Publications

2025

• PhysioBlocks: an Opensource Python Library for Simulating Block Diagrams of Dynamical Physiological Systems
  
  • Chapelle Dominique
  • Drieu Colin
  • Kimmig François
  , 2025. The PhysioBlocks Python library is designed to simulate the dynamics of physiological systems (in particular cardiovascular systems) represented by block diagrams, in order to provide built-in modularity. Accordingly, a system is represented by a network of modules (blocks) connected by nodes in which they share quantities (degrees of freedom) and exchange fluxes. The user can easily create a new network by combining existing blocks. At a more advanced level, new blocks can be defined. The library is distributed under the LGPL-3.0-only license, and the initial distribution focuses on providing building blocks associated with lumped-parameter models of the cardiovascular system.
• A High-order Multi-scale Finite Element Method (MsFEM) for solving Oseen problems in heterogeneous media
  
  • Balazi Loïc
  • Omnes Pascal
  , 2025. An enriched non-conforming Multi-scale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media was proposed in [Q. Feng, G. Allaire, and P. Omnes, Multiscale Model. Simul., 20(1):462–492, 2022] and further studied in [L. Balazi, G. Allaire, and P. Omnes, preprint \url{https://hal.science/hal-05198860}, 2025]. The main feature of this MsFEM is the consideration of high-order sets of weighting functions: for the velocity, they are polynomials of order $n$ on the faces and of order $n-1$ in the volume of the elements; for the pressure they are polynomials of order $n$ in the element volume. The present paper proposes to extend this method to the Oseen problem in heterogeneous porous media. Through numerical simulations, specially for the case $n=2$, we show that the developed MsFEM is able to deal with high Reynolds numbers.
• Optimal control under unknown intensity with Bayesian learning
  
  • Baradel Nicolas
  • Cormier Quentin
  , 2024. We consider an optimal control problem inspired by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an uncertain parameter. Given a prior distribution for the unknown parameter, we describe its evolution according to Bayes' rule. We reformulate the optimization problem using Girsanov's theorem and establish a dynamic programming principle. Finally, we characterize the value function as the unique viscosity solution to a finite-dimensional Hamilton-Jacobi-Bellman equation, which can be solved numerically.
• Efficient Monte-Carlo sampling of metastable systems using non-local collective variable updates
  
  • Schönle Christoph
  • Carbone Davide
  • Gabrié Marylou
  • Lelièvre Tony
  • Stoltz Gabriel
  , 2025. Monte-Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several works. Here, we generalize these approaches and explicitly spell out an algorithm for non-linear CVs and underdamped Langevin dynamics. We prove reversibility of the resulting scheme and demonstrate its performance on several numerical examples, observing a substantial performance increase compared to methods based on overdamped Langevin dynamics as considered previously. Advances in generative machine-learning-based proposal samplers now enable efficient sampling in CV spaces of intermediate dimensionality (tens to hundreds of variables), and our results extend their applicability toward more realistic molecular systems.
• Hierarchical Reinforcement Learning for Large Scale Problems
  
