Publications

2026

• Stochastic-structural modelling of particle-laden turbulent flows based on wavelet reconstruction
  
  • Morhain Clément
  • Letournel Roxane
  • Massot Marc
  • Vié Aymeric
  Computers and Fluids, Elsevier, 2026. Reduced-order modelling and simulation of turbulent particle-laden flows is required in numerous configurations, where the resolution of the whole spectrum of turbulent scales through DNS is out of reach. Whereas structural or stochastic models have been derived in order to provide a synthetic turbulent model for the non-resolved scales of the fluid flow field, reproducing particle dynamics is challenging because it requires capturing both spatial and temporal correlations. We present a reduced-order framework that combines wavelet-based structural modelling with stochastic evolution. Using compactly supported divergence-free wavelets within a multiresolution analysis, the method provides direct control over spatial structures and correlations of synthetic multiscale incompressible velocity fields. In contrast to Fourier modes, the wavelet basis functions are localized in space and spectrally non-sharp in Fourier space, and spread over a range of wavenumbers, which requires a dedicated procedure to enforce a prescribed turbulent energy spectrum. The stochastic evolution of wavelet coefficients further ensures consistent temporal correlations. The proposed framework is evaluated in homogeneous isotropic turbulence under a fully reduced setting, where all turbulent scales must be provided by the model. When coupled to a disperse phase in the one-way coupled framework, results show that it reproduces particle preferential concentration across a wide range of Stokes numbers as well as the pair-dispersion regimes, achieving similar agreement with DNS data as for classical Fourier-based Kinematic Simulation. This establishes a physically consistent turbulence model, which combines structural fidelity with stochastic dynamics, providing an alternative framework for synthetic turbulence modelling and investigating particle–turbulence interactions resolution.
• A two-scale two-phase flow model for the separate-to-disperse phase transition in atomizing flows
  
  • Haegeman Ward
  • Orlando Giuseppe
  • Kokh Samuel
  • Massot Marc
  , 2026. An original two-scale, isothermal compressible two-phase flow model with surface tension is presented. The model allows for a unified description of the separate interface and disperse phase regimes. The inter-scale mass transfer terms, activated when the local curvatures exceed a physical and grid-independent length threshold, allow for the transition from the former regime, to the latter, through atomization. This mass transfer process is obtained through a pressure relaxation towards a modified Laplace law such that local curvatures do not exceed the prescribed threshold. It leads to a local and dissipative regularization of the large-scale interface, while retaining a sub-scale representation of the small-scale flow features. The backbone of the model is derived through the use of Hamilton's Stationary Action Principle. The source terms are derived such that the inter-scale mass transfer is dissipative for the extended thermodynamics, which includes the surface energies at both scales. The methodology that is developed allows for the derivation of a thermodynamically consistent model which admits a supplementary conservation law for the entropy and real characteristics.
• Fourier-Laplace Transforms of the Brownian Signature via Riccati Equations on the Tensor Algebra
  
  • Abi Jaber Eduardo
  • Attal Elie
  • Sotnikov Dimitri
  , 2026. We establish an infinite-dimensional affine transform theory for the time-augmented Brownian signature. Our first main result shows that, for a suitable class of linear functions of the signature, the conditional Fourier-Laplace transform admits an entire signature expansion. We prove that the associated coefficients solve an infinite-dimensional linear differential equation on the extended tensor algebra. Our second main result shows that the logarithm admits a local signature expansion whose coefficients satisfy a Riccati equation on the extended tensor algebra, revealing a generalized affine structure of the Brownian signature in a genuinely path-dependent setting. In contrast to conventional affine processes, we show that this representation is intrinsically local: zeros of the Fourier-Laplace transform in the complex plane prevent any global expansion. To recover global representations, we introduce a new class of randomized Riccati equations with path-dependent terminal conditions through a recentering argument. Furthermore, we establish uniqueness of solutions to the linear and Riccati equations within a suitable class of solutions. Our results provide a theoretical framework for transform methods in non-Markovian settings, with applications to the computation of conditional distributions.
• Rémy's diffusion on Brownian trees
  
  • Curien Nicolas
  • Marzouk Cyril
  , 2026. Rémy's algorithm is a famous recursive construction of uniform random binary trees of growing size by a local grafting operation. In this work we construct a continuous version, a new local diffusion on the space of real trees of growing Brownian Continuum Random Trees (CRT's). It appears as the scaling limit of a variant of Rémy's algorithm due to Bacher, Bodini, and Jacquot. Once the trees are rescaled to have constant mass, this diffusion uncovers an ergodic dynamics on trees with the Brownian CRT as unique invariant law.
• Wiring the Fly Brain into a Hierarchical World Model A self-supervised JEPA world model of a complete connectome Team Piaget
  
