Publications

2026

• Accelerating Nash learning from human feedback via Mirror Prox
  
  • Tiapkin Daniil
  • Calandriello Daniele
  • Belomestny Denis
  • Moulines Eric
  • Naumov Alexey
  • Rasul Kashif
  • Valko Michal
  • Ménard Pierre
  , 2025.
• Semi-discrete convergence analysis of a numerical method for waves in nearly-incompressible media with spectral finite elements
  
  • Ramiche Zineb
  • Imperiale Sébastien
  , 2026. In this work, we present a semi-discrete convergence analysis of a high-order space discretization approach for the computation of elastic field propagation in a nearly incompressible medium. Our approach relies on the use of high-order continuous spectral finite elements with mass-lumping. We present an approach that is valid for full hexahedral and quadrilateral meshes, where the elastic field is sought in the space of Q_k continuous finite elements and the pressure in Q_k-2 discontinuous finite elements. We further provide a proof of the inf-sup stability of the finite element discretization. This allows us to carry out error estimates for the semi-discrete problem in space, accounting in particular for quadrature errors.
• Nonparametric generative modeling for time series via Schrödinger bridge
  
  • Hamdouche Mohamed
  • Henry-Labordere Pierre
  • Pham Huyên
  , 2026. We propose a novel generative model for time series based on Schr\"odinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respec\-ting the temporal dynamics of the time series distribution. We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with autoregressive models, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal, temporal dependencies metrics, and predictive scores. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets.
• Autoregressive Multiplier Bootstrap for In-situ Error Estimation and Quality Monitoring of Finite Time Averages in Turbulent Flow Simulations
  
  • Papagiannis Christos
  • Balarac Guillaume
  • Congedo Pietro Marco
  • Le Maître Olivier P
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2026, 452, pp.118664. In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flows Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the methods applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness. (10.1016/j.cma.2025.118664)
  DOI : 10.1016/j.cma.2025.118664
• A stability result on optimal Skorokhod embedding
  
  • Guo Gaoyue
  , 2017. Motivated by the model- independent pricing of derivatives calibrated to the real market, we consider an optimization problem similar to the optimal Skorokhod embedding problem, where the embedded Brownian motion needs only to reproduce a finite number of prices of Vanilla options. We derive in this paper the corresponding dualities and the geometric characterization of optimizers. Then we show a stability result, i.e. when more and more Vanilla options are given, the optimization problem converges to an optimal Skorokhod embedding problem, which constitutes the basis of the numerical computation in practice. In addition, by means of different metrics on the space of probability measures, a convergence rate analysis is provided under suitable conditions.
• Constructive existence proofs and stability of stationary solutions to parabolic PDEs using Gegenbauer polynomials
  
  • Breden Maxime
  • Cadiot Matthieu
  • Zurek Antoine
  , 2026. In this paper, we present a computer-assisted framework for constructive proofs of existence for stationary solutions to one-dimensional parabolic PDEs and the rigorous determination of their linear stability. By expanding solutions in Gegenbauer polynomials, we first develop a general approach for boundary value problems (BVPs), corresponding to the stationary part of the PDE. This yields a computationally efficient sparse structure for both differential and multiplication operators. By deriving sharp, explicit and quantitative estimates for the inverse of differential operators, we implement a Newton-Kantorovich approach. Specifically, given a numerical approximation <span>u&#772;</span>, we prove the existence of a true stationary solution u within a small, rigorously quantified neighborhood of <span>u&#772;</span>. A key advantage of this approach is that the sharp control over the defect u -<span>u&#772;</span>, integrated with the spectral properties of the Gegenbauer basis, enables an accurate enclosure of the linearization's spectrum around u. This allows for a definitive conclusion regarding the (in)stability of the verified solution, which is the main contribution of the paper. We demonstrate the efficacy of this method through several applications, capturing both stable and unstable equilibrium states.
• Systematic modelling of a large-scaled, historicised, well-detailed building land-use, with the fusion of massive and heterogeneous datasets
  