  • Forghieri Orso
  , 2025. Cette thèse traite de la résolution de problèmes d’apprentissage par renforcement de grande dimension au moyen d’approches hiérarchiques, visant à réduire la complexité d’apprentissage et à améliorer l’interpretabilité des décisions.Dans un cadre discret, nous proposons d’abord une approche model-based : connaissant la dynamique du MDP, nous en extrayons une version abstraite raffinée par programmation dynamique approximée.Cette méthode permet une résolution rapide avec garanties théoriques et produit une représentation compacte du MDP par agrégation d’états similaires. L’abstraction est ajustée automatiquement par un processus de raffinement guidé par l’analyse des regroupements d’états, dont l’efficacité est démontrée sur des problèmes de grande taille et des cas réels.Nous étendons ensuite cette idée aux méthodes de différence temporelle via l’estimation d’intervalles de confiance, afin de construire des abstractions vérifiant des critères de précision avec haute probabilité. Cette approche améliore notablement l’efficacité d’échantillon du Q-Learning tout en conservant la convergence vers la politique optimale. Des comparaisons expérimentales confirment sa compétitivité face aux méthodes de référence.Enfin, nous appliquons l’apprentissage par renforce-ment profond à un problème de contrôle sur graphe issu du edge computing. En intégrant des connaissances a priori dans l’architecture de l’agent via le cadre des options, nous concevons un agent généralisable à des instances de plus grande échelle.Nous analysons aussi les performances pratiques de la programmation dynamique, montrant leur dépendance à la structure du MDP et identifiant un solveur Python performant sur une large gamme d’instances. (10.70675/a219f822z598cz4c3bz8ea5z1092e3db2513)
  DOI : 10.70675/a219f822z598cz4c3bz8ea5z1092e3db2513
• A framework for enhancing machine learning-based control of chemical processes : Addressing output constraints and multi-layer decision integration
  
  • Abou El Qassime Mehdi
  , 2025. Modern industrial and production systems, such as chemical, petrochemical and energy systems, are becoming increasingly complex in terms of i) scale: dozens/hundreds of units and components with complicated physical and functional interconnections and interdependencies), ii) integration of technologies from different fields.These complicated characteristics pose a major challenge to the development of efficient methods and tools for their optimal operation through classical approaches, typically based on the analytical or First Principle Models (FPM) of the system and on the expert knowledge of the operator.The goal of this Ph.D. is to provide a framework for the efficient development of methods based on AI and ML techniques, in particular Deep Learning, to improve decision-making in the control and monitoring of industrial processes.The proposal is articulated around three major research axes, in which significant advances are expectedi) surrogate modeling for explicit Model Predictive Control (MPC),ii) multivariate dynamic modeling and multilevel prediction. (10.70675/c7109a37zab18z48d3za358zb19cd26f609e)
  DOI : 10.70675/c7109a37zab18z48d3za358zb19cd26f609e
• Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk
  
  • de Crescenzo Anna
  • de Feo Filippo
  • Pham Huyên
  , 2025. We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new infinite-dimensional system of Riccati equations, for which we establish existence and uniqueness. To illustrate our results, we apply this framework to a systemic risk model involving heterogeneous banks, demonstrating the impact of agent heterogeneity on optimal risk mitigation strategies.
• Spatio-temporal equilibrium thermodynamics of guided optical waves at positive and negative temperatures
  
  • Zanaglia Lucas
  • Garnier Josselin
  • Michel Claire
  • Doya Valérie
  • Ferraro Mario
  • Wabnitz Stefan
  • Carusotto Iacopo
  • Picozzi Antonio
  , 2025. Optical thermalization has been recently studied theoretically and experimentally in the 2D spatial evolution of (quasi-)monochromatic light waves propagating in multimode fibers. In this work, we investigate the spatio-temporal equilibrium properties of incoherent multimode optical waves through the analysis of the (2+1)D Bose-Einstein thermal distribution and the corresponding classical Rayleigh-Jeans approximation. In the anomalous dispersion regime, the spatio-temporal equilibrium is characterized by positive temperatures. In this regime, we show that as the number of modes of the waveguide increases, the fundamental spatial mode becomes macroscopically populated, while its temporal spectrum undergoes significant narrowing, ultimately leading to complete (2+1)D spatio-temporal condensation in the thermodynamic limit. In the normal dispersion regime, the spatio-temporal equilibrium is characterized by negative temperature states that exhibit a hybrid character: the spatial equilibrium displays an inverted modal population, whereas the temporal spectrum remains peaked around the fundamental (carrier) optical frequency. In this regime, we predict that spatio-temporal light waves exhibit a phase transition to Bose-Einstein condensation at negative temperatures, which occurs by increasing the temperature above a negative critical value. Our work opens new avenues for future research, including the possibility for a dual spatio-temporal beam cleaning through full spatio-temporal light condensation, and lay the groundwork for the development of spatio-temporal optical thermodynamics. (10.48550/arXiv.2512.07784)
  DOI : 10.48550/arXiv.2512.07784
• Estimation of extreme quantile from heavy tailed distributions with neural networks
  
