Publications

2026

• Transport of dissolved and particulate arsenic in the Orbiel River during minor flood events downstream the historic Salsigne gold mining district, Southern France
  
  • Carrière Lali
  • Resongles Eléonore
  • Heydon Marie
  • Roux Hélène
  • Viers Jérôme
  • Schreck Eva
  • Freydier Rémi
  • Marchand Pierre
  • Domeau Aurélien
  • Horgue Pierre
  • Behra Philippe
  • Casiot Corinne
  Journal of Contaminant Hydrology, Elsevier, 2026, 281, pp.104955. (10.1016/j.jconhyd.2026.104955)
  DOI : 10.1016/j.jconhyd.2026.104955
• Risk-Averse Control for Continuous-Time Stochastic System Under Signal Temporal Logic Constraints
  
  • Lai En
  • Bonalli Riccardo
  • Girard Antoine
  • Jean Frédéric
  , 2026. Signal Temporal Logic (STL) has become a powerful formalism for specifying complex temporal-spatial behaviors in autonomous systems. Handling STL constraints within stochastic setting has received increasing research interest but still poses challenges. This paper proposes a general framework to efficiently solve continuous-time nonlinear stochastic optimal control problems under chance STL constraints. The STL formulae are implemented through extended dynamics, yielding a more classical chance constraint on the terminal state uniquely that we reliably relax via Conditional Value-at-Risk. The resulting new optimal control problem is then solved using established algorithms from risk--averse control. The efficiency and feasibility of the proposed approach are demonstrated through numerical simulations.
• Numerical analysis of an optimal control approach to solve a tsunami inverse problem
  
  • Bourgeois Laurent
  • Moireau Philippe
  • Terrine Raphaël
  , 2026. This paper concerns the reconstruction of an abrupt bottom displacement of the ocean from the measurement of the induced perturbation of the free surface, which is a severely ill-posed inverse problem. This problem is solved by using an optimal control approach, the physics being governed by a time evolution system based on a simple oceanography model. We firstly recast the problem in an abstract framework, secondly propose an implicit Euler scheme for the time discretization combined with a Finite Element method for the space discretization. The main result is an error estimate between the solution to the discrete control optimal problem and the solution to the continuous optimal problem, which is obtained by considering the discrete and continuous weak mixed formulations that characterize the optimality for these two problems. Some numerical experiments illustrate the efficiency of our approach and the consistency of our error estimate.
• No-regret optimization of time-varying bilevel problems
  
  • Mauduit Eliabelle
  • Berthier Eloïse
  • Simonetto Andrea
  , 2026. Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear bilevel programs are strongly NP-hard. In this work, we consider bilevel optimization with a known upper-level objective and an unknown, potentially time-varying lower-level response, accessible only through noisy zeroth-order observations. We propose W-SparQ-BL, a Bayesian optimization framework that models the lower-level mapping using multi-output Gaussian processes and enables efficient optimization under uncertainty. Our approach leverages a sparse, observation-based approximation to control the effect of noise and temporal variability, while requiring only limited access to additional information over time. We establish regularity results linking the lower-level response to standard RKHS assumptions for common kernels, including Matérn and squared exponential. We prove that W-SparQ-BL achieves sublinear dynamic regret in both stationary and time-varying settings. Experiments on representative time-varying game-theoretic problems demonstrate the effectiveness of our approach.
• An inverse tsunami problem in the time domain: a well-posedness analysis of the forward problem and an inversion strategy based on a mixed formulation of the Tikhonov regularization
  
  • Bourgeois Laurent
  • Moireau Philippe
  • Terrine Raphaël
  , 2026. This contribution concerns an inverse problem related to a tsunami in the ocean, the tsunami being caused by a submarine earthquake. Considering the very beginning of the phenomenon, a simple linear model incorporating both gravity and acoustic waves is proposed. The main objective is to develop a strategy to solve the inverse problem of retrieving the bottom displacement from the induced free surface perturbation. Such strategy is based on a mixed formulation of the Tikhonov regularization in the space/time domain, the regularization parameter being determined by using the Morozov principle by means of duality in optimization. Some numerical experiments in 2D, which rely on a tensorized finite element method, show that our strategy is effective. A secondary objective is to prove existence and uniqueness of both strong and variational solutions to the forward problem.
• Eigenvalue falls in thin broken quantum strips
  
