Publications

2025

• Meta-modelling paths of simple climate models using Neural Networks and Dirichlet polynomials: An application to DICE
  
  • Gobet Emmanuel
  • Liu Yushan
  • Vermandel Gauthier
  , 2025. Our study focuses on climate models extensively employed in climate science and climate-economy research, which project temperature outcomes from carbon emission trajectories. Addressing the need for rapid evaluation in Integrated Assessment Models (IAMs) -- critical tools for carbon emission mitigation policy analysis -- we design a neural network (NN) meta-model as an efficient surrogate for mapping, in an infinite horizon setting, emission trajectories into temperature trajectories (usually modeled as coupled systems of differential equations). Our approach combines a projection on Generalized Dirichlet polynomials, whose coefficients are inputs of the NN and a suitable time change for handling infinite horizon: we prove that the quantity of interest is, under some assumptions, a smooth function of the inputs and therefore, is prone to accurate NN approximation. After a training with augmented Shared Socioeconomic Pathway scenarios, the NN achieves high-fidelity approximations of the original climate model. Additionally, we establish theoretical accuracy guarantees for both the encoding and neural network approximation. Our numerical experiments demonstrate the framework's accuracy, and computational efficiency is improved by a factor of 100 in comparison to traditional ODE solvers. As an application to Actuarial Sciences, we illustrate the use of the metamodel to quantify the distribution of future scorching days.
• Fredholm Approach to Nonlinear Propagator Models
  
  • Abi Jaber Eduardo
  • Bondi Alessandro
  • de Carvalho Nathan
  • Neuman Eyal
  • Tuschmann Sturmius
  , 2025. We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution strategies under exponential and power-law decay.
• The Volterra Stein-Stein model with stochastic interest rates
  
  • Abi Jaber Eduardo
  • Hainaut Donatien
  • Motte Edouard
  , 2025. <div><p>We introduce the Volterra Stein-Stein model with stochastic interest rates, where both volatility and interest rates are driven by correlated Gaussian Volterra processes. This framework unifies various wellknown Markovian and non-Markovian models while preserving analytical tractability for pricing and hedging financial derivatives. We derive explicit formulas for pricing zero-coupon bond and interest rate cap or floor, along with a semi-explicit expression for the characteristic function of the log-forward index using Fredholm resolvents and determinants. This allows for fast and efficient derivative pricing and calibration via Fourier methods. We calibrate our model to market data and observe that our framework is flexible enough to capture key empirical features, such as the humped-shaped term structure of ATM implied volatilities for cap options and the concave ATM implied volatility skew term structure (in loglog scale) of the S&amp;P 500 options. Finally, we establish connections between our characteristic function formula and expressions that depend on infinite-dimensional Riccati equations, thereby making the link with conventional linear-quadratic models.</p></div>
• Complex discontinuities of the square root of Fredholm determinants in the Volterra Stein-Stein model
  
  • Abi Jaber Eduardo
  • Guellil Maxime
  , 2025. <div><p>Fourier-based methods are central to option pricing and hedging when the Fourier–Laplace transform of the log-price and integrated variance is available semi-explicitly. This is the case for the Volterra Stein–Stein stochastic volatility model, where the characteristic function is known analytically. However, naive evaluation of this formula can produce discontinuities due to the complex square root of a Fredholm determinant, particularly when the determinant crosses the negative real axis, leading to severe numerical instabilities. We analyze this phenomenon by characterizing the determinant’s crossing behavior for the joint Fourier–Laplace transform of integrated variance and log-price. We then derive an expression for the transform to account for such crossings and develop efficient algorithms to detect and handle them. Applied to Fourier-based pricing in the rough Stein–Stein model, our approach significantly improves accuracy while drastically reducing computational cost relative to existing methods.</p></div>
• On the strong law of large numbers and Llog L condition for supercritical general branching processes
  
  • Bansaye Vincent
  • Berah Tresnia
  • Cloez Bertrand
  , 2025. We consider branching processes for structured populations: each individual is characterized by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may survive and grow and the trait distribution converges. The branching process is then expected to be driven by the positive triplet of first eigenvalue problem of the first moment semigroup. Under the assumption of convergence of the renormalized semigroup in weighted total variation norm, we prove strong convergence of the normalized empirical measure and non-degeneracy of the limiting martingale. Convergence is obtained under an Llog L condition which provides a Kesten-Stigum result in infinite dimension and relaxes the uniform convergence assumption of the renormalized first moment semigroup required in the work of Asmussen and Hering in 1976. The techniques of proofs combine families of martingales and contraction of semigroups and the truncation procedure of Asmussen and Hering. We also obtain L^1 convergence of the renormalized empirical measure and contribute to unifying different results in the literature. These results greatly extend the class of examples where a law of large numbers applies, as we illustrate it with absorbed branching diffusion, the house of cards model and some growth-fragmentation processes.
• Sufficient dimension reduction for regression with spatially correlated errors: application to prediction
  