  • Girard Stéphane
  • Allouche Michaël
  • Gobet Emmanuel
  , 2025. We propose new parameterizations for neural networks in order to estimate extreme risk measures, such as conditional tail moments or extreme quantiles, in heavy-tailed settings. The proposed neural network estimator is able to extrapolate in the distribution tails thanks to an extension of the usual extreme-value second-order condition to an arbitrary order. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail.
• Constrained deep learning for pricing and hedging european options in incomplete markets
  
  • Baradel Nicolas
  , 2025. In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies that minimize the Profit and Loss (P&L) distribution around zero. We employ a single neural network to represent the option price function, with its gradient serving as the hedging strategy, optimized via a loss function enforcing the self-financing portfolio condition. A key challenge arises from the non-smooth nature of option payoffs (e.g., vanilla calls are non-differentiable atthe-money, while digital options are discontinuous), which conflicts with the inherent smoothness of standard neural networks. To address this, we compare unconstrained networks against constrained architectures that explicitly embed the terminal payoff condition, drawing inspiration from PDE-solving techniques. Our framework assumes two tradable assets: the underlying and a liquid call option capturing volatility dynamics. Numerical experiments evaluate the method on simple options with varying non-smoothness, the exotic Equinox option, and scenarios with market jumps for robustness. Results demonstrate superior P&L distributions, highlighting the efficacy of constrained networks in handling realistic payoffs. This work advances machine learning applications in quantitative finance by integrating boundary constraints, offering a practical tool for pricing and hedging in incomplete markets.
• Formalization of efficient polyhedral computations
  
  • Canu Quentin
  , 2025. The study of the complexity of the simplex algorithm is an open problem marked by several key events. The refutation of Hirsch conjecture, which sought to determine an upper bound on the number of pivots required to execute the simplex method, is one of them. However, this proof required a stage of numerical computations which, although feasible by hand, show that the need for a computer-certified calculation could be an asset in the search for other completeness results of the simplex algorithm.Proof assistants are the preferred tools for certifying programs and formalizing mathematics. They are based on programming languages that allow high-level data types to be defined, so that they can be manipulated to obtain proof terms. However, these same data types are inefficient when used for numerical computations. We prefer data types that are closer to machine representation. Solving the issue of numerical computations within proof assistants requires solving the problem of managing equivalence between these different representations of the same data.The aim of this thesis is to study the place of numerical computations within proof assistants, by implementing in Coq an algorithm for certifying the structure of a polytope, the geometric object underlying the execution of the simplex algorithm. By implementing two versions of this same algorithm, manipulating high-level data on the one hand and low-level data on the other, we set up a methodology for refining the data and proving equivalence between the two programs. The two versions are then proven to be equivalent using this methodology, and each serves its own purpose. The low-level version is run directly in Coq and therefore performs numerical computations. The high-level version is proved correct, and so its output value can be used as a hypothesis in writing other proofs. To illustrate how this works, we produce a formal proof of the refutation of Hirsch's conjecture, entrusting the computations to the low-level algorithm and interpreting the results obtained using the high-level algorithm.Nevertheless, the performance of the low-level algorithm, dedicated to numerical computations, suffers in comparison with informal solutions with the same aim. Another aim of this thesis work is to interpret and propose solutions to improve these performance results. We have identified that the arithmetic of the rationals constitutes a real limitation during the execution of the algorithm. We therefore propose a number of solutions aimed at limiting this impact, by means of finer control over the size of the coefficients computed or the size of the files manipulated. Our most promising solution aims to limit the number of operations on the rationals by imitating the lazy evaluation strategy, which performs a computation only when it has never been performed before. (10.70675/64aa4352z6772z4979zb41ez23f78ecd985a)
  DOI : 10.70675/64aa4352z6772z4979zb41ez23f78ecd985a
• Certificates for nonnegativity of multivariate integer polynomials under perturbations
  
