosity regime. In the last part of the thesis, we explore alternative mean field dynamics that originate from convex optimization problems. For the entropy-regularized optimization, we study a fictitious self-play dynamics and a self-interacting diffusion and show their long-time convergences to the solution of the optimization problem. We also consider a non-linear Schrödinger semigroup, which is a gradient flow for the optimization problem regularized by Fisher information, and show its exponential convergence under a uniform spectral gap condition. (10.70675/f864c5ffz4a06z4c7fz8a0az1ab47a4f7535)
  DOI : 10.70675/f864c5ffz4a06z4c7fz8a0az1ab47a4f7535
• Open-Canopy: Towards Very High Resolution Forest Monitoring
  
  • Fogel Fajwel
  • Perron Yohann
  • Besic Nikola
  • Saint-André Laurent
  • Pellissier-Tanon Agnès
  • Schwartz Martin
  • Boudras Thomas
  • Fayad Ibrahim
  • d'Aspremont Alexandre
  • Landrieu Loic
  • Ciais Philippe
  , 2025. Estimating canopy height and its changes at meter resolution from satellite imagery remains a challenging computer vision task with critical environmental applications. However, the lack of open-access datasets at this resolution hinders the reproducibility and evaluation of models. We introduce Open-Canopy, the first open-access, country-scale benchmark for very high-resolution (1.5 m) canopy height estimation, covering over 87,000 km² across France with 1.5 m panchromatic resolution satellite imagery and aerial LiDAR data. Additionally, we present Open-Canopy-$\Delta$, a benchmark for canopy height reduction detection between images from different years at tree level---a difficult task for current computer vision models. We evaluate state-of-the-art architectures on these benchmarks, highlighting significant challenges and opportunities for improvement. Our datasets and code are publicly available at \url{https://github.com/fajwel/Open-Canopy}. (10.1109/CVPR52734.2025.00138)
  DOI : 10.1109/CVPR52734.2025.00138
• A theoretical perspective on mode collapse in variational inference
  
  • Soletskyi Roman
  • Gabrié Marylou
  • Loureiro Bruno
  Machine Learning : Science and Technology, IOP Publishing Ltd, 2025, 6 (2), pp.025056. While deep learning has expanded the possibilities for highly expressive variational families, the practical benefits of these tools for variational inference (VI) are often limited by the minimization of the traditional Kullback–Leibler objective, which can yield suboptimal solutions. A major challenge in this context is mode collapse : the phenomenon where a model concentrates on a few modes of the target distribution during training, despite being statistically capable of expressing them all. In this work, we carry a theoretical investigation of mode collapse for the gradient flow on Gaussian mixture models. We identify the key low-dimensional statistics characterizing the flow, and derive a closed set of low-dimensional equations governing their evolution. Leveraging this compact description, we show that mode collapse is present even in statistically favorable scenarios, and identify two key mechanisms driving it: mean alignment and vanishing weight. Our theoretical findings are consistent with the implementation of VI using normalizing flows, a class of popular generative models, thereby offering practical insights. (10.1088/2632-2153/adde2a)
  DOI : 10.1088/2632-2153/adde2a
• Wave turbulence, thermalization and multimode locking in optical fibers
  
  • Ferraro M.
  • Baudin K.
  • Gervaziev M.
  • Fusaro A.
  • Picozzi Antonio
  • Garnier J.
  • Millot G.
  • Kharenko D.
  • Podivilov E.
  • Babin S.
  • Mangini F.
  • Wabnitz S.
  Physica D: Nonlinear Phenomena, Elsevier, 2025, 481, pp.134758. We present a comprehensive overview of recent advances in theory and experiments on complex light propagation phenomena in nonlinear multimode fibers. On the basis of the wave turbulence theory, we derive kinetic equations describing the out-of-equilibrium process of optical thermalization toward the Rayleigh-Jeans (RJ) equilibrium distribution. Our theory is applied to explain the effect of beam self-cleaning (BSC) in graded-index (GRIN) fibers, whereby a speckled beam transforms into a bell-shaped beam at the fiber output as the input peak power grows larger. Although the output beam is typically dominated by the fundamental mode of the fiber, higher-order modes (HOMs) cannot be fully depleted, as described by the turbulence cascades associated to the conserved quantities. We theoretically explore the role of random refractive index fluctuations along the fiber core, and show how these imperfections may turn out to assist the observation of BSC in a practical experimental setting. This conclusion is supported by the derivation of wave turbulence kinetic equations that account for the presence of a time-dependent disorder (random mode coupling). The kinetic theory reveals that a weak disorder accelerates the rate of RJ thermalization and beam cleaning condensation. On the other hand, although strong disorder is expected to suppress wave condensation, the kinetic equation reveals that an out-of-equilibrium process of condensation and RJ thermalization can occur in a regime where disorder predominates over nonlinearity. In general, the kinetic equations are validated by numerical simulations of the generalized nonlinear Schrodinger equation. We outline a series of recent experiments, which permit to confirm the statistical mechanics approach for describing beam propagation and thermalization. For example, we highlight the demonstration of entropy growth, and point out that there are inherent limits to peak-power scaling in multimode fiber lasers. We conclude by pointing out the experimental observation that BSC is accompanied by an effect of modal phase-locking. From the one hand this explains the observed preservation of the spatial coherence of the beam, but also it points to the need of extending current descriptions in future research.
• Mesh Adaptation Strategies for CFD Simulations Over a Set of Operating Conditions
  