  • Colomb Maxime
  • Perret Julien
  , 2026. Buildings are the primary venues for human activity. Generating precise numeric building models is of great interest for many applications. At regional and national scales, many different formalisms are employed to represent the various components of buildings, yet the building land-use is frequently oversimplified — even when mixed-use buildings are considered. Inferring a realistic building land-use, defined as an inventory of the distinct functional spaces hosted by a building, brings valuable knowledge for building models. Manual measurement can produce highly realistic interior models, but such approaches are labour-intensive and must be carried out case by case. We introduce a fully automated workflow that systematically simulates a well-described building land-use by integrating three complementary tasks: (1) usage-oriented building object modelling – defining building objects that capture building land-use, (2) activity census and conflation – aggregating and reconciling activity records from heterogeneous datasets, and (3) logical attribute generation – deriving detailed attributes for housing units and activities in relation to the characteristics of their host building and other environmental factors. The workflow adapts to varying levels of data availability and attribute richness, and it supports “recent-period” historicisation (i.e., reconstructing past states of the built environment). Because the entire pipeline is automated, it can be deployed at large scale; we demonstrate its application to an entire country. We evaluate the method through multiple validation procedures, including comparisons with ground-truth measurements, showing that the approach reliably reproduces building land-use.
• Young's law for a nonlocal isoperimetric model of charged capillarity droplets
  
  • Goldman Michael
  • Novaga Matteo
  • Prade Adriano
  , 2026. We study a variational problem modeling equilibrium configurations of charged liquid droplets resting on a surface under a convexity constraint. In the two-dimensional case with Coulomb interactions, we establish the validity of Young's law for the contact angle for small enough charges.
• Stability analysis and long-time convergence of a partial differential equation model of two-phase ageing
  
  • Breuil Luce
  , 2026. Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The model includes a coupling of both equations through birth and transition between phases and non-linearities due to competition. We show the existence, positivity and uniqueness of weak solutions in a general setting. For a simplified system of ordinary differential equations (ODE), we show existence and uniqueness of a strictly positive steady state attracting all trajectories. We study another simplification, a coupled PDE-ODE model, for which we prove existence, uniqueness and local asymptotic stability of a strictly positive steady state. Under further assumptions, but without assuming weak non-linearities, we show the global asymptotic stability of that steady state. The uniqueness of steady states and absence of oscillations in these systems show that the proportion of individuals in each phase at equilibrium is a unique feature of the model. This paves the way to ecological applications as the experimental measure of such a proportion could help gain some insight on the health of a wild population.
• Bayesian methods for the Calibration of two-phase flow models
  
  • Janati Idrissi Sanae
  , 2026. Accurate predictions of flows are essential for studying the behavior of coolant in nuclear reactors, under normal and accidental conditions. While physical experiments can be infeasible and expensive, simulations are a widely used alternative for a better understanding of the physical phenomena. However, numerical simulations are affected by multiple sources of uncertainty, including parameter uncertainty, model discrepancy and measurement error in the data used for validation. Consequently, the quantification of uncertainty in the models is an elementary step to improve the predictive capacity of the models.This thesis bridges Bayesian inference and simulations of two-phase flows, addressing the challenge of robust calibration under uncertainty of complex physical models, particularly in the presence of model discrepancy. When the model is misspecified, the results of calibration, prediction, and model selection are altered. The proposed framework is based on Bayesian calibration techniques with model discrepancy, and it is applied to calibrate the source terms in the all-regimes model by combining experimental data with simulations based on the industrial code Neptune CFD. Due to the high computational cost of the numerical code, a Gaussian Process surrogate model is used, and an adaptive strategy for improving the quality of the approximation is proposed. Furthermore, this work analyzes the outcomes of Bayesian model selection in the presence of model error and suggests a complementary diagnosis based on the posterior inferred discrepancy. The framework is used to compare the different models used for the source and sink terms in the interfacial area transport equation.
• Randomised study of human machine collaboration for cardiotocography interpretation during labour
  