  • Bender Matías R
  • Kozhasov Khazhgali
  • Tsigaridas Elias
  • Zhu Chaoping
  , 2025. We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions typically required by other approaches, namely that the polynomial attains its infimum and zero-dimensionality of the gradient ideal. Our approach combines a denominator-free stereographic transformation with a refined variant of the Hanzon–Jibetean perturbation scheme. The stereographic transformation preserves nonnegativity while making the polynomial coercive, with explicit bounds on the radius of positivity and on the nonzero critical values. Subsequently, we apply carefully constructed explicit perturbations that enforce zero-dimensionality of the gradient ideal without altering nonnegativity, allowing us to invoke recent algorithms to derive algebraic certificates or rational witness points. We present three algorithms implementing our framework and analyze their bit complexity in detail, which is single exponential with respect to the number of variables. A second contribution is a new explicit SOS perturbation scheme, which allows us to perturb any nonnegative polynomial in such a way that it can be written as a sum of squares (SOS). In contrast to Lasserre’s classical SOS approximation, which guaranties density but currently does not provide an effective control over the perturbation size, we only derive concrete perturbation bounds ensuring that a nonnegative polynomial enters the SOS cone.
• Duality between polyhedral approximation of value functions and optimal quantization of measures
  
  • Mehamdi Abdellah Bulaich
  • van Ackooij Wim
  • Brotcorne Luce
  • Gaubert Stéphane
  • Jacquet Quentin
  , 2025. Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse of dimensionality in optimal control to bi-level optimization. We establish a connection between this problem and the optimal quantization of a positive measure. Building on recent stability results in optimal transport, by Delalande and Mérigot, we deduce that the polyhedral approximation of a convex function is equivalent to the quantization of the Monge-Ampère measure of its Legendre-Fenchel dual. This duality motivates a simple greedy method for computing a parsimonious approximation of a polyhedral convex function, by clustering the vertices of a Newton polytope. We evaluate our algorithm on two applications: 1) A high-dimensional optimal control problem (quantum gate synthesis), leveraging McEneaney's max-plus-based curse-of-dimensionality attenuation method; 2) A bi-level optimization problem in electricity pricing. Numerical results demonstrate the efficiency of this approach.
• A generic framework to derive systems of conservation laws with source terms and its application to heat conduction in fluid flows: an alternative to the method of moments in kinetic theory of gases?
  
  • Haegeman Ward
  • Kokh Samuel
  • Massot Marc
  • Orlando Giuseppe
  ESAIM: Proceedings and Surveys, EDP Sciences, 2025, 78, pp.80-97. A generic framework to derive systems of conservation laws through the Stationary Action Principle is proposed. The equations are expressed in Eulerian coordinates while the variation of the action assumes an underlying Lagrangian description thus avoiding the need for any Lin constraint. The resulting models admit a supplementary conservation equation for the evolution of the Hamiltonian. We then use the newly developed framework to derive a hyperbolic model that includes heat conduction in the compressible fluid dynamics equations through the introduction of a new variable called the thermal impulse. The resulting model has already been obtained previously through the Stationary Action Principle but its derivation relied on several non-standard assumptions. Our new framework allows not only to lift these assumptions, but also to recover them as a consequence of the Stationary Action Principle. Finally, a comparison with a model including heat conduction derived through the kinetic theory of gases is conducted. (10.1051/proc/202578080)
  DOI : 10.1051/proc/202578080
• Smile dynamics, rough volatility, volatility with memory
  