  • Dornier Hugo
  • Le Maître Olivier P
  • Congedo Pietro Marco
  • Salah El Din Itham
  • Bourasseau Sébastien
  • Marty Julien
  , 2025. In computational fluid dynamics, evaluating accurately quantities of interest (global or local) requires capturing complex local phenomena and interactions, such as shocks and flow separations, while controlling the global error. The latter depends highly on the discretization of the computational domain, hence the mesh. In general, the location of the flow structures within the domain is sensitive to boundary and flow conditions. Proposing an a priori mesh with a discretization effort that concentrates on the demanding parts of the domain is thus usually impossible. Adaptive Mesh Refinement (AMR, [1,2,3,4]) is a method developed to iteratively adjust the local mesh resolution to the computed flow structures and construct meshes that achieve a prescribed accuracy for limited discretization and computational cost. This work concerns the problem of mesh adaptation when the operating conditions are variable and follow a prescribed continuous distribution. For instance, variability of the flow conditions appears in uncertainty quantification, operating domain analysis, and robust optimization. These analyses typically require many simulations for different conditions, making the cost-accuracy trade-off even more crucial for these problems. Several mesh adaption methods have been proposed for variable conditions ([5,6,7,8]), but they typically focus primarily on error control without simultaneously optimizing for cost. In this context, we propose two original methodologies. The first one, called Mean Mesh adaptation (MMA, [9,10]), builds a unique adapted mesh to minimize the average error over the continuous operating conditions for a given discretization effort. A key ingredient of MMA is using a small sample set of conditions to estimate the local average error at each iteration of the AMR process. The second method, Error-based Mesh Selection (EMS), tackles the optimal element selection within a library of adapted meshes to achieve the smallest possible error for any given flow conditions. The library consists of meshes independently adapted for different conditions in an offline stage, for cost efficiency, the selection uses a priori error estimations requiring no additional simulation. We used analytical and full CFD supersonic simulations [11,12] to analyze the proposed methods. We show that MMA is robust and accurately approximates the optimal mesh minimizing the average error for a limited construction cost (see figures 1 and 2). Similarly, EMS provides a robust approximation of the optimal selection with limited cost overheads (see figure 3). The EMS method is suitable to be extended for progressive library enrichment and a-posteriori correction of the error estimates.
• Stochastic Dynamics of Incoherent Branched Flows
  
  • Garnier Josselin
  • Picozzi Antonio
  • Torres Theo
  Physical Review Letters, American Physical Society, 2025, 134 (22), pp.223803. (10.1103/PhysRevLett.134.223803)
  DOI : 10.1103/PhysRevLett.134.223803
• Estimation of extreme risk measures with neural networks
  
  • Girard Stéphane
  • Allouche Michaël
  • Gobet Emmanuel
  , 2025, pp.1-6. We propose new parameterizations for neural networks in order to estimate extreme risk measures, such as conditional tail moments, in heavy-tailed settings. The proposed neural network estimator is able to extrapolate in the distribution tails thanks to an extension of the usual extreme-value second-order condition to an arbitrary order. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. Finally, the neural network estimator is tested on real data to investigate the behavior of cryptocurrency extreme loss returns.
• Design of experiments based on a low fidelity model for seismic fragility curves estimation
  