  • Ben M’barek Imane
  • Ben M’barek Badr
  • Jauvion Grégoire
  • Whelehan Virginia
  • Papageorghiou Aris
  • Le Pennec Erwan
  • Stirnemann Julien
  npj Digital Medicine, Nature Research, 2026, 9 (1), pp.365. (10.1038/s41746-026-02556-y)
  DOI : 10.1038/s41746-026-02556-y
• An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle
  
  • Haegeman Ward
  • Orlando Giuseppe
  • Kokh Samuel
  • Massot Marc
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, 2026, 482 (2334), pp.20250835. We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action Principle framework. It is fully closed and introduces a new interfacial quantity, the interfacial work. The closures for the interfacial quantities are provided by the variational principle. They are physically sound and well-defined for all types of flow topologies. The model is shown to be hyperbolic, symmetrizable, and admits an entropy conservation law. Its non-conservative products yield uniquely defined jump conditions which are provided. As such, it allows for the proper treatment of weak solutions. In the multi-dimensional setting, the model presents lift forces which are discussed. The model constitutes a sound basis for future numerical simulations. (10.1098/rspa.2025.0835)
  DOI : 10.1098/rspa.2025.0835
• Nouveaux outils d’apprentissage statistiques pour l’imputation et le pronostic en conservation : Exploitation de la base NOIRœS dans le projet M(IA)²
  
  • ALAO AFOLABI Shadé
  • Hélou-de la Grandière Pauline
  • Ben Jelloul Marouane
  • Thoury Mathieu
  • Le Pennec Erwan
  • Cohen Serge X.
  , 2026.
• Nonnegativity certificates for finite semi-algebraic sets
  
  • Bender Matías R
  • Tsigaridas Elias
  • Zenkovich Alexander
  , 2026. <div><p>We introduce new certificates for nonnegativity of multivariate polynomials with rational coefficients over zero-dimensional semi-algebraic sets. They are perfectly complete, certifying every nonnegative polynomial, and perfectly sound, correctly identifying negativity. We rely on resultants computations and Rational Univariate Representations (RUR) and make no assumptions on the input.</p><p>For the univariate case, we introduce a perturbation technique that avoids root approximation and does not alter the (bit)size of the input. For multivariate polynomials, we make a reduction to the univariate case using RUR.</p><p>For the dense case, we compute a certificate in OB(d 4n+3 (d + τ )) bit operations; it involves numbers of bitsize O(d 3n+2 (d + τ )), where n is the number of variables, d the degree, and τ the maximum coefficient bitsize of the polynomials. For the sparse case, we provide the first sparse certificate based on the Newton polytope Q of the input polynomials. We compute in OB(vol(Q) 8 (n!) 8 2 5n+3 (n + τ )),</p><p>For semi-algebraic sets with s inequalities, we present two approaches. The first performs a reduction to the algebraic case and has complexity OB(2 (3ω+3)s d 5n τ ); it is purely algebraic approach and does not require root approximation. The second exploits approximate Lagrange interpolation and matches the O(sd 4n τ ) bitsize bounds of recent work by Baldi, Krick, and Mourrain [2] while improving complexity by orders of magnitude and removing all structural assumptions on the input.</p><p>Additionally, we provide a witness of negativity, ensuring that we either obtain a certificate or it does not exist.</p></div>
• Modeling the risks within the protocol Aave, with an application to portfolio allocation
  
  • Gobet Emmanuel
  • Latournerie Louis
  , 2026. Decentralized Finance (DeFi) lending and borrowing protocols enable investors to take leveraged long and short positions on digital assets without centralized intermediaries, but expose them to a distinctive form of risk: on-chain liquidation triggered by debt and collateral value fluctuations. In this work, we provide a detailed formalization of Aave's lending, borrowing, and liquidation mechanisms, grounded in the protocol's open-source implementation. In doing so, we propose a mathematical modeling of the risk of liquidation, including some stochastic approximations with the purpose of efficient analysis, with different applications. Among them, portfolio optimization problem.
• Fast, faithful and photorealistic diffusion-based image super-resolution with enhanced Flow Map models
  
