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Sont listées ci-dessous, par année, les publications figurant dans l'archive ouverte HAL.

2026

A fictitious domain method with enhanced interfacial mass conservation for immersed FSI with thin-walled solids
- Corti Daniele
- Diaz Jérôme
- Vidrascu Marina
- Chapelle Dominique
- Moireau Philippe
- Fernández Miguel Angel
Journal of Computational Physics, Elsevier, 2026, 556, pp.114754. In this paper, we extend the low-order fictitious domain method with enhanced mass conservation, introduced in [ESAIM: Math. Model. Numer. Anal., 58(1):303--333, 2024], to fluid-structure interaction with immersed thin-walled solids. The key idea is to improve mass conservation across the interface by imposing a single global velocity constraint on one side of the interface using a scalar Lagrange multiplier. Both 2D and 3D shell models are considered for the description of the solid, including contact between solids. For both models, the interface coupling is enforced on the mid-surface of the shell using a stabilized Lagrange multiplier formulation. Numerical examples in two and three dimensions illustrate the effectiveness of the proposed method, including its successful application to the simulation of aortic heart valve dynamics. (10.1016/j.jcp.2026.114754)
DOI : 10.1016/j.jcp.2026.114754
Asymptotic approaches in inverse problems for depolymerization estimation
- Doumic Marie
- Moireau Philippe
Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2026, 20, pp.105-155. Depolymerization reactions constitute frequent experiments, for instance in biochemistry for the study of amyloid fibrils. The quantities experimentally observed are related to the time dynamics of a quantity averaged over all polymer sizes, such as the total polymerised mass or the mean size of particles. The question analysed here is to link this measurement to the initial size distribution. To do so, we first derive, from the initial reaction system<p>two asymptotic models: at first order, a backward transport equation, and at second order, an advection-diffusion/Fokker-Planck equation complemented with a mixed boundary condition at x = 0. We estimate their distance to the original system solution. We then turn to the inverse problem, i.e., how to estimate the initial size distribution from the time measurement of an average quantity, given by a moment of the solution. This question has been already studied for the first order asymptotic model, and we analyse here the second order asymptotic. Thanks to Carleman inequalities and to log-convexity estimates, we prove observability results and error estimates for a Tikhonov regularization.</p><p>We then develop a Kalman-based observer approach, and implement it on simulated observations. Despite its severely ill-posed character, the secondorder approach appears numerically more accurate than the first-order one.</p> (10.3934/ipi.2025020)
DOI : 10.3934/ipi.2025020
Entropic Mirror Monte Carlo
- Cherradi Anas
- Janati Yazid
- Durmus Alain
- Le Corff Sylvain
- Petetin Yohan
- Stoehr Julien
, 2026. Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.
A 3D-shell model of left atrial electromechanics
- Ruz Oscar
- Brito-Pacheco Carlos
- Vidrascu Marina
- Chapelle Dominique
- Fernández Miguel Angel
, 2026. The thin-walled nature of the atrial myocardium can lead to artificial stiffening when full 3D electromechanical models are discretized using standard finite elements. In this work, we propose an electromechanical model of the left atrium based on a 3D-shell formulation that overcomes these limitations. The model incorporates both passive and active components of atrial tissue mechanics, while atrioventricular interaction is described by the coupling with a 0D electromechanical model of the left ventricle. The proposed approach is assessed under physiological and pathological conditions and systematically compared with the standard full 3D formulation. The results demonstrate the superior robustness and computational efficiency of the proposed 3D-shell electromechanical model.
Synchronous vs Asynchronous Active Learning
- Binois Mickael
- Le Riche Rodolphe
, 2026. These slides are a short class summarizing the main result in synchronous and asynchronous optimization. The material covers batch acquisition criteria, their theoretical step-ahead pendants, and the asynchronous versions.
A benchmark of expert-level academic questions to assess AI capabilities
- Phan Long
- Gatti Alice
- Han Ziwen
- Li Nathaniel
- Hu Josephina
- Zhang Hugh
- Shi Sean
- Choi Michael
- Agrawal Anish
- Chopra Arnav
- Khoja Adam
- Kim Ryan
- Hausenloy Jason
- Zhang Oliver
- Mazeika Mantas
- Anderson Daron
- Nguyen Tung
- Mahmood Mobeen
- Feng Fiona
- Feng Steven Y.