  • Thil Lucas
  • Nowak Assis Daniel
  • Berthier Louis
  • Jlidi Adam
  , 2026. World models predict the future of an environment in an abstract latent space, the kind of prediction a brain is thought to perform. We ask whether such a model can learn the dynamics of a real brain rather than a metaphor for one. We take the FlyWire connectome of the adult Drosophila, the only animal whose brain is fully mapped (∼139,000 neurons, ∼50M synapses), turn it into a spiking brain model embodied in a physics simulation of the fly's body, and let it act in a closed sensorimotor loop. On the resulting whole-brain spike trains we train a hierarchy of region-level world models (Joint-Embedding Predictive Architectures, JEPAs), one per brain region, coupled along the connectome's own sensory → integration → motor flow. To our knowledge this is the first JEPA world model of a complete brain. We report three findings: the motor (descending) pathway behaves as a genuine world model, forecasting its own activity and linearly decoding real motor commands; the extreme sparsity of spike codes induces a characteristic latent collapse, diagnosable by participation ratio, which a connectome-derived encoder helps counteract; and coupling regions along the connectome's feedforward structure measurably improves prediction, with the gain growing over longer horizons. The brain's wiring does not merely inspire the architecture, it improves the model of the world.
• Nonequilibrium and multiscale fluids: Models and approximations
  
  • Pichard Teddy
  , 2026.
• Optimized high-order IMEX-RK schemes for degenerate diffusion-reaction problems with application to travelling waves phenomena
  
  • Antonietti Paola F.
  • Corti Mattia
  • Orlando Giuseppe
  , 2026. We study a class of IMplicit-EXplicit Runge--Kutta (IMEX-RK) schemes for the numerical approximation of reaction and diffusion-reaction problems arising in a variety of biological and physical applications. Such models may admit travelling wave solutions, with the Fisher--Kolmogorov equation representing a prototypical example. Motivated by this feature, the proposed time integration schemes are designed to accurately capture sharp propagating fronts. We also investigate a less standard use of IMEX-RK methods that circumvents a splitting of reaction terms into linear and nonlinear components, while still requiring the solution of linear systems at each stage. This semi-implicit formulation, referred to as SI-IMEX-RK, enables a targeted treatment of stiffness by isolating its relevant contributions. The time discretization is coupled with a high-order polygonal discontinuous Galerkin method for space discretization, resulting in a flexible and robust framework for the treatment of multiscale dynamics in complex geometries. A comprehensive validation strategy is presented to assess the accuracy and stability properties of the proposed schemes across a hierarchy of increasingly challenging test problems.
• Mean field games with incomplete information
  
  • Bertucci Charles
  , 2026. This paper is concerned with mean field games in which the players do not know the repartition of the other players. First a case in which the players do not gain information is studied. Results of existence and uniqueness are proved and discussed. Then, a case in which the players observe the payments is investigated. A master equation is derived and partial results of uniqueness are given for this more involved case.
• Entropic Mirror Monte Carlo
  
  • Cherradi Anas
  • Janati Yazid
  • Durmus Alain
  • Le Corff Sylvain
  • Petetin Yohan
  • Stoehr Julien
  , 2026. Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.
• 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.
• 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.
• On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplers
  
  • Durmus Alain
  • Gruffaz Samuel
  • Kailas Miika
  • Saksman Eero
  • Vihola Matti
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2026, 36 (3). There is substantial empirical evidence about the success of dynamic implementations of Hamiltonian Monte Carlo (HMC), such as the No U-Turn Sampler (NUTS), in many challenging inference problems but theoretical results about their behavior are scarce. The aim of this paper is to fill this gap. More precisely, we consider a general class of MCMC algorithms we call dynamic HMC. We show that this general framework encompasses NUTS as a particular case, implying the invariance of the target distribution as a by-product. Second, we establish conditions under which NUTS is irreducible and aperiodic and as a corrolary ergodic. Under conditions similar to the ones existing for HMC, we also show that NUTS is geometrically ergodic. Finally, we improve existing convergence results for HMC showing that this method is ergodic without any boundedness condition on the stepsize and the number of leapfrog steps, in the case where the target is a perturbation of a Gaussian distribution. (10.1214/25-AAP2269)
  DOI : 10.1214/25-AAP2269
• The Mortensen observer on the space of probability measures
  