  • Noble Maxence
  • Quintana Gonzalo Iñaki
  • Aubin Benjamin
  • Chadebec Clément
  , 2026. Diffusion-based image super-resolution (SR) has recently attracted significant attention by leveraging the expressive power of large pre-trained text-to-image diffusion models (DMs). A central practical challenge is resolving the trade-off between reconstruction faithfulness and photorealism. To address inference efficiency, many recent works have explored knowledge distillation strategies specifically tailored to SR, enabling one-step diffusion-based approaches. However, these teacher-student formulations are inherently constrained by information compression, which can degrade perceptual cues such as lifelike textures and depth of field, even with high overall perceptual quality. In parallel, self-distillation DMs, known as Flow Map models, have emerged as a promising alternative for image generation tasks, enabling fast inference while preserving the expressivity and training stability of standard DMs. Building on these developments, we propose FlowMapSR, a novel diffusion-based framework for image super-resolution explicitly designed for efficient inference. Beyond adapting Flow Map models to SR, we introduce two complementary enhancements: (i) positive-negative prompting guidance, based on a generalization of classifier free-guidance paradigm to Flow Map models, and (ii) adversarial fine-tuning using Low-Rank Adaptation (LoRA). Among the considered Flow Map formulations (Eulerian, Lagrangian, and Shortcut), we find that the Shortcut variant consistently achieves the best performance when combined with these enhancements. Extensive experiments show that FlowMapSR achieves a better balance between reconstruction faithfulness and photorealism than recent state-of-the-art methods for both x4 and x8 upscaling, while maintaining competitive inference time. Notably, a single model is used for both upscaling factors, without any scale-specific conditioning or degradation-guided mechanisms.
• Sampling from multi-modal distributions on Riemannian manifolds with training-free stochastic interpolants
  
  • Durmus Alain
  • Noble Maxence
  • Pellerin Thibaut
  , 2026. In this paper, we propose a general methodology for sampling from un-normalized densities defined on Riemannian manifolds, with a particular focus on multi-modal targets that remain challenging for existing sampling methods. Inspired by the framework of diffusion models developed for generative modeling, we introduce a sampling algorithm based on the simulation of a non-equilibrium deterministic dynamics that transports an easy-to-sample noise distribution toward the target. At the marginal level, the induced density path follows a prescribed stochastic interpolant between the noise and target distributions, specifically constructed to respect the underlying Riemannian geometry. In contrast to related generative modeling approaches that rely on machine learning, our method is entirely training-free. It instead builds on iterative posterior sampling procedures using only standard Monte Carlo techniques, thereby extending recent diffusion-based sampling methodologies beyond the Euclidean setting. We complement our approach with a rigorous theoretical analysis and demonstrate its effectiveness on a range of multi-modal sampling problems, including high-dimensional and heavy-tailed examples.
• Sparse recovery of Diffusion Dynamics: Handling High-Dimensionality in Repeated Short Trajectories
  
  • Bayraktar Elise
  • Dion-Blanc Charlotte
  , 2026. Viewed as systems of interacting particles, high-dimensional stochastic differential equations encode complex interaction structures within their drift component. We propose a novel approach to estimate this drift from independent high-frequency trajectory data observed over a short time horizon. Each trajectory is modelled as the solution of a Brownian-driven stochastic differential equation, while the number of time points within each path tends to infinity. We further assume that the drift function governing the dynamics can be expressed as a linear combination of a growing number of Lipschitz basis functions. To promote accurate recovery of the underlying dynamics under sparsity constraints, we propose a Lasso-regularised likelihood criterion. Under suitable regularity conditions, we establish convergence rates for the resulting estimator and emphasise how they depend on the dimensional parameters of the problem, in particular on the number of observed trajectories. We assess the performance of the estimator on synthetic datasets, both from an estimation and a generative perspective. Finally, we illustrate the practical relevance of the approach on a real-world climate dataset, highlighting its ability to perform variable selection.
• Robust a posteriori estimation of probit-lognormal seismic fragility curves via sequential design of experiments and constrained reference prior
  