  • Chesnel Lucas
  • Nazarov Sergei A.
  , 2025. We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in trapezoids of thickness $\varepsilon>0$ small. We give an asymptotic expansion of the first eigenvalues and corresponding eigenfunctions as $\varepsilon$ tends to zero. The new point in this work is to study the dependence with respect to $\alpha$. We highlight a curious phenomenon of diving eigenvalues: when the strip is more and more broken, at certain critical angles, that we characterize, an eigenvalue moves down very rapidly below the pack of other eigenvalues. We prove that this occurs more gently at $\alpha=0$ than at positive critical angles.
• Réduction de modèles pour les interactions fluide-structure : exploitation des fonctions de Green adaptées
  
  • Chaillat Stéphanie
  • Pacaut Louise
  • Mercier Jean-François
  • Serre Gilles
  • Trafny Nicolas
  , 2026. Nous considérons un problème d’interaction fluide-structure sur une géométrie complexe, pour lequel nous souhaitons calculer la réponse à des excitations variables. Pour réduire considérable- ment le coût de calcul de cette étude paramétrique sans sacrifier la précision, nous proposons une ap- proche de réduction de modèle séparant les effets de la géométrie et de la source. La méthode repose sur le calcul d’une fonction de Green adaptée au couplage fluide-structure et à la géométrie complexe. Pour rendre le coût de la phase offline acceptable, nous exploitons des méthodes d’éléments de frontière rapides.
• Méthode d'éléments finis discontinus hybridisée pour la résolution itérative accélérée de problèmes d'ondes en fréquence
  
  • Modave Axel
  • Greffe Roland
  • Geuzaine Christophe
  • Rappaport Ari
  • Chabib Ahmed
  , 2026. La discrétisation de problèmes de propagation d’ondes en régime harmonique par éléments finis conduit à des systèmes linéaires coûteux à résoudre. Nous considérons une méthode d’éléments finis discontinus hybridisée en utilisant des variables de transmission aux interfaces entre les mailles. Cette approche permet d’accélérer la convergence des schémas itératifs et possède une structure algo- rithmique adaptée au calcul parallèle, notamment sur cartes graphiques. Nous présentons et étudions des implémentations de cette méthode au moyen de résultats 3D obtenus avec un code C++ dédié.
• Space and Time Decompositions for LQG Problems in Decision-Hazard Information Structure
  
  • Carpentier Pierre
  , 2026. <div><p>In this paper, we implement spatial decomposition, temporal block decomposition, and the combination of these two decompositions for a Linear Quadratic Gaussian (LQG) problem that can be decomposed into subproblems linked by linear coupling constraints, with an optimization span comprising two time scales. This allows us to solve only quadratic problems under linear constraints during the decompositions, which we address by establishing the Riccati equation adapted to the different cases considered, and thus to be able to efficiently solve the different subproblems appearing in the decompositions. We can also compute the solution of the global problem using Riccati and thus measure the quality of the solutions obtained by the decompositions.</p></div>
• A non-local singular non-linear Fokker-Planck PDE
  
  • Bondi Luca
  • Issoglio Elena
  • Russo Francesco
  , 2026. The focus of this paper is a non-local singular non-linear Fokker-Planck partial differential equation (PDE). The peculiarity of this PDE feature is in its divergence coefficient, which presents a product between a Besov distribution and a non-linearity. The latter involves the convolution between an integrable kernel K and the solution of the PDE, which leads to a non-locality of the first order term in the PDE. We prove existence and uniqueness of a solution to the PDE as well as continuity results on its coefficients. Previous analytical results are then applied to the study of well-posedness in law for a non-local singular McKean stochastic differential equation. As byproduct of that probabilistic representation, we establish mass conservation and positivity preserving for the PDE.
• Poisson-type problems with transmission conditions at boundaries of infinite metric trees
  
  • Kachanovska Maryna
  • Naderi Kiyan
  • Pankrashkin Konstantin
  Journal of Mathematical Analysis and Applications, Elsevier, 2026, 557 (1), pp.130261. The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching along a compact surface (interface). The lower-dimensional piece is a so-called infinite metric tree (one-dimensional branching structure), and the key ingredient of the study is a rigorous definition of the gluing conditions between the two components. These constructions are based on the recent concept of embedded trace maps and some abstract machineries derived from a suitable Green-type formula. The problem is then reduced to the study of Fredholm properties of a linear combination of Dirichlet-to-Neumann maps for the tree and the Euclidean domain, which yields desired existence and uniqueness results. One also shows that large finite sections of the tree can be used for an efficient approximation of solutions (10.1016/j.jmaa.2025.130261)
  DOI : 10.1016/j.jmaa.2025.130261
• Fault Volume Digital Twin to Reproduce the Full Slip Spectrum, Scaling, and Statistical Laws
  
