Publications

2026

• 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.
• 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.
• 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.
• 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} $v$.
• 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.
• 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>
• State-constrained optimal control on Wasserstein spaces over Riemannian manifolds
  
  • Treumún Ernesto
  • Zidani Hasnaa
  , 2026. We study a state-constrained optimal control problem in Mayer form on the Wasserstein space P 2 (M ) of a complete (possibly non-compact) Riemannian manifold M . The controlled dynamics is given by a nonlocal continuity equation, where the velocity field depends on both the space variable and the evolving probability measure. In the presence of state constraints, the associated value function may fail to be continuous, which prevents a direct characterization through Hamilton-Jacobi-Bellman equations (HJB). Following a level-set approach, we introduce an auxiliary value function defined on an extended space and prove that its zero-sublevel set recovers the epigraph of the original value function. Our main result shows that this auxiliary function is the unique viscosity solution of a suitable HJB equation on P 2 (M ). To prove uniqueness, we develop a comparison principle based on directional differentiability properties of the squared Wasserstein distance. These properties are shown to hold under a geometric assumption on the underlying manifold, satisfied in particular by Cartan-Hadamard manifolds and spaces with sectional curvature bounded from below. This extends previous results obtained in the unconstrained case and in Euclidean or compact settings to the state-constrained framework on general complete Riemannian manifolds.
• Fluid-structure Green's functions via BEM/BEM coupling for flow induced noise in arbitrary elastic geometries
  
  • Pacaut Louise
  • Chaillat Stéphanie
  • Mercier Jean-François
  • Serre Gilles
  , 2026. We address the challenge of efficiently simulating the noise generated by the interaction of a turbulent flow noise with complex elastic structures, a coupled fluid/structure interaction (FSI) problem. Current approaches typically separate vibro-acoustic and hydro-acoustic contributions, limiting the accuracy of hydrodynamic noise predictions. To overcome this limitation, we develop a numerical method for computing a Green's function tailored to the coupled FSI problem, enabling a monolithic prediction of the radiated noise without separating the two components. This approach not only improves the accuracy of hydrodynamic noise simulations but also significantly reduces computational costs. The Green's function is constructed using a novel integral formulation and solved numerically via a coupled fast BEM/ BEM solver.
• Stochastic Optimal Feedforward-Feedback Control for Partially Observable Sensorimotor Systems
  
  • Berret Bastien
  • Jean Frédéric
  , 2026. Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven feedback corrections to ensure stable behaviors. However, deriving a general continuous-time framework to determine such optimal control policies for partially observable, stochastic, nonlinear, and high-dimensional systems remains a formidable computational challenge. Here, we introduce a framework that extends neighboring optimal control by enabling the feedforward plan to explicitly account for feedback uncertainties and latencies. Using statistical linearization, we transform the stochastic problem into an approximately equivalent deterministic optimization within a tractable, augmented state space that retains critical nonlinearities, offering both mechanistic interpretability and theoretical guarantees on approximation fidelity. We apply this framework to human neuromechanics, demonstrating that muscle co-contraction emerges as an optimal adaptation to task demands, given the characteristics of our sensorimotor system. Our results provide a computational foundation for neuromotor control and a generalizable tool for the control of nonlinear stochastic systems.
• Metamaterials and Fluid Flows
  
  • Avallone Francesco
  • Bosia Federico
  • Chen Yi
  • Colombo Giada
  • Craster Richard
  • de Ponti Jacopo Maria
  • Fabbiane Nicolò
  • Haberman Michael
  • Hussein Mahmoud
  • Hwang Wontae
  • Iemma Umberto
  • Juhl Abigail
  • Kadic Muamer
  • Kotsonis Marios
  • Laude Vincent
  • Marquet Olivier
  • Mery Fabien
  • Michelis Theodoros
  • Nouh Mostafa
  • Ragni Daniele
  • Touboul Marie
  • Wegener Martin
  • Krushynska Anastasiia
  Nature Communications, Nature Publishing Group, 2026. (10.1038/s41467-026-70163-2)
  DOI : 10.1038/s41467-026-70163-2
• Dominance Properties for Fair Electricity Supply Planning in Collective Self-Consumption
  
  • Jorquera-Bravo Natalia
  • Elloumi Sourour
  • Kedad-Sidhoum Safia
  • Plateau Agnès
  , 2026. <div><p>This study addresses the problem of fair electricity supply planning within collective self-consumption communities, focusing on shared distributed energy sources and a common electricity storage system. The objective is to determine an electricity supply plan that ensures a fair allocation of shared resources. We formulate the electricity supply planning problem as a mixed integer linear programming (MILP) model, subsequently reformulated into a linear programming (LP) model thanks to some dominance properties. We then propose a series of fairness measures for the allocation of green electricity and shared economic benefits, including proportional allocation and max-min fairness. We prove that the dominance properties can be extended in most of these fairness models. We conduct numerical experiments based on a real case study, as well as on a set of generated instances. The results illustrate their impact on the use of green electricity produced, resource allocation, and participant costs. They also underscore the trade-offs between achieving fairness and maintaining operational efficiency, thereby offering insights for the fair management of energy resources in self-consumption communities.</p></div>
• On the Low Autocorrelation Binary Sequence Problem
  
  • Elloumi Sourour
  • Palagi Laura
  , 2026. On the Low Autocorrelation Binary Sequence Problem