  • Morange Martin
  , 2026. We study a deterministic filtering problem formulated directly on the Wasserstein space of probability measures with finite second moment. Motivated by the Mortensen minimum-energy observer, we consider the reconstruction of an evolving probability density from partial observations by minimizing an action functional combining a kinetic transport cost and a time-dependent observation mismatch. The resulting value function is defined on the infinite-dimensional manifold (P_2(R^d), W_2) and satisfies a Hamilton-Jacobi-Bellman equation involving the Wasserstein gradient. Under suitable regularity and growth assumptions on the observation functional, we establish dynamic programming principles, continuity of the value function, existence of minimizing trajectories, and viscosity solution properties of the associated Hamilton-Jacobi equation. We provide two complementary notions of viscosity solutions: a geometric formulation based on subdifferentials in Wasserstein space, and a Hilbertian formulation inspired by Lions' lifting approach. This allows us to prove a comparison principle and uniqueness of solutions. Extensions to transport equations with drift are also discussed. Finally, we introduce a semi-Lagrangian scheme in order to approximate the value function, and show Γ-convergence of the scheme.
• The Wasserstein cost of importance sampling
  
  • Coste Simon
  • Goldman Michael
  , 2026. Importance sampling (IS) consists in biasing samples from a distribution $f$ towards another distribution $g$. Concretely, given samples $X_i$ from $f$, the IS measure is $$\hat{g}_n = \frac{1}{Z_n}\sum_{i=1}^n \frac{g(X_i)}{f(X_i)} \delta_{X_i},$$ with $Z_n = \sum_{i=1}^n \frac{g(X_i)}{f(X_i)}$. The random measure $\hat{g}_n$ approximates $g$, and is used in many contexts ranging from Monte Carlo integration to Bayesian inference. We show that, in high dimension ($d \geqslant 3$), the Wasserstein cost $W_p^p(\hat{g}_n, g)$ has order $n^{-p/d}$ in expectation, i.e. $$\beta^{\mathrm{low}}_{p,d}\int gf^{-p/d}\leqslant \liminf_{n \to \infty} n^{p/d} \mathbb{E}[W_p^p(\hat{g}_n, g)] \leqslant \limsup_{n \to \infty} n^{p/d} \mathbb{E}[W_p^p(\hat{g}_n, g)] \leqslant\beta_{p,d} \int g f^{-p/d}$$ where $\beta^{\mathrm{low}}_{p,d}\leqslant \beta_{p,d}$ are constants depending only on $p$ and $d$, which are equal for $p=2$ and conjectured to be equal for any $p\geqslant 1$. Our results are valid for all $p\geqslant 1$ and $d\geqslant 3$. In the case where $\beta^{\mathrm{low}}_{p,d}= \beta_{p,d}$, we show that the asymptotically optimal sampling distribution $f^*$ for importance sampling is not equal to $g$ but to a tempered version of $g$, namely $f^* \propto g^{d/(p+d)}$, which is reminiscent of Zador’s theorem in the domain of measure quantization.
• Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
  
  • Matalon Pierre
  • Spillane Nicole
  , 2026. The convergence of the GMRES linear solver is notoriously hard to predict. A particularly enlightening result by [Greenbaum, Pták, Strakoš, 1996] is that, given any convergence curve, one can build a linear system for which GMRES realizes that convergence curve. What is even more extraordinary is that the eigenvalues of the problem matrix can be chosen arbitrarily. We build upon this idea to derive novel results about weighted GMRES. We prove that for any linear system and any prescribed convergence curve, there exists a weight matrix M for which weighted GMRES (i.e. GMRES in the inner product induced by M ) realizes that convergence curve, and we characterize the form of M . Additionally, we exhibit a necessary and sufficient condition on M for the simultaneous prescription of two convergence curves, one realized by GMRES in the Euclidean inner product, and the other in the inner product induced by M . These results are then applied to infer some properties of preconditioned GMRES when the preconditioner is applied either on the left or on the right. For instance, we show that any two convergence curves are simultaneously possible for left and right preconditioned GMRES.
• Comparison Between Effective and Individual Growth Rates in a Heterogeneous Population
  