  • Forzani Liliana
  • Arancibia Rodrigo García
  • Gieco Antonella
  • Llop Pamela
  • Yao Anne-Françoise
  , 2025. In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension reduction (SDR) paradigm, which reduces the predictor space while retaining relevant information about the response. To achieve this, we impose two different spatial models on the inverse regression: the separable spatial covariance model (SSCM) and the spatial autoregressive error model (SEM). For these models, we derive maximum likelihood estimators for the reduction and use them to predict the response via nonparametric rules for forward regression. Through simulations and real data applications, we demonstrate the effectiveness of our approach for spatial data prediction. (10.48550/arXiv.2502.02781)
  DOI : 10.48550/arXiv.2502.02781
• Interior Point Methods Are Not Worse than Simplex
  
  • Allamigeon Xavier
  • Dadush Daniel
  • Loho Georg
  • Natura Bento
  • Végh László
  SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2025, 54 (5), pp.FOCS22-178-FOCS22-264. (10.1137/23M1554588)
  DOI : 10.1137/23M1554588
• Ancestral lineages and sampling in populations with density-dependent interactions
  
  • Kubasch Madeleine
  , 2025. We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. First, using an appropriate change in probability, we exhibit a time-inhomogeneous Markov process, the auxiliary process, which allows to capture the behavior of a sampled lineage in the population process. This is achieved through a many-to-one formula, which relates the average of a function over ancestral lineages sampled in the population processes to its average over the auxiliary process, yielding a direct interpretation of the underlying survivorship bias. In addition, this construction allows for more general sampling procedures than what was previously obtained in the literature, such as sampling restricted to subpopulations. Second, we consider the large population regime, when the population size grows to infinity. Under classical assumptions, the population type distribution can then be approached by a diffusion approximation, which captures the fluctuations of the population process around its deterministic large population limit. We establish a many-to-one formula allowing to sample in the diffusion approximation, and quantify the associated approximation error.
• Applications of new boundary conditions for the Boltzmann equation derived from a kinetic model of gas-surface interaction
  
  • Kosuge Shingo
  • Aoki Kazuo
  • Giovangigli Vincent
  • Golse François
  , 2024. Recently, new models of the boundary condition for the Boltzmann equation were proposed on the basis of a kinetic model of gas-surface interactions [K. Aoki et.al., Phys. Rev. E 106(3), 035306 (2022)]. In the present paper, the kernel representations of the models are given, and the models are applied to some basic problems of a rarefied gas between two parallel plates. To be more specific, the heat-transfer between the plates with different temperatures, plane Couette flow, and plane Poiseuille flow driven by an external force are numerically investigated by using the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the new models of the boundary condition. The results are compared with those based on the conventional Maxwell-type boundary conditions.
• Wave dispersion and bifurcation analyses of eikonal gradient-enhanced isotropic damage models
  
  • Ribeiro Nogueira Breno
  • Rastiello Giuseppe
  • Giry Cédric
  • Gatuingt Fabrice
  European Journal of Mechanics - A/Solids, Elsevier, 2025, pp.105643. (10.1016/j.euromechsol.2025.105643)
  DOI : 10.1016/j.euromechsol.2025.105643
• A two spaces extension of Cauchy-Lipschitz Theorem
  
  • Bertucci Charles
  • Lions Pierre-Louis
  Journal of Differential Equations, Elsevier, 2025, 421, pp.524-530. We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider ẋ = f (x, x) for a function f : V × E → E where E is a Banach space and V → E a normed vector space. This structure allows us to distinguish between the two dependencies of f in x and allows to generalize classical results. We also prove a similar results for partial differential equations. (10.1016/j.jde.2024.12.031)
  DOI : 10.1016/j.jde.2024.12.031
• Open Problem: Two Riddles in Heavy-Ball Dynamics
  
  • Goujaud Baptiste
  • Taylor Adrien
  • Dieuleveut Aymeric
  , 2025. This short paper presents two open problems on the widely used Polyak's Heavy-Ball algorithm. The first problem is the method's ability to exactly \textit{accelerate} in dimension one exactly. The second question regards the behavior of the method for parameters for which it seems that neither a Lyapunov nor a cycle exists. For both problems, we provide a detailed description of the problem and elements of an answer.
• CoHiRF: A Scalable and Interpretable Clustering Framework for High-Dimensional Data
  