  • Delemotte Jules
  , 2025. In this thesis we address the question of the static and dynamical properties of implied volatility surfaces of equity indices. In the first part, we focus on the at-the-money (ATM) skewterm-structure. We first underline the fact thatthe assumed power-law behavior with coefficient close to − 12 is only valid for maturities above acouple of months. Focusing on the short-termpart, we observe another power law behavior withs maller exponent close to −0.3 and we developa parametrization that embodies this new shape.In the second part we direct our efforts toward dynamical aspects through the Skew-StickinessRatio (SSR). This ratio links increments of theunderlying to increments of its implied volatil-ity. After recovering the empirical results already computed by Bergomi, we develop a new efficient estimator to compute the ATM SSR in models through finite differences. We find that rough and classical models studied generate close SSRs thatare significantly impacted by the non flat initialforward variance curve mandatory to fit marketdata. We also extend the work of Bergomi byderiving a first order expansion in small vol-of-vol of the ATM SSR in closed form. In the lastpart, we focus on the path properties of markets and models through the SPX-VIX joint calibration problem. Based on the observations of Guyonand Lekeufack, we design a Bergomi with memory model and look at how the path-dependent component of the volatility process helps to generate better SPX and VIX smiles simultaneously. We also present a new expansion in small vol-of-vol inthis type of model. (10.70675/6004c604z3067z42bez9d1dz176937bf1f6d)
  DOI : 10.70675/6004c604z3067z42bez9d1dz176937bf1f6d
• Continuity and approximability of competitive spectral radii
  
  • Akian Marianne
  • Gaubert Stéphane
  • Marchesini Loïc
  • Morris Ian
  , 2025. The competitive spectral radius extends the notion of joint spectral radius to the two-player case: two players alternatively select matrices in prescribed compact sets, resulting in an infinite matrix product; one player wishes to maximize the growth rate of this product, whereas the other player wishes to minimize it. We show that when the matrices represent linear operators preserving a cone and satisfying a "strict positivity" assumption, the competitive spectral radius depends continuously - and even in a Lipschitz-continuous way - on the matrix sets. Moreover, we show that the competive spectral radius can be approximated up to any accuracy. This relies on the solution of a discretized infinite dimensional non-linear eigenproblem. We illustrate the approach with an example of age-structured population dynamics.
• Towards Secure and Trustworthy Machine Learning : From Data Poisoning to Ownership Verification
  
  • Bouaziz Wassim
  , 2025. In order to build capable artificial intelligence systems, researchers and practitioners have relied on massive volumes of hard-to-curate data: billions of images, terabytes of text, decades of audio recordings. Collected from the web, this data are humanly impossible to assess in terms of e.g. quality, truthfulness, or relevance. Machine learning algorithms can extract subtle dependencies from it to solvemany tasks. These complex dependencies can notonly be hard to identify for a human but also difficult to extract and interpret from the model itself. This canlead to degenerated behaviors: relying on spurious correlations, exploiting loopholes in the training objective, or exhibiting unreliable patterns learned from the inexorable biases in the data. Several studies haveshown the possibility to strategically craft training datato covertly guide AI models towards such cases. Amalicious actor could thus manipulate data to cause an AI system make a biased decision (e.g. affect theoutcome of a loan application or a job recruitment),or to make it perform harmful actions (e.g. alter the trajectory of an autonomous vehicle). This not only represents a risk to the integrity and trustworthiness of machine learning systems, but also highlights theneed for tracking data provenance and for a better understandingof how algorithms learn from data. This thesis explore these questions across three axis.In a first part, we study the potential of data manipulationattacks and the robustness of machine learning algorithms against them. In a second part, we introducea novel method to track data usage in machine learning models in a privacy-preserving manner, and demonstrate its effectiveness for different modalities:images, audio, and textual data. In a third part, westudy how processing units emerge in neural networks and how training data can enforce their appearance.The contributions from this thesis shed light on the risks associated with the controllability of trainingdata, both in terms of potential attacks and the ability to track data usage. Ultimately, this work helps lay thegroundwork for AI that can scale without sacrificing safety, transparency, and purpose alignment. (10.70675/40ca82e7z4eb9z4bf3zaae6z2bad8b029427)
  DOI : 10.70675/40ca82e7z4eb9z4bf3zaae6z2bad8b029427
• Variational inference for approximate objective priors using neural networks
  