  • Doumic Marie
  • Rat Anaïs
  • Tournus Magali
  Royal Society Open Science, The Royal Society, 2026, 13 (5), pp.251119. Is there an advantage to heterogeneity in a population where individuals grow and divide by fission? This is a broad question, to which there is no easy universal answer. This article aims to provide a quantitative answer in the specific context of growth rate heterogeneity by comparing the fitness of homogeneous versus heterogeneous populations. We focus on size-structured populations, where the growth rate of each individual is set at birth by heredity and/or random mutations. The fitness (or Malthus parameter, or effective fitness) of such heterogeneous population is defined by its long-term behaviour, and we introduce the effective growth rate as the individual growth rate in the homogeneous population with the same fitness. We derive analytical formulae linking effective and individual growth rates in two paradigmatic cases: first, constant growth and division rates, second, linear growth rates and uniform fragmentation. Surprisingly, these two cases yield similar expressions. Then, by comparing the fitness and the effective growth rates of populations with different degrees of heterogeneity or different laws of heredity/mutation to those of average homogeneous populations, we quantitatively investigate the combined influence of heredity and heterogeneity, and revisit previous results stating that heterogeneity is beneficial in the case of strong heredity. (10.1098/rsos.251119)
  DOI : 10.1098/rsos.251119
• Volterra clocks and their pure-jump limits: hitting times of curved boundaries
  
  • Abi Jaber Eduardo
  • Attal Elie
  • Søjmark Andreas
  , 2026. We introduce a class of continuous Volterra processes, called Volterra clocks, and study their singular limit as the memory kernel collapses to a Dirac mass at zero. The dynamics are parametrised by a function f acting as a nonlinear time- change, generalising the Volterra square-root process and recovering it when f is affine. In the singular limit, the continuous Volterra clock converges weakly to a pure-jump process given by first passage times of a Brownian motion to curved boundaries, including affine and square-root boundaries when f is, respectively, affine or quadratic. Outside the affine setting, characteristic function methods are no longer available, and we instead identify the limit directly from the dynamics. We do this through a topological framework adapted to the time-change structure which involves Skorokhod’s M1 topology and a decorated notion of convergence. Our analysis unifies several regimes of interest for general Volterra clocks, including large-time asymptotics, fast mean reversion, and hyper-roughness. In particular, this subsumes and extends existing results in the affine setting.
• Assessing Per-Sample Membership Inference Vulnerability without Retraining
  
  • Dorseuil Valentin
  • Atif Jamal
  • Cappé Olivier
  , 2026. Recent work in the privacy literature shows that sample-targeted membership inference attacks (MIAs) significantly outperform untargeted approaches by a wide margin. Motivated by this observation, we address the following question: can the privacy vulnerability of individual training points be assessed without training shadow models? We show that per-sample exposure to MIA is governed not only by a point's loss, but also by a data-dependent geometric measure. In the linear setting, we derive a closed-form decomposition of individual black-box MIA vulnerability into a population leverage score and a residual loss term, making explicit how sample-dependent geometry translates into privacy exposure. Since the final layer of most modern architectures is linear, we extend this framework to deep networks and propose a surrogate score operating on last-layer representations that requires only a single trained model and no shadow models. Empirical evaluations across diverse datasets and architectures show that our score outperforms loss and gradient-norm baselines at identifying the highest-risk points under state-of-the-art attacks, providing a computationally efficient and theoretically grounded tool for per-sample privacy risk assessment.
• High-order adaptive discontinuous finite elements for the shallow water equations with sub-grid irregular bathymetry
  
  • Arpaia Luca
  • Orlando Giuseppe
  • Ferrarin Christian
  • Bonaventura Luca
  , 2026. We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number of mathematical properties specific to the proposed method that is well-balanced, mass-conserving and positivity-preserving under a mild CFL condition also in the presence of wet-dry fronts. The method includes a consistent conservative discretization for passive tracers. We use 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 adaptive strategies which are tested in a coastal environment. Idealized test cases show the robustness in presence of irregular bathymetries also with under-resolved features at the grid scale. A benchmark with realistic bathymetry and a complex domain shows the potential of the proposed discretization for adaptive simulations of coastal flows.
• Erratum for Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models
  
  • Giovangigli Vincent
  • Nabet Flore
  , 2023. An inaccurate assumption has been identified in Vincent Giovangigli, Yoann Le Calvez and Flore Nabet ``Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models'', J.~Math.~Fluid Dyn., Volume 25, 82, (2023),https://doi.org/10.1007/s00021-023-00825-4 and is corrected here.
• Certified Per-Instance Unlearning Using Individual Sensitivity Bounds
  