  • Belucci Bruno
  • Lounici Karim
  • Meziani Katia
  , 2025. Clustering high-dimensional data poses significant challenges due to the curse of dimensionality, scalability issues, and the presence of noisy and irrelevant features. We propose Consensus Hierarchical Random Feature (CoHiRF), a novel clustering method designed to address these challenges effectively. CoHiRF leverages random feature selection to mitigate noise and dimensionality effects, repeatedly applies K-Means clustering in reduced feature spaces, and combines results through a unanimous consensus criterion. This iterative approach constructs a cluster assignment matrix, where each row records the cluster assignments of a sample across repetitions, enabling the identification of stable clusters by comparing identical rows. Clusters are organized hierarchically, enabling the interpretation of the hierarchy to gain insights into the dataset. CoHiRF is computationally efficient with a running time comparable to K-Means, scalable to massive datasets, and exhibits robust performance against state-of-the-art methods such as SC-SRGF, HDBSCAN, and OPTICS. Experimental results on synthetic and real-world datasets confirm the method's ability to reveal meaningful patterns while maintaining scalability, making it a powerful tool for high-dimensional data analysis.
• An inverse problem in cell dynamics: Recovering an initial distribution of telomere lengths from measurements of senescence times
  
  • Olayé Jules
  , 2025. Telomeres are repetitive sequences situated at both ends of the chromosomes of eukaryotic cells. At each cell division, they are eroded until they reach a critical length that triggers a state in which the cell stops to divide: the senescent state. In this work, we are interested in the link between the initial distribution of telomere lengths and the distribution of senescence times. We propose a method to retrieve the initial distribution of telomere lengths, using only measurements of senescence times. Our approach relies on approximating our models with transport equations, which provide natural estimators for the initial telomere lengths distribution. We investigate this method from a theoretical point of view by providing bounds on the errors of our estimators, pointwise and in all Lebesgue spaces. We also illustrate it with estimations on simulations, and discuss its limitations related to the curse of dimensionality.
• Stochastic Tangential Pareto Dynamics Provably Samples the Whole Pareto Set
  
  • Jones Zachary
  • Congedo Pietro Marco
  • Le Maitre Olivier
  , 2025. The framework of stochastic multi-objective programming allows for the inclusion of uncertainties in multi-objective optimization problems at the cost of transforming the set of objectives into a set of expectations of random quantities. The stochastic multigradient descent algorithm (SMGDA) gives a solution to these types of problems using only noisy gradient information. However, a bias in the algorithm causes it to converge to only a subset of the whole Pareto front, limiting its use. We analyze the source of this bias and prove the convergence of SMGDA to a stationary point in the nonconvex L-lipschitz smooth case. First, based on this analysis, we propose to reduce the bias of the stochastic multi-gradient calculation using an exponential smoothing technique. We then propose a novel approach to exploring the whole Pareto set by combining the debiased stochastic multigradient with an additive non-vanishing noise that guides the dynamics of the iterates tangential to the Pareto set. We finish by proving that our algorithm, Stochastic Tangential Pareto Dynamics (STPD), generates samples concentrated on the whole Pareto set.
• Discrete Markov Probabilistic Models
  
  • Pham Le-Tuyet-Nhi
  • Shariatian Dario
  • Ocello Antonio
  • Conforti Giovanni
  • Durmus Alain
  , 2025. This paper introduces the Discrete Markov Probabilistic Model (DMPM), a novel algorithm for discrete data generation. The algorithm operates in the space of bits {0, 1} d , where the noising process is a continuous-time Markov chain that can be sampled exactly via a Poissonian clock that flips labels uniformly at random. The time-reversal process, like the forward noise process, is a jump process, with its intensity governed by a discrete analogue of the classical score function. Crucially, this intensity is proven to be the conditional expectation of a function of the forward process, strengthening its theoretical alignment with score-based generative models while ensuring robustness and efficiency. We further establish convergence bounds for the algorithm under minimal assumptions and demonstrate its effectiveness through experiments on low-dimensional Bernoulli-distributed datasets and high-dimensional binary MNIST data. The results highlight its strong performance in generating discrete structures. This work bridges theoretical foundations and practical applications, advancing the development of effective and theoretically grounded discrete generative modeling.
• The N-link model for slender rods in a viscous fluid: well-posedness and convergence to classical elastohydrodynamics equations
  