  • Baillie Nils
  • Van Biesbroeck Antoine
  • Gauchy Clément
  Computo, Société Française de Statistique, 2025. In Bayesian statistics, the choice of the prior can have an important influence on the posterior and the parameter estimation, especially when few data samples are available. To limit the added subjectivity from a priori information, one can use the framework of objective priors, more particularly, we focus on reference priors in this work. However, computing such priors is a difficult task in general. Hence, we consider cases where the reference prior simplifies to the Jeffreys prior. We develop in this paper a flexible algorithm based on variational inference which computes approximations of priors from a set of parametric distributions using neural networks. We also show that our algorithm can retrieve modified Jeffreys priors when constraints are specified in the optimization problem to ensure the solution is proper. We propose a simple method to recover a relevant approximation of the parametric posterior distribution using Markov Chain Monte Carlo (MCMC) methods even if the density function of the parametric prior is not known in general. Numerical experiments on several statistical models of increasing complexity are presented. We show the usefulness of this approach by recovering the target distribution. The performance of the algorithm is evaluated on both prior and posterior distributions, jointly using variational inference and MCMC sampling. (10.57750/76fh-t442)
  DOI : 10.57750/76fh-t442
• Do sufficiency consumption changes drive emissions down? A production network approach
  
  • Escribe Célia
  • Quirion Philippe
  Journal of Environmental Economics and Management, Elsevier, 2025, 136, pp.103258. Energy efficiency and decarbonized energy sources are essential yet insufficient for meeting ambitious climate change mitigation goals. Sufficiency strategies, which involve reducing consumption and shifting to less environmentally impactful lifestyles, are increasingly recognized as crucial for decarbonization. However, their wider economic implications remain underexplored. This paper develops a static macroeconomic model with a detailed microeconomic production framework to analyze these implications. We derive comparative statics to unravel three primary propagation channels for consumption changes: direct demand effects, price effects, and substitution effects, based on the production network structure and elasticities of substitution. Using multi-regional input-output data, we assess the impacts of two sufficiency-driven consumption changes: adopting a vegetarian diet and reducing energy use. Our findings reveal significant rebound effects, up to 38% for domestic emissions and 60% for global emissions (accounting for carbon leakage), compared to estimates excluding behavioral aspects. Rebound effects from sufficiency strategies are smaller than those from energy efficiency improvements. Alternatively, conceptualizing sufficiency as increased leisure time preference results in reduced rebound effects and negative carbon leakage. (10.1016/j.jeem.2025.103258)
  DOI : 10.1016/j.jeem.2025.103258
• Equality of tropical rank and dimension for tropical linear series
  
  • Amini Omid
  • Gaubert Stéphane
  • Gierczak Lucas
  , 2024. The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically independent elements within the semimodule, this quantity has remained elusive due to the challenges of computing it in practice. In this note, we establish that the tropical rank is, in fact, precisely equal to the topological dimension of the semimodule, one more than the dimension of the associated linear system of divisors. Moreover, we show that the equality of divisorial and tropical ranks in the definition of tropical linear series is equivalent to the pure dimensionality of the corresponding linear system. We conclude with several complementary results and questions on combinatorial, topological, and computability properties of the tropical rank.
• Quantitative rigidity of the Wasserstein contraction under convolution
  