  • Van Biesbroeck Antoine
  • Gauchy Clément
  • Feau Cyril
  • Garnier Josselin
  ESAIM: Proceedings and Surveys, EDP Sciences, 2025, 79, pp.96-109. Seismic fragility curves are key quantities of interest for Seismic Probabilistic Risk Assessment studies. They express the probability of failure of a mechanical structure of interest conditional to a scalar value derived from the ground motion signal coined Intensity Measure. In the literature, Bayesian approaches have emerged to enable their estimation within the difficult context of limited data availability. Yet, the log-normal modeling over which most of them are based requires the use of computationally expensive Markov chain Monte Carlo methods for providing Bayesian estimators. In this work, we propose an efficient modeling for the estimation of fragility curves in the Bayesian context, based on a low fidelity model of the structure's response to the ground motion signal and an objective prior. The analytical expression of our modeling allows fast generation of estimates. Also, the representative bias arisen by the modeling choice is handled with a judicious design of experiments methodology. Finally, our method is evaluated on a real case study, and the results highlight its efficiency and its ability to robustly overcome any bias when coupled with the design of experiments we propose. (10.1051/proc/202579096)
  DOI : 10.1051/proc/202579096
• Automatically generated cardiovascular digital twin in critical care: a proof of concept study
  
  • Kimmig François
  • Le Gall Arthur
  • Windsor Camille
  • Vallée Fabrice
  • Chapelle Dominique
  • Moireau Philippe
  , 2025. This proof of concept study demonstrates the capabilities of a virtually automatically generated digital twin framework for enhancing hemodynamic monitoring in critical care. By combining a deterministic cardiovascular model with patient-specific data through data assimilation techniques, the digital twin can act as a data denoiser, reconstruct physiological waveforms that are typically unavailable in critical care settings and generate clinically relevant biomarkers. Validation was performed using real data from patients under general anesthesia. The proposed framework efficient calibration and ability to follow the patient's state over time supports the possibility of real-time bedside applications. (10.1007/978-3-031-94562-5_35)
  DOI : 10.1007/978-3-031-94562-5_35
• A high-order matrix-free adaptive solver for the shallow water equations with irregular bathymetry
  
  • Arpaia Luca
  • Orlando Giuseppe
  • Ferrarin Christian
  • Bonaventura Luca
  , 2025. We present the first step in the development of an Adaptive Mesh Refinement (AMR) solver for coastal engineering applications, based on a high-order Discontinuous Galerkin (DG) method as implemented in the deal.II library. This environment provides efficient and native parallelization techniques and automatically handles non-conforming meshes to implement both static and dynamic AMR approaches. The proposed method is automatically well-balanced, allows the use of realistic bathymetry data without any regularity assumption, and includes a consistent conservative discretization for transported chemical species. Numerical experiments on idealized benchmarks validate the proposed approach, while results obtained on realistic bathymetries and complex domains show its potential for accurate and efficient adaptive simulations of coastal flows.
• Dynamics of screened particles towards equi-spaced ground states
  
  • de Luca Lucia
  • Goldman Michael
  • Ponsiglione Marcello
  , 2025. This paper deals with the dynamics - driven by the gradient flow of negative fractional seminorms - of empirical measures towards equi-spaced ground states. Specifically, we consider periodic empirical measures $\mu$ on the real line that are screened by the Lebesgue measure, i.e., with $\mu- d x$ having zero average. To each of these measures $\mu$ we associate a (periodic) function $u$ satisfying $u'= d x - \mu$. For $s\in (0,\frac 12)$ we introduce energy functionals $\mathcal E^s(\mu)$ that can be understood as the density of the $s$-Gagliardo seminorm of $u$ per unit length. Since for $s\ge \frac 12$, the $s$-Gagliardo seminorms are infinite on functions with jumps, some regularization procedure is needed: For $s\in[\frac 12,1)$ we define $\mathcal E_\varepsilon^s(\mu):= \mathcal E^s(\mu_\varepsilon)$, where $\mu_\varepsilon$ is obtained by mollifying $\mu$ on scale $\varepsilon$. We prove that the minimizers of $\mathcal E^s$ and $\mathcal E_\varepsilon^s$ are the equi-spaced configurations of particles with lattice spacing equal to one. Then, we prove the exponential convergence of the corresponding gradient flows to the equi-spaced steady states. Finally, although for $s\in[\frac 12 ,1)$ the energy functionals $\mathcal E_\varepsilon^s$ blow up as $\varepsilon\to 0$, their gradients are uniformly bounded (with respect to $\varepsilon$), so that the corresponding trajectories converge, as $\varepsilon\to 0$, to the gradient flow solution of a suitable renormalized energy.
• Numerical strategies for the microscale simulation of Li-ion batteries
  