- Zhao Haoran
- Yu Michael
- Gangal Varun
- Zou Chelsea
- Wang Zihan
- Wang Jessica P.
- Kumar Pawan
- Pokutnyi Oleksandr
- Gerbicz Robert
- Popov Serguei
- Levin John-Clark
- Kazakov Mstyslav
- Schmitt Johannes
- Galgon Geoff
- Sanchez Alvaro
- Lee Yongki
- Yeadon Will
- Sauers Scott
- Roth Marc
- Agu Chidozie
- Riis Søren
- Giska Fabian
- Utpala Saiteja
- Giboney Zachary
- Goshu Gashaw M.
- Xavier Joan of Arc
- Crowson Sarah-Jane
- Naiya Mohinder Maheshbhai
- Burns Noah
- Finke Lennart
- Cheng Zerui
- Park Hyunwoo
- Fournier-Facio Francesco
- Wydallis John
- Nandor Mark
- Singh Ankit
- Gehrunger Tim
- Cai Jiaqi
- Mccarty Ben
- Duclosel Darling
- Nam Jungbae
- Zampese Jennifer
- Hoerr Ryan G.
- Bacho Aras
- Loume Gautier Abou
- Galal Abdallah
- Cao Hangrui
- Garretson Alexis C
- Sileo Damien
- Ren Qiuyu
- Cojoc Doru
- Arkhipov Pavel
- Qazi Usman
- Li Lianghui
- Motwani Sumeet
- de Witt Christian Schroeder
- Taylor Edwin
- Veith Johannes
- Singer Eric
- Hartman Taylor D.
- Rissone Paolo
- Jin Jaehyeok
- Shi Jack Wei Lun
- Willcocks Chris G.
- Robinson Joshua
- Mikov Aleksandar
- Prabhu Ameya
- Tang Longke
- Alapont Xavier
- Uro Justine Leon
- Zhou Kevin
- Santos Emily de Oliveira
- Maksimov Andrey Pupasov
- Vendrow Edward
- Zenitani Kengo
- Guillod Julien
- Li Yuqi
- Vendrow Joshua
- Kuchkin Vladyslav
- Ze-An Ng
- Marion Pierre
- Efremov Denis
- Lynch Jayson
- Liang Kaiqu
- Gritsevskiy Andrew
- Martinez Dakotah
- Pageler Ben
- Crispino Nick
- Zvonkine Dimitri
- Fraga Natanael Wildner
- Soori Saeed
- Press Ori
- Tang Henry
- Salazar Julian
- Green Sean R.
- Brüssel Lina
- Twayana Moon
- Dieuleveut Aymeric
- Rogers T. Ryan
- Zhang Wenjin
- Li Bikun
- Yang Jinzhou
- Rao Arun
- Loiseau Gabriel
- Kalinin Mikhail
- Lukas Marco
- Manolescu Ciprian
- Mishra Subrata
- Kamdoum Ariel Ghislain Kemogne
- Kreiman Tobias
- Hogg Tad
- Jin Alvin
- Bosio Carlo
- Sun Gongbo
- Coppola Brian P
- Tarver Tim
- Heidinger Haline
- Sayous Rafael
- Ivanov Stefan
- Cavanagh Joseph M
- Shen Jiawei
- Imperial Joseph Marvin
- Schwaller Philippe
- Senthilkuma Shaipranesh
- Bran Andres M
- Dehghan Ali
- Algaba Andres
- Verbeken Brecht
- Noever David
- P V Ragavendran
- Schut Lisa
- Sucholutsky Ilia
- Zheltonozhskii Evgenii
- Lim Derek
- Stanley Richard
- Sivarajan Shankar
- Yang Tong
- Maar John
- Wykowski Julian
- Oller Martí
- Sandlin Jennifer
- Sahu Anmol
- Hu Yuzheng
- Fish Sara
- Heydari Nasser
- Apronti Archimedes
- Rawal Kaivalya
- Vilchis Tobias Garcia
- Zu Yuexuan
- Lackner Martin
- Koppel James
- Nguyen Jeremy
- Antonenko Daniil S.