  • Alouges François
  • Lefebvre-Lepot Aline
  • Levillain Jessie
  • Moreau Clément
  , 2025. Flexible fibers at the microscopic scale, such as flagella and cilia, play essential roles in biological and synthetic systems. The dynamics of these slender filaments in viscous flows involve intricate interactions between their mechanical properties and hydrodynamic drag. In this paper, considering a 1D, planar, inextensible Euler-Bernoulli rod in a viscous fluid modeled by Resistive Force Theory, we establish the existence and uniqueness of solutions for the $N$-link model, a mechanical model, designed to approximate the continuous filament with rigid segments. Then, we prove the convergence of the $N$-link model's solutions towards the solutions to classical elastohydrodynamics equations of a flexible slender rod. This provides an existence result for the limit model, comparable to those by Mori and Ohm [Nonlinearity, 2023], in a different functional context and with different methods. Due to its mechanical foundation, the discrete system satisfies an energy dissipation law, which serves as one of the main ingredients in our proofs. Our results provide mathematical validation for the discretization strategy that consists in approximating a continuous filament by the mechanical $N$-link model, which does not correspond to a classical approximation of the underlying PDE.
• A Surrogate Modelling Approach Based on Anti-Resonance Properties for FRF Prediction of Uncertain Dynamical Systems
  
  • Denimal Goy Enora
  , 2025, pp.81 - 92. Quantifying uncertainties of dynamical responses is crucial for the design of robust mechanical structures. Computing the Frequency Response Function (FRF) is a classical tool in this context. So far, basic approaches to propagateuncertainties have led to poor prediction accuracy due to convergence issues around the peaks. Some previous works proposed numerical strategies to deal with this limitations for small systems and in specific cases. The present work proposed a new approach based on resonance and antiresonance properties to split the FRF in different sections, a surrogate can then be constructed on each section leading to better performances than classical strategies. The methodology is illustrated on a 2 dof academic system. (10.13052/97887-438-0148-1)
  DOI : 10.13052/97887-438-0148-1
• Topology Optimization of Isolated Response Curves in 3D Geometrically-nonlinear Beam
  
  • Denimal Goy Enora
  • Shen Yichang
  • Fruchard Samuel
  • Mélot Adrien
  • Renson Ludovic
  , 2025, pp.81 - 92. Topology optimisation is a powerful tool for designing efficient and light structures. However, classical topology optimisation methods (SIMP, LSF), which are gradient-based, are not adapted to deal with nonlinear vibrations in the context of geometrical nonlinearities as the simulation of such systems is computationally expensive, and the strong nonlinearbehaviour makes the objective function non-convex with many local minima. The present work investigates the potential of using global optimisation methods to topology optimise those structures. To provide more robust nonlinear features in the optimisation, the bifurcations are directly tracked and optimised. The strategy is applied to a 3D finite element model of a beam (10.13052/97887-438-0146-7)
  DOI : 10.13052/97887-438-0146-7
• Classical Myelo-Proliferative Neoplasms emergence and development based on real life incidence and mathematical modeling
  
  • Baranda Ana Fernández
  • Bansaye Vincent
  • Lauret Evelyne
  • Mounier Morgane
  • Ugo Valérie
  • Meleard Sylvie
  • Giraudier Stéphane
  , 2024. Mathematical modeling offers the opportunity to test hypothesis concerning Myeloproliferative emergence and development. We tested different mathematical models based on a training cohort (n=264 patients) (Registre de la côte d'Or) to determine the emergence and evolution times before JAK2V617F classical Myeloproliferative disorders (respectively Polycythemia Vera and Essential Thrombocytemia) are diagnosed. We dissected the time before diagnosis as two main periods: the time from embryonic development for the JAK2V617F mutation to occur, not disappear and enter in proliferation, and a second time corresponding to the expansion of the clonal population until diagnosis. We demonstrate using progressively complexified models that the rate of active mutation occurrence is not constant and doesn't just rely on individual variability, but rather increases with age and takes a median time of 63.1+/-13 years. A contrario, the expansion time can be considered as constant: 8.8 years once the mutation has emerged. Results were validated in an external cohort (national FIMBANK Cohort, n=1248 patients). Analyzing JAK2V617F Essential Thrombocytema versus Polycythemia Vera, we noticed that the first period of time (rate of active homozygous mutation occurrence) for PV takes approximatively 1.5 years more than for ET to develop when the expansion time was quasi-similar. In conclusion, our multi-step approach and the ultimate time-dependent model of MPN emergence and development demonstrates that the emergence of a JAK2V617F mutation should be linked to an aging mechanism, and indicates a 8-9 years period of time to develop a full MPN. (10.48550/arXiv.2406.06765)
  DOI : 10.48550/arXiv.2406.06765
• Convergence of a discrete selection-mutation model with exponentially decaying mutation kernel to a Hamilton-Jacobi equation
  