  • Van Biesbroeck Antoine
  • Gauchy Clément
  • Feau Cyril
  • Garnier Josselin
  Nuclear Engineering and Design, Elsevier, 2026, 448, pp.114695. A seismic fragility curve expresses the probability of failure of a structure conditional to an intensity measure (IM) derived from seismic signals. When only limited data is available, the practitioner often refers to the probit-lognormal model coupled with maximum likelihood estimation (MLE) to obtain estimates of these curves. This means that only a binary indicator of the state (BIS) of the structure is known, namely a failure or non-failure state indicator, when it is subjected to a seismic signal with an intensity measure IM. In this context, the objective of this work is to propose a method for optimally estimating such curves by obtaining the most precise estimate possible with the minimum of data. The novelty of our work is twofold. First, we present and show how to mitigate the likelihood degeneracy problem which is ubiquitous with small data sets and hampers frequentist approaches such as MLE. Second, we propose a novel strategy for sequential design of experiments (DoE) that selects seismic signals from a large database of synthetic or real signals via their IM values, to be applied to structures to evaluate the corresponding BISs. This strategy relies on a criterion based on information theory in a Bayesian framework. It therefore aims to sequentially designate the IM value such that the pair (IM, BIS) has on average, with respect to the BIS of the structure, the greatest impact on the posterior distribution of the fragility curve. The methodology is applied to a case study from the nuclear industry. The results demonstrate its ability to efficiently and robustly estimate the fragility curve, and to avoid degeneracy even with a limited amount of data, i.e., less than 100. Furthermore, we demonstrate that the estimates quickly reach the model bias induced by the probit-lognormal modeling. Eventually, two criteria are suggested to help the user stop the DoE algorithm. (10.1016/j.nucengdes.2025.114695)
  DOI : 10.1016/j.nucengdes.2025.114695
• Bigraded Castelnuovo-Mumford regularity and Groebner bases
  
  • Bender Matías R
  • Busé Laurent
  • Checa Carles
  • Tsigaridas Elias
  Journal of Symbolic Computation, Elsevier, 2026, 133, pp.26. We study the relation between the bigraded Castelnuovo-Mumford regularity of a bihomogeneous ideal $I$ in the coordinate ring of the product of two projective spaces and the bidegrees of a Groebner basis of $I$ with respect to the degree reverse lexicographical monomial order in generic coordinates. For the single-graded case, Bayer and Stillman unraveled all aspects of this relationship forty years ago and these results led to complexity estimates for computations with Groebner bases. We build on this work to introduce a bounding region of the bidegrees of minimal generators of bihomogeneous Groebner bases for $I$. We also use this region to certify the presence of some minimal generators close to its boundary. Finally, we show that, up to a certain shift, this region is related to the bigraded Castelnuovo-Mumford regularity of $I$. (10.1016/j.jsc.2025.102487)
  DOI : 10.1016/j.jsc.2025.102487
• Asymptotic behavior of some stochastic models in population dynamics: a Hamilton-Jacobi approach
  
  • Jeddi Anouar
  , 2026. In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first, the case of critical or subcritical branching population processes in a regime combining a discretization of the trait space, small mutations, large time and large initial population size, where we are able to characterize using a Hamilton-Jacobi approach, the survival set of the population, and the asymptotic of the logarithmic scaling of subpopulation sizes. Second, we generalize by a direct method the convergence to the classical Hamilton-Jacobi equation obtained in the super-critical branching regime considered in [6] to a more general trait space and under weaker assumptions. Moreover, we establish that the stochastic and the deterministic dynamics are asymptotically equivalent in large population.
• samurai/ponio: two complementary software libraries for the efficient implementation of adaptive space/time numerical schemes
  