- Chern Steffi
- Zhao Bingchen
- Arsene Pierrot
- Goldfarb Alan
- Ivanov Sergey
- Poświata Rafał
- Wang Chenguang
- Li Daofeng
- Crisostomi Donato
- Achilleos Andrea
- Myklebust Benjamin
- Sen Archan
- Perrella David
- Kaparov Nurdin
- Inlow Mark H
- Zang Allen
- Thornley Elliott
- Orel Daniil
- Poritski Vladislav
- Ben-David Shalev
- Berger Zachary
- Whitfill Parker
- Foster Michael
- Munro Daniel
- Ho Linh
- Hava Dan Bar
- Kuchkin Aleksey
- Lauff Robert
- Holmes David
- Sommerhage Frank
- Schneider Keith
- Kazibwe Zakayo
- Stambaugh Nate
- Singh Mukhwinder
- Magoulas Ilias
- Clarke Don
- Kim Dae Hyun
- Dias Felipe Meneguitti
- Elser Veit
- Agarwal Kanu Priya
- Vilchis Victor Efren Guadarrama
- Klose Immo
- Demian Christoph
- Anantheswaran Ujjwala
- Zweiger Adam
- Albani Guglielmo
- Li Jeffery
- Daans Nicolas
- Radionov Maksim
- Rozhoň Václav
- Ma Ziqiao
- Stump Christian
- Berkani Mohammed
- Platnick Jacob
- Nevirkovets Volodymyr
- Basler Luke
- Piccardo Marco
- Jeanplong Ferenc
- Cohen Niv
- Tkadlec Josef
- Rosu Paul
- Padlewski Piotr
- Barzowski Stanislaw
- Montgomery Kyle
- Menezes Aline
- Patel Arkil
- Wang Zixuan
- Tucker-Foltz Jamie
- Stade Jack
- Goertzen Tom
- Kazemi Fereshteh
- Milbauer Jeremiah
- Ambay John Arnold
- Shukla Abhishek
- Labrador Yan Carlos Leyva
- Givré Alan
- Wolff Hew
- Rossbach Vivien
- Aziz Muhammad Fayez
- Kaddar Younesse
- Chen Yanxu
- Zhang Robin
- Pan Jiayi
- Terpin Antonio
- Muennighoff Niklas
- Schoelkopf Hailey
- Zheng Eric
- Carmi Avishy
- Jones Adam
- Shah Jainam
- Brown Ethan D. L.
- Zhu Kelin
- Bartolo Max
- Wheeler Richard
- Ho Andrew
- Barkan Shaul
- Wang Jiaqi
- Stehberger Martin
- Kretov Egor
- Sridhar Kaustubh
- El-Wasif Zienab
- Zhang Anji
- Pyda Daniel
- Tam Joanna
- Cunningham David M.
- Goryachev Vladimir
- Patramanis Demosthenes
- Krause Michael
- Redenti Andrew
- Bugas Daniel
- Aldous David
- Lai Jesyin
- Coleman Shannon
- Bahaloo Mohsen
- Xu Jiangnan
- Lee Sangwon
- Zhao Sandy
- Tang Ning
- Cohen Michael K.
- Carroll Micah
- Paradise Orr
- Kirchner Jan Hendrik
- Steinerberger Stefan
- Ovchynnikov Maksym
- Matos Jason O.
- Shenoy Adithya
- Junior Benedito Alves de Oliveira
- Wang Michael
- Nie Yuzhou
- Giordano Paolo
- Petersen Philipp
- Sztyber-Betley Anna
- Shukla Priti
- Crozier Jonathan
- Pinto Antonella
- Verma Shreyas
- Joshi Prashant
- Yong Zheng-Xin
- Tee Allison
- Andréoletti Jérémy
- Weller Orion
- Singhal Raghav
- Zhang Gang
- Ivanov Alexander
- Khoury Seri
- Mostaghimi Hamid
- Thaman Kunvar
- Chen Qijia
- Khánh Tran Quoc
- Loader Jacob
- Cavalleri Stefano
- Szlyk Hannah
- Brown Zachary
- Roberts Jonathan
- Alley William
- Sun Kunyang
- Stendall Ryan
- Lamparth Max
- Reuel Anka
- Wang Ting
- Xu Hanmeng
- Raparthi Sreenivas Goud
- Hernández-Cámara Pablo
- Martin Freddie
- Malishev Dmitry
- Preu Thomas
- Korbak Tomek
- Abramovitch Marcus
- Williamson Dominic
- Chen Ziye
- Bálint Biró
- Bari M Saiful
- Kassani Peyman
- Wang Zihao
- Ansarinejad Behzad
- Goswami Laxman Prasad
- Sun Yewen
- Elgnainy Hossam
- Tordera Daniel
- Balabanian George
- Anderson Earth
- Kvistad Lynna
- Moyano Alejandro José
- Maheshwari Rajat
- Sakor Ahmad
- Eron Murat
- Mcalister Isaac C.