  • Asad Ali
  , 2025. In this thesis, we develop and analyze numerical strategies for the simulation of lithium-ion batteries (LIBs) based on their continuum description at the microscale. Our focus is on addressing the computational challenges posed by this inherently multiphysics and multiscale problem, particularly the nonlinearity at the reaction interface and the stiffness of the governing equations.In the first phase of this doctoral work, we tackle the temporal multiscale nature of LIBs by decoupling the domains into subproblems that can be solved independently. Building upon an adaptive high-order coupling strategy, we implement this approach in a Python code. The effectiveness and performance of the method are demonstrated through 1D LIB half-cell simulations. Additionally, we discuss how this promising numerical strategy can be extended to 3D LIB simulations.The multiphysics nature of the LIB model further motivates us to explore adaptive methods in both space and time to reduce computational costs. To extend our study to higher dimensions, we employ a C++ framework with a monolithic solution strategy. Specifically, we implement a multiresolution-based adaptive mesh refinement (AMR) technique using SAMURAI and an adaptive high-order implicit time integrator using PETSc, examining their performance when used together. Using this fully adaptive implementation, we conduct parametric studies to evaluate the impact of interdigitated electrodes on the performance and behavior of 2D LIB half cells.The thesis concludes by synthesizing the two numerical strategies developed to address the computational challenges of LIB microscale simulations. As a natural extension of this work, we propose a unified framework that integrates these approaches, providing a robust foundation for tackling additional complexities that may arise in future microscale LIB model developments. (10.70675/15a07578zf225z4733za8c0zd2c75c9e0284)
  DOI : 10.70675/15a07578zf225z4733za8c0zd2c75c9e0284
• Faster Latency Constrained Service Placement in Edge Computing with Deep Reinforcement Learning
  
  • Forghieri Orso
  • Carlinet Yannick
  • Hyon Emmanuel
  • Le Pennec Erwan
  • Perrot Nancy
  , 2025. To enhance the user experience on mobile devices, Mobile Edge Computing (MEC) is a paradigm which integrates computing capabilities directly within access networks. However, designing efficient computation offloading policies in MEC systems remains a challenge. In particular, the decision on whether to process an incoming computation task locally on the mobile device or offload it to the cloud must intelligently adapt to dynamic environmental conditions. This article presents a novel approach that aims to address an edge computing optimization problem, issued from industrial cases, by modeling it as a combinatorial optimization problem combining multicommodity flow and linear latencies constraints. We develop an equivalent linear formulation of the Service Placement Problem, allowing us to use traditional Integer Linear Programming (ILP) methods that turns out to be inefficient in practice. We therefore develop a use-case-based heuristic and a Reinforcement Learning (RL) methodology to model the network configuration under orchestration actions. The latest allows us to transfer learning across pre-training of the agent and shows proof of its efficiency on a dynamic real-world instance, aiming for practical deployment conditions. This comparison reveals that RL is a robust approach that can solve large realistic instances, reaching an optimality gap smaller than 25% on average below a second of runtime for dynamic service placement.
• Optimizing the diffusion coefficient of overdamped Langevin dynamics
  
  • Lelièvre Tony
  • Pavliotis Grigorios A.
  • Robin Geneviève
  • Santet Régis
  • Stoltz Gabriel
  Mathematics of Computation, American Mathematical Society, 2025. Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian inference. By varying the diffusion coefficient, there are in fact infinitely many overdamped Langevin dynamics which are reversible with respect to the target probability measure at hand. This suggests to optimize the diffusion coefficient in order to increase the convergence rate of the dynamics, as measured by the spectral gap of the generator associated with the stochastic differential equation. We analytically study this problem here, obtaining in particular necessary conditions on the optimal diffusion coefficient. We also derive an explicit expression of the optimal diffusion in some appropriate homogenized limit. Numerical results, both relying on discretizations of the spectral gap problem and Monte Carlo simulations of the stochastic dynamics, demonstrate the increased quality of the sampling arising from an appropriate choice of the diffusion coefficient. (10.1090/mcom/4098)
  DOI : 10.1090/mcom/4098