  • Jeddi Anouar
  , 2024. In this paper we derive a Hamilton-Jacobi equation with obstacle from a discrete linear integro-differential model in population dynamics, with exponentially decaying mutation kernel. The fact that the kernel has exponential decay leads to a modification of the classical Hamilton-Jacobi equation obtained previously from continuous models in \cite{BMP}. We consider a population parameterized by a scaling parameter $K$ and composed of individuals characterized by a quantitative trait, subject to selection and mutation. In the regime of large population $K\rightarrow +\infty,$ small mutations and large time we prove that the WKB transformation of the density converges to the unique viscosity solution of a Hamilton-Jacobi equation with obstacle. (10.48550/arXiv.2412.06657)
  DOI : 10.48550/arXiv.2412.06657
• Constrained non-linear estimation and links with stochastic filtering
  
  • Chaintron Louis-Pierre
  • Mertz Laurent
  • Moireau Philippe
  • Zidani Hasnaa
  , 2025. This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the estimation problem is a viscosity solution of a Hamilton Jacobi Bellman equation whose sub and super solutions have different Neumann type boundary conditions. This intricacy arises from the non-reversibility in time of the non-smooth dynamics, and hinders the derivation of a comparison principle and the uniqueness of the solution in general. Nonetheless, we identify conditions on the drift (including zero drift) coefficient in the non-smooth dynamics that make such a derivation possible. On the other hand, we show in a general situation that the value function appears in the small noise limit of the corresponding stochastic filtering problem by establishing a large deviation result. We also give quantitative approximation results when replacing the non-smooth dynamics with a smooth penalised one.
• Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics
  
  • Durmus Alain
  • Enfroy Aurélien
  • Moulines Éric
  • Stoltz Gabriel
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2025, 61 (1). We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to approximatively sample from a target distribution of interest. We show first that, for a very large class of schemes, a minorization condition uniform in the stepsize holds. This class encompasses popular methods such as the Euler-Maruyama scheme and the schemes based on splitting strategies. Second, we provide mild conditions ensuring that the class of schemes that we consider satisfies a geometric Foster--Lyapunov drift condition, again uniform in the stepsize. This allows us to derive geometric convergence bounds, with a convergence rate scaling linearly with the stepsize. This kind of result is of prime interest to obtain estimates on norms of solutions to Poisson equations associated with a given numerical method. (10.1214/23-AIHP1442)
  DOI : 10.1214/23-AIHP1442
• Learning extreme Expected Shortfall and Conditional Tail Moments with neural networks. Application to cryptocurrency data
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  Neural Networks, Elsevier, 2025, 182, pp.106903. We propose a neural networks method to estimate extreme Expected Shortfall, and even more generally, extreme conditional tail moments as functions of confidence levels, in heavy-tailed settings. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established leveraging extreme-value theory (in particular the high-order condition on the distribution tails) and using critically two activation functions (eLU and ReLU) for neural networks. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors using synthetic heavy-tailed data. The experiments reveal that our method largely outperforms others. In addition, the selection of the anchor point appears to be much easier and stabler than for other methods. Finally, the neural network estimator is tested on real data related to extreme loss returns in cryptocurrencies: here again, the accuracy obtained by cross-validation is excellent, and is much better compared with competitors. (10.1016/j.neunet.2024.106903)
  DOI : 10.1016/j.neunet.2024.106903
• Annealed limit for a diffusive disordered mean-field model with random jumps
  
  • Erny Xavier
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2025, 61 (1), pp.510-532. We study a sequence of $N-$particle mean-field systems, each driven by $N$ simple point processes $Z^{N,i}$ in a random environment. Each $Z^{N,i}$ has the same intensity $(f(X^N_{t-}))_t$ and at every jump time of $Z^{N,i},$ the process $X^N$ does a jump of height $U_i/\sqrt{N}$ where the $U_i$ are disordered centered random variables attached to each particle. We prove the convergence in distribution of $X^N$ to some limit process $\bar X$ that is solution to an SDE with a random environment given by a Gaussian variable, with a convergence speed for the finite-dimensional distributions. This Gaussian variable is created by a CLT as the limit of the patial sums of the $U_i.$ To prove this result, we use a coupling for the classical CLT relying on the result of [Koml\'os, Major and Tusn\'ady (1976)], that allows to compare the conditional distributions of $X^N$ and $\bar X$ given the random environment, with the same Markovian technics as the ones used in [Erny, L\"ocherbach and Loukianova (2022)]. (10.1214/23-AIHP1432)
  DOI : 10.1214/23-AIHP1432