- Gimenez Javier
- Enyekwe Innocent
- O. Andrew Favre D.
- Shah Shailesh
- Zhou Xiaoxiang
- Kamalov Firuz
- Clark Ronald
- Abdoli Sherwin
- Santens Tim
- Meer Khalida
- Wang Harrison K
- Ramakrishnan Kalyan
- Chen Evan
- Tomasiello Alessandro
- de Luca G. Bruno
- Looi Shi-Zhuo
- Le Vinh-Kha
- Kolt Noam
- Mündler Niels
- Semler Avi
- Rodman Emma
- Drori Jacob
- Fossum Carl J
- Jagota Milind
- Pradeep Ronak
- Fan Honglu
- Shah Tej
- Eicher Jonathan
- Chen Michael
- Thaman Kushal
- Merrill William
- Harris Carter
- Gross Jason
- Gusev Ilya
- Sharma Asankhaya
- Agnihotri Shashank
- Zhelnov Pavel
- Usawasutsakorn Siranut
- Mofayezi Mohammadreza
- Bogdanov Sergei
- Piperski Alexander
- Carauleanu Marc
- Zhang David K.
- Ler Dylan
- Leventov Roman
- Soroko Ignat
- Jansen Thorben
- Lauer Pascal
- Duersch Joshua
- Taamazyan Vage
- Morak Wiktor
- Ma Wenjie
- Held William
- Huy Tran Đuc
- Xian Ruicheng
- Zebaze Armel Randy
- Mohamed Mohanad
- Leser Julian Noah
- Yuan Michelle X
- Yacar Laila
- Lengler Johannes
- Shahrtash Hossein
- Oliveira Edson
- Jackson Joseph W.
- Gonzalez Daniel Espinosa
- Zou Andy
- Chidambaram Muthu
- Manik Timothy
- Haffenden Hector
- Stander Dashiell
- Dasouqi Ali
- Shen Alexander
- Duc Emilien
- Golshani Bita
- Stap David
- Uzhou Mikalai
- Zhidkovskaya Alina Borisovna
- Lewark Lukas
- Vincze Mátyás
- Wehr Dustin
- Tang Colin
- Hossain Zaki
- Phillips Shaun
- Muzhen Jiang
- Ekström Fredrik
- Hammon Angela
- Patel Oam
- Remy Nicolas
- Farhidi Faraz
- Medley George
- Mohammadzadeh Forough
- Peñaflor Madellene
- Kassahun Haile
- Friedrich Alena
- Sparrow Claire
- Sakal Taom
- Dhamane Omkar
- Mirabadi Ali Khajegili
- Hallman Eric
- Battaglia Mike
- Maghsoudimehrabani Mohammad
- Hoang Hieu
- Amit Alon
- Hulbert Dave
- Pereira Roberto
- Weber Simon
- Mensah Stephen
- Andre Nathan
- Peristyy Anton
- Harjadi Chris
- Gupta Himanshu
- Malina Stephen
- Albanie Samuel
- Cai Will
- Mehkary Mustafa
- Reidegeld Frank
- Dick Anna-Katharina
- Friday Cary
- Sidhu Jasdeep
- Kim Wanyoung
- Costa Mariana
- Gurdogan Hubeyb
- Weber Brian
- Kumar Harsh
- Jiang Tong
- Agarwal Arunim
- Ceconello Chiara
- Vaz Warren S.
- Zhuang Chao
- Park Haon
- Tawfeek Andrew R.
- Aggarwal Daattavya
- Kirchhof Michael
- Dai Linjie
- Kim Evan
- Ferret Johan
- Wang Yuzhou
- Yan Minghao
- Burdzy Krzysztof
- Zhang Lixin
- Franca Antonio
- Pham Diana T.
- Loh Kang Yong
- Robinson Joshua
- Gul Shreen
- Chhablani Gunjan
- Du Zhehang
- Cosma Adrian
- White Colin
- Riblet Robin
- Saxena Prajvi
- Votava Jacob
- Vinnikov Vladimir
- Delaney Ethan
- Halasyamani Shiv
- Shahid Syed M.