  • Dubois Sébastien
  • Gouarin Loïc
  • Hoffmann Alexandre
  • Massot Josselin
  • Massot Marc
  • Matalon Pierre
  • Series Laurent
  , 2026. We present two complementary open-source C ++ libraries for the numerical simulation of multiscale physical systems. samurai provides an efficient adaptive Cartesian meshing framework, while ponio offers a wide range of time-integration schemes for ordinary differential equations. Together, they enable the rapid implementation and testing of high-performance, adaptive space-time numerical methods for PDEs. Both libraries emphasize modularity, data locality, and modern C ++ design. Their capabilities are illustrated through applications developed during the Modeling Summer Visit 2025, including two-phase flows, rarefied gases, and reactive flows for aerospace applications relevant to NASA.
• A projection scheme for an incompressible soft material poromechanics model
  
  • Barré Mathieu
  • Grandmont Céline
  • Moireau Philippe
  IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2026. In this work, we propose and analyse a new scheme to discretize the linearized version of a rather general poromechanics model adapted to biological tissues perfusion. This model, which is related to – albeit different from – Biot equations, involves unsteady solid and fluid momentum balance equations that are further coupled through an incompressibility constraint, a pore pressure and permeability terms. The key feature of the scheme is to decouple the solid, fluid and pressure unknowns at each time step by means of a projection method, composed of a prediction and a correction step. We perform a complete stability analysis of the scheme depending on the implicit or explicit treatment of friction and pressure in the prediction step. Several boundary conditions are considered, including conditions coupling the solid and fluid phases on the boundary that are imposed at the discrete level using a Robin-Robin method. In the case of Dirichlet boundary conditions, we also provide a fully discrete error estimate as long as a discrete inf-sup condition is satisfied. The scheme properties and robustness with respect to physical parameters are illustrated by numerical experiments. Finally, its computational performance is compared with that of a monolithic approach.
• Validation du simulateur ICI de propagation d'épidémies à l'aide des données publiques recueillies pendant la première vague de la pandémie de COVID-19
  
  • Colomb Maxime
  • Talay Denis
  • Carneiro Viana Aline
  • Cormier Quentin
  • Garnier Josselin
  • Gilet Nicolas
  • Graham Carl
  • Grigori Laura
  • Perret Julien
  • Porcher Raphael
  • Ravaud Philippe
  • Stanica Razvan
  • Tomasevic Milica
  • Tran Viet-Thi
  , 2026. Ce rapport a pour premier objectif de présenter le simulateur ICI de propagation d'épidémies fondé sur des jumeaux numériques de territoires géographiques, de populations synthétiques statistiquement conformes aux populations réelles, et à la simulation numérique des agendas horaires et des interactions sociales des individus, ainsi que des contaminations entre individus. Par méthode de Monte-Carlo ICI fournit des informations statistiques précises, différenciées par zones géographiques et par catégories de population, sur les évolutions d'épidémies. Ces informations permettent de comparer quantitativement les impacts attendus de politiques sanitaires variées. Le second objectif est de dresser le bilan de nos tests sur la capacité d’ICI à reproduire quantitativement la dynamique épidémiologique et hospitalière observée lors de la première vague de Covid-19 à Paris, et d'analyser les capacités et les limites d'ICI pour des analyses contrefactuelles. Nos résultats montrent que d'ores et déjà ICI est un outil numérique opérationnel d'aide à la décision préalable aux interventions publiques contre les épidémies futures, prêt à être déployé sur des territoires multiples et pour des types variés d'épidémies.
• Learning with Locally Private Examples by Inverse Weierstrass Private Stochastic Gradient Descent
  
  • Dufraiche Jean
  • Mangold Paul
  • Perrot Michaël
  • Tommasi Marc
  , 2026. <div><p>Releasing data once and for all under noninteractive Local Differential Privacy (LDP) enables complete data reusability, but the resulting noise may create bias in subsequent analyses. In this work, we leverage the Weierstrass transform to characterize this bias in binary classification. We prove that inverting this transform leads to a biascorrection method to compute unbiased estimates of nonlinear functions on examples released under LDP. We then build a novel stochastic gradient descent algorithm called Inverse Weierstrass Private SGD (IWP-SGD). It converges to the true population risk minimizer at a rate of O(1/n), with n the number of examples. We empirically validate IWP-SGD on binary classification tasks using synthetic and real-world datasets.</p></div>