  • Almakari Michelle
  • Kheirdast Navid
  • Villafuerte Carlos
  • Thomas M.
  • Dubernet Pierpaolo
  • Cheng Jinhui
  • Gupta Ankit
  • Romanet P.
  • Chaillat S.
  • Bhat H.
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2026, 131 (5), pp.e2025JB032915. Seismological and geodetic observations of fault zones reveal diverse slip dynamics, scaling, and statistical laws. Existing mechanisms explain some but not all of these behaviors. We show that incorporating an off‐fault damage zone—characterized by distributed fractures surrounding a main fault—can reproduce many key features observed in seismic and geodetic data. We model a 2D shear fault zone in which off‐fault cracks follow power‐law size and density distributions, and are oriented either optimally or parallel to the main fault. All fractures follow rate‐and‐state friction with parameters enabling slip instabilities. We do not introduce spatial heterogeneities in frictional properties. Using quasi‐dynamic boundary integral simulations accelerated by hierarchical matrices, we simulate slip dynamics and analyze events produced both on and off the main fault. Despite spatially uniform frictional properties, we observe a natural continuum from slow to fast ruptures, as seen in nature. Our simulations reproduce the Omori law, inverse Omori law, Gutenberg‐Richter scaling, and moment‐duration scaling. We observe seismicity localizing toward the main fault before nucleation of main‐fault events. During slow slip events (SSEs), off‐fault seismicity migrates in patterns resembling fluid diffusion fronts, despite the absence of fluids. We show that tremors, very low‐frequency earthquakes, low frequency earthquakes, SSEs, and earthquakes can all emerge naturally within this fault volume framework, making it an ideal digital twin for testing hypotheses, performing ground‐truth inversions, and probing mechanical properties inaccessible with natural observations. (10.1029/2025JB032915)
  DOI : 10.1029/2025JB032915
• A Rellich-type theorem for the Helmholtz equation in a junction of stratified media
  
  • Al Humaikani Sarah
  • Bonnet-Ben Dhia Anne-Sophie
  • Fliss Sonia
  • Hazard Christophe
  , 2026. <div><p>We prove that there are no non-zero square-integrable solutions to a two-dimensional Helmholtz equation in some unbounded inhomogeneous domains which represent junctions of stratified media. More precisely, we consider domains that are unions of three half-planes, where each half-plane is stratified in the direction orthogonal to its boundary. As for the well-known Rellich uniqueness theorem for a homogeneous exterior domain, our result does not require any boundary condition. Our proof is based on half-plane representations of the solution which are derived through a generalization of the Fourier transform adapted to stratified media. A byproduct of our result is the absence of trapped modes at the junction of open waveguides as soon as the angles between branches are greater than π/2.</p></div>
• Stochastic transport by Gaussian noise
  
  • Flandoli Franco
  • Russo Francesco
  , 2026. Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain cases represents the equation for the mean value. From this equation we observe a reduced dissipation property for small times and an enhanced diffusion for large times, with respect to delta correlated noise when regularity is higher than the one of Brownian motion, a fact interpreted qualitatively here as a signature of the modified dissipation observed for 2D turbulent fluids due to the inverse cascade. We give results also for the variance of the solution and for a scaling limit of a two-component noise input.
• Stability of time stepping methods for discontinuous Galerkin discretizations of Friedrichs' systems
  
  • Imperiale Sébastien
  • Joly Patrick
  • Rodríguez Jerónimo
  , 2025. In this work we study new various energy-based theoretical results on the stability of s-stages, s-th order explicit Runge-Kutta integrators as well as a modified leap-frog scheme applied to discontinuous Galerkin discretizations of transient linear symmetric hyperbolic Friedrichs' systems. We restrict the present study to conservative systems and Cauchy problems.
• Slip optimization on arbitrary 3D microswimmers: a reduced-dimension and boundary-integral framework
  
  • Bonnet Marc
  • Das Kausik
  • Veerapaneni Shravan
  • Zhu Hai
  , 2026. This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid. The objective is to minimize the hydrodynamic power dissipation required to maintain unit speed along the net swimming direction. By exploiting the linearity of the Stokes equations and the Lorentz reciprocal theorem, we derive an explicit linear operator that maps the tangential surface slip velocity to the resulting rigid-body translational and rotational velocities, effectively decoupling the hydrodynamic boundary value problem from the optimization loop. The a priori infinite-dimensional search space for the slip optimization is reduced to the finite dimension $r$ of rigid-body motions by finding an appropriate subspace of the operator's domain. This reduces the PDE-constrained optimization to a low-dimensional programming problem that can be solved at negligible computational cost once the system matrices are assembled. The optimization algorithm requires 2$r$ auxiliary flow problems that are solved numerically using a high-order boundary integral method. We validate the accuracy of the proposed method and present optimal slip profiles and swimming trajectories for a variety of microswimmer shapes. We investigate the effect of some common geometrical symmetries of the swimmer shape on the resulting optimal motion, and in particular present a modified version of the slip optimization algorithm for axisymmetric shapes, where tangential rigid-body velocities may occur
• A posteriori error estimates for mixed finite element discretization of the multigroup Neutron Simplified Transport equations with Robin boundary condition
  