  • Benarroch Hanna
  • Atif Jamal
  • Cappé Olivier
  , 2026. Certified machine unlearning can be achieved via noise injection leading to differential privacy guarantees, where noise is calibrated to worst-case sensitivity. Such conservative calibration often results in performance degradation, limiting practical applicability. In this work, we investigate an alternative approach based on adaptive per-instance noise calibration tailored to the individual contribution of each data point to the learned solution. This raises the following challenge: how can one establish formal unlearning guarantees when the mechanism depends on the specific point to be removed? To define individual data point sensitivities in noisy gradient dynamics, we consider the use of per-instance differential privacy. For ridge regression trained via Langevin dynamics, we derive high-probability per-instance sensitivity bounds, yielding certified unlearning with substantially less noise injection. We corroborate our theoretical findings through experiments in linear settings and provide further empirical evidence on the relevance of the approach in deep learning settings.
• Métamodélisation par processus gaussiens de l'analyse vibratoire de rotors sous incertitudes et analyse de sensibilité aux paramètres
  
  • Dehillerin Erwan
  • Denimal Goy Enora
  • Sinou Jean-Jacques
  , 2026. La connaissance précise des vitesses critiques de la dynamique d’un rotor est cruciale afin de prévenir ses déformations et son endommagement. Or ces grandeurs dépendent de différents paramètres, eux-mêmes sujets à des incertitudes. Ce travail cherche ainsi à étudier les propriétés dynamiques d’un rotor dont les incertitudes portent sur les paramètres de conception. Une métamodélisation par processus gaussiens permet de comprendre la propagation des incertitudes en dimension élevée et aboutit à une étude de sensibilité qui classe et catégorise les influences des paramètres.
• Optimisation topologique robuste avec microstructure incertaine pour la fabrication additive métallique
  
  • Masson Hugo
  • Denimal Goy Enora
  • Peigney Michael
  • Renson Ludovic
  , 2026, pp.8 p.. Ce travail propose de prendre en compte la variabilité de microstructure observée en fabrication additive métallique à travers un modèle matériau simple et incertain. Ce modèle est intégré à une optimisation topologique par densité, pour une minimisation de souplesse. Les incertitudes son propagées par quadrature de Gauss. La méthode réduit la variabilité de performance des formes optimisées, même dans le cas de propriétés matériaux réalistes. Des premiers résultats sur un cas industriel d’aube en 3D sont présentés.
• Development of a 2D test bench for characterising the dynamic mechanical response of a solid rocket propellant under rapid depressurisation
  
  • Distelzwey Léo
  • Levard Quentin
  • François Laurent
  • Voreux Olivier
  , 2026. The ignition of a solid rocket propellant is a critical moment during which the material is subjected to a rapid and large variation in chamber pressure. This occurs especially when the operculum sealing the throat is blown off as the pressure rises. Depending on the internal geometry, the ensuing pressure drop can sometimes cause rapid deformation of the propellant. In this paper we present the development of an experimental setup dedicated to the study of the 2D dynamic response of a solid propellant to propagating pressure waves. The experiment is first intended to assess whether the propellant’s response can be measured using various diagnostic techniques. The rectangular (parallelepiped‑shaped) chamber is slowly filled with air until the operculum bursts, causing the rapid depressurisation of the chamber. The resulting pressure wave travels through the chamber, impinging a specific shape of the propellant load, and induces oscillation as the wave reflects off the walls. The results show that the propellant obstacle, made of a conventional AP/HTPB research composition, oscillates in response to the pressure excitation as well as its internal mechanical forces. The test campaign is carried out at various pressure levels by adjusting the operculum thickness and involves complementary measurement techniques, such as pressure sensors that allow us to track the wave travelling through the chamber, while strain gauges measure the deformation directly on the propellant obstacle. Specific optical diagnostics (digital image correlation and point-tracking) are performed through side‑mounted windows. The setup and the measurement methods give very promising results for the characterisation of the dynamic behaviour of solid propellants during ignition, offering useful data for the development of mechanical models of the solid propellant. (10.60711/SPC2026.20260603.225861734990091247)
  DOI : 10.60711/SPC2026.20260603.225861734990091247
• Méthode de méta-modélisation par décomposition de domaines et processus Gaussiens pour la prédiction de fonctions de réponse en fréquences de structures incertaines
  
  • Denimal Goy Enora
  , 2026. L’utilisation de méthodes de méta-modélisation est une stratégie classique pour limiter le coût numérique associé aux études de propagation d’incertitudes. Une quantité d’intérêt classique pour les systèmes dynamiques est la Fonction de Réponse en Fréquence (FRF). Ce travail présente une stratégie de méta-modélisation basée sur de la décomposition de domaines, en exploitant les phénomènes de résonance et anti-résonance, et des processus Gaussiens pour pouvoir construire efficacement un méta- modèle de FRF. Les résultats sont illustrés sur un modèle éléments finis de poutre.