  • Fathi Max
  • Goldman Michael
  • Tsodyks Daniel
  , 2025. <div><p>The aim of this paper is to investigate the contraction properties of p-Wasserstein distances with respect to convolution in Euclidean spaces both qualitatively and quantitatively. We connect this question to the question of uniform convexity of the Kantorovich functional on which there was substantial recent progress (mostly for p = 2 and partially for p &gt; 1). Motivated by this connection we extend these uniform convexity results to the case p = 1, which is of independent interest.</p></div>
• Preconditioned Langevin Dynamics with Score-based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
  
  • Baldassari Lorenzo
  • Garnier Josselin
  • Sølna Knut
  • de Hoop Maarten V.
  , 2025. Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite‑dimensional function spaces – where such problems are naturally formulated – is crucial to ensure stability and convergence as the discretization of the underlying problem is refined. In this paper, we contribute to this line of work by analyzing a widely used sampler for linear inverse problems: Langevin dynamics driven by score‑based generative models (SGMs) acting as priors, formulated directly in function space. Building on the theoretical framework for SGMs in Hilbert spaces, we give a rigorous definition of this sampler in the infinite-dimensional setting and derive, for the first time, error estimates that explicitly depend on the approximation error of the score. As a consequence, we obtain sufficient conditions for global convergence in Kullback–Leibler divergence on the underlying function space. Preventing numerical instabilities requires preconditioning of the Langevin algorithm and we prove the existence and form of an optimal preconditioner. The preconditioner depends on both the score error and the forward operator and guarantees a uniform convergence rate across all posterior modes. Our analysis applies to both Gaussian and a general class of non‑Gaussian priors. Finally, we present examples that illustrate and validate our theoretical findings.
• Efficient multi-fidelity Gaussian process regression for noisy outputs and non-nested experimental designs
  
  • Baillie Nils
  • Kerleguer Baptiste
  • Feau Cyril
  • Garnier Josselin
  , 2025. This paper presents a multi-fidelity Gaussian process surrogate modeling that generalizes the recursive formulation of the auto-regressive model when the high-fidelity and low-fidelity data sets are noisy and not necessarily nested. The estimation of high-fidelity parameters by the EM (expectation-maximization) algorithm is shown to be still possible in this context and a closed-form update formula is derived when the scaling factor is a parametric linear predictor function. This yields a decoupled optimization strategy for the parameter selection that is more efficient and scalable than the direct maximum likelihood maximization. The proposed approach is compared to other multi-fidelity models, and benchmarks for different application cases of increasing complexity are provided.
• A holographic non-uniqueness for the Helmholtz equation
  
  • Novikov Roman
  • Sivkin Vladimir
  , 2025. We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in $\mathbb{R}^d$ , $d \geq 2$, outside the origin. We consider a sphere $S$ centered at the origin in $\mathbb{R}^d$ . We show that the radiation solution on $S$ is not uniquely determined by the intensity of the total solution on $S$. Extensions of this result to the case of other surfaces in place of $S$ are also mentioned. Our construction involves and develops technique of scattering on obstacles with Dirichlet boundary condition.
• Tight analyses of first-order methods with error feedback
  
  • Thomsen Daniel Berg
  • Taylor Adrien
  • Dieuleveut Aymeric
  , 2025. Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To counteract the degradation in convergence associated with compressed communication, error feedback schemes -- most notably $\mathrm{EF}$ and $\mathrm{EF}^{21}$ -- were introduced. In this work, we provide a tight analysis of both of these methods. Specifically, we find the Lyapunov function that yields the best possible convergence rate for each method -- with matching lower bounds. This principled approach yields sharp performance guarantees and enables a rigorous, apples-to-apples comparison between $\mathrm{EF}$, $\mathrm{EF}^{21}$, and compressed gradient descent. Our analysis is carried out in the simplified single-agent setting, which allows for clean theoretical insights and fair comparison of the underlying mechanisms. (10.48550/arXiv.2506.05271)
  DOI : 10.48550/arXiv.2506.05271