  • Ciarlet Patrick
  • Do Minh-Hieu
  • Gervais Mario
  • Madiot François
  , 2026. We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) equations, in the case where a Robin (or Fourier type) boundary condition is imposed on the boundary. This boundary condition is of particular importance in neutronics, since it corresponds to the well-known vacuum boundary condition. We provide guaranteed and locally efficient estimators. In particular, a specific estimator is designed to handle the Robin boundary condition. We also develop the theory in the case of mixed imposed boundary conditions, of Dirichlet, Neumann or Fourier type. The approach is further extended to a Domain Decomposition Method, the so-called DD+L 2 jumps method. In this framework, the adaptive mesh refinement strategy is implemented for a discretization using Cartesian meshes on each subdomain. Numerical experiments illustrate the theory.
• Analysis of a two-level domain decomposition preconditioner for the time-harmonic Maxwell equations in anisotropic media
  
  • Bonazzoli Marcella
  • Ciarlet Patrick
  • Modave Axel
  • Rappaport Ari
  , 2026. We analyze a domain decomposition preconditioner, namely a two-level additive Schwarz method, for the time-harmonic Maxwell equations in anisotropic media. The material law is described by a tensor-valued electric permittivity ε, magnetic permeability µ and conductivity σ which are assumed to be uniformly symmetric positive definite in the physical domain. Convergence estimates for the preconditioned GMRES solver are obtained through bounds on the norm and the field-of-values (FOV) of the preconditioned operator. Our purpose is to extend the convergence analysis available for scalar and constant coefficients established in Bonazzoli et al. [5] to this tensorial setting. While the overall argument follows the additive Schwarz framework therein, the anisotropic case requires substantial new ingredients. Among these are a coefficient-weighted discrete Helmholtz decomposition, regularity estimates adapted to the anisotropic setting, and a stronger "high frequency regime" assumption. The latter allows control of unsigned terms that vanish via orthogonality in the scalar case. These tools are crucial for the main technical result: bounding the FOV away from the origin through estimates explicit in the frequency and anisotropy parameters, under suitable resolution assumptions.
• Exponential twist of probability measures: drift correction in term of a generalized gradient
  
  • Bourdais Thibaut
  • Oudjane Nadia
  • Russo Francesco
  , 2026. In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure $\P$. This type of transformation naturally appears in variational representation formulae originating from the theory of large deviations and can be interpreted in some cases, as the solution of a specific stochastic control problem. Under a very general Markovian assumption on $\P$, we fully characterize the exponential twist probability measure as the solution of a martingale problem and prove that it inherits the Markov property of the reference measure. The ''generator'' of the martingale problem shows a drift depending on a {\it generalized gradient} of some suitable {\it value function} $v$.
• High-Resolution Inertial Dynamics with Time-Rescaled Gradients for Nonsmooth Convex Optimization
  
  • Le Manh Hung
  • Simonetto Andrea
  , 2026. We study nonsmooth convex minimization through a continuous-time dynamical system that can be seen as a high-resolution ODE of Nesterov Accelerated Gradient (NAG) adapted to the nonsmooth case. We apply a time-varying Moreau envelope smoothing to a proper convex lower semicontinuous objective function and introduce a controlled time-rescaling of the gradient, coupled with a Hessian-driven damping term, leading to our proposed inertial dynamic. We provide a well-posedness result for this dynamical system, and construct a Lyapunov energy function capturing the combined effects of inertia, damping, and smoothing. For an appropriate scaling, the energy dissipates and yields fast decay of the objective function and gradient, stabilization of velocities, and weak convergence of trajectories to minimizers under mild assumptions. Conceptually, the system is a nonsmooth high-resolution model of Nesterov's method that clarifies how time-varying smoothing and time rescaling jointly govern acceleration and stability. We further extend the framework to the setting of maximally monotone operators, for which we propose and analyze a corresponding dynamical system and establish analogous convergence results. We also present numerical experiments illustrating the effect of the main parameters and comparing the proposed system with several benchmark dynamics. (10.48550/arXiv.2603.25401)
  DOI : 10.48550/arXiv.2603.25401
• Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion
  
  • Darche Michaël
  • Assier Raphaël
  • Guenneau Sebastien
  • Lombard Bruno
  • Touboul Marie
  , 2026. We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass and rigidity interface parameters are modulated in time. Low-frequency homogenisation yields a leading-order model described by an effective time-dependent wave equation, i.e. a wave equation with effective mass density and Young's modulus which are homogeneous in space but depend on time. This means that time-dependent bulk effective properties can be created by an array where only interfaces are modulated in time. The occurrence of k-gaps in case of a periodic modulation is also analysed. Second-order homogenisation is then performed and leads to an effective model which is reciprocal but encapsulates higher-order dispersive effects. These findings and the limitations of the models are illustrated through time-domain simulations.
• A neural operator framework for solving inverse scattering problems
  
  • Chenu Victor
  • Haddar Houssem
  • Montanelli Hadrien
  , 2026. We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within the Linear Sampling Method to validate the initial reconstruction. The neural operator is implemented as a DeepONet with a fixed radial-basis-function trunk, while the noise level required for rescaling is estimated using a dedicated neural network. A neural tangent kernel analysis guides the architectural design, reducing the network tuning to a single discretization parameter, adjustable according to the wavelength. Two-dimensional numerical experiments demonstrate the method's effectiveness, with a Python toolbox provided for reproducibility.
• Degenerate McKean-Vlasov equations with drift in anisotropic negative Besov spaces
  
  • Issoglio Elena
  • Pagliarani Stefano
  • Russo Francesco
  • Trevisani Davide
  , 2024. The paper is concerned with a McKean-Vlasov type SDE with drift in anisotropic Besov spaces with negative regularity and with degenerate diffusion matrix under the weak Hörmander condition. The main result is of existence and uniqueness of a solution in law for the McKean-Vlasov equation, which is formulated as a suitable martingale problem. All analytical tools needed are derived in the paper, such as the well-posedness of the Fokker-Planck and Kolmogorov PDEs with distributional drift, as well as continuity dependence on the coefficients. The solutions to these PDEs naturally live in anisotropic Besov spaces, for which we developed suitable analytical inequalities, such as Schauder estimates.
• Accelerating the Method of Reflections with Domain Decomposition techniques for Boundary Integral Equations in Multiple Scattering
  
  • Chaillat Stéphanie
  • Darbas Marion
  • Gander Martin J
  • Halpern Laurence
  , 2026. The Method of Reflections was historically introduced to obtain approximate solu-tions as series expansions for the motion of particles in suspension. It can however equally well be used for solving multiple scattering problems numerically. We show for Helmholtz multiple scattering problems that the Method of Reflections, whether applied in its alternating or parallel version, suffers from convergence problems when scatterers are close. We use boundary integral equations to formulate the methods, and then identify them as algebraic Schwarz methods, thereby interpreting them as boundary domain decomposition techniques. This connection allows us to introduce remedies such as overlap (which can be partial, covering only the illuminating region of the obstacles) and coarse spaces from domain decomposition into the Method of Reflections. This leads to substantially accelerated variants, and also naturally makes them suitable preconditioners for GMRES. These new approaches are particularly efficient for closeby obstacles. Moreover, numerical experiments show that the number of iterations remains robust with respect to the wavenumber.
• A comparative analysis of different carbon cap policies on the economic lot-sizing problem with remanufacturing
  
  • Vallecilla Andrés
  • Dávila-Gálvez Sebastián
  • Quezada Franco
  International Journal of Production Research, Taylor & Francis, 2026. <div><p>This paper investigates the implementation of carbon cap policies within a remanufacturing production system, focusing on a single-item lot-sizing problem aimed at meeting the demand for end-of-life products under four distinct carbon cap policies. Our study, motivated by the operational dynamics of ECOCITEX, a Chilean textile remanufacturing company, explores the balance between operational costs, carbon emissions, and production levels in response to environmental policies. We introduce a mixed-integer linear programming (MILP) formulation to address economic lot-sizing with considerations for both remanufacturing and carbon emissions constraints. Through extensive computational experiments, we assess the impact of various carbon emissions policies on production and emissions levels and their associated costs, finding that global and rolling-horizon policies offer the best tradeoff between emission reductions and production cost increases. This leads to more environmentally friendly production policies for remanufactured products without compromising financial sustainability. The findings underscore the importance of flexibility in environmental policies for remanufacturing operations, suggesting that stringent carbon caps, while beneficial for emission reductions, may pose challenges to demand fulfillment and cost management. For managers, this highlights the critical need for adaptive policy frameworks that support sustainable production objectives without impeding operational efficiency.</p></div>