- Mourrat Jean-Christophe
- Vetoshkin Lavr
- Bacho Renas
- Ginis Vincent
- Maksapetyan Aleksandr
- de la Rosa Florencia
- Li Xiuyu
- Malod Guillaume
- Lang Leon
- Laurendeau Julien
- Adesanya Fatimah
- Portier Julien
- Hollom Lawrence
- Souza Victor
- Zhou Yuchen Anna
- Yalın Yiğit
- Obikoya Gbenga Daniel
- Arnaboldi Luca
- Bigi Filippo
- Bacho Kaniuar
- Clavier Pierre
- Recchia Gabriel
- Popescu Mara
- Shulga Nikita
- Tanwie Ngefor Mildred
- Lux Thomas C. H.
- Rank Ben
- Ni Colin
- Yakimchyk Alesia
- Liu Huanxu
- Häggström Olle
- Verkama Emil
- Narayan Himanshu
- Gundlach Hans
- Brito-Santana Leonor
- Amaro Brian
- Vajipey Vivek
- Grover Rynaa
- Fan Yiyang
- Silva Gabriel Poesia Reis E
- Xin Linwei
- Kratish Yosi
- Łucki Jakub
- Li Wen-Ding
- Xu Justin
- Scaria Kevin Joseph
- Vargus Freddie
- Habibi Farzad
- Rodolà Emanuele
- Robins Jules
- Cheng Vincent
- Grabb Declan
- Bosio Ida
- Fruhauff Tony
- Akov Ido
- Lo Eve J. Y.
- Qi Hao
- Jiang Xi
- Segev Ben
- Fan Jingxuan
- Martinson Sarah
- Wang Erik Y.
- Hausknecht Kaylie
- Brenner Michael P.
- Mao Mao
- Jiang Yibo
- Zhang Xinyu
- Avagian David
- Scipio Eshawn Jessica
- Siddiqi Muhammad Rehan
- Ragoler Alon
- Tan Justin
- Patil Deepakkumar
- Plecnik Rebeka
- Kirtland Aaron
- Montecillo Roselynn Grace
- Durand Stephane
- Bodur Omer Faruk
- Adoul Zahra
- Zekry Mohamed
- Douville Guillaume
- Karakoc Ali
- Santos Tania C. B.
- Shamseldeen Samir
- Karim Loukmane
- Liakhovitskaia Anna
- Resman Nate
- Farina Nicholas
- Gonzalez Juan Carlos
- Maayan Gabe
- Hoback Sarah
- Pena Rodrigo de Oliveira
- Sherman Glen
- Mariji Hodjat
- Pouriamanesh Rasoul
- Wu Wentao
- Demir Gözdenur
- Mendoza Sandra
- Alarab Ismail
- Cole Joshua
- Ferreira Danyelle
- Johnson Bryan
- Milliron Hsiaoyun
- Safdari Mohammad
- Dai Liangti
- Arthornthurasuk Siriphan
- Pronin Alexey
- Fan Jing
- Ramirez-Trinidad Angel
- Cartwright Ashley
- Pottmaier Daphiny
- Taheri Omid
- Outevsky David
- Stepanic Stanley
- Perry Samuel
- Askew Luke
- Rodríguez Raúl Adrián Huerta
- Dendane Abdelkader
- Ali Sam
- Lorena Ricardo
- Iyer Krishnamurthy
- Salauddin Sk Md
- Islam Murat
- Gonzalez Juan
- Ducey Josh
- Campbell Russell
- Somrak Maja
- Mavroudis Vasilios
- Vergo Eric
- Qin Juehang
- Borbás Benjámin
- Chu Eric
- Lindsey Jack
- Radhakrishnan Anil
- Jallon Antoine
- Mcinnis I. M. J.
- Hoover Alex
- Möller Sören
- Bian Song
- Lai John
- Patwardhan Tejal
- Yue Summer
- Wang Alexandr
- Hendrycks Dan
Nature, Nature Publishing Group, 2026, 649 (8099), pp.1139-1146. Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve more than 90% accuracy on popular benchmarks such as Measuring Massive Multitask Language Understanding1, limiting informed measurement of state-of-the-art LLM capabilities. Here, in response, we introduce Humanity’s Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be an expert-level closed-ended academic benchmark with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable but cannot be quickly answered by internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a marked gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai. (10.1038/s41586-025-09962-4)
DOI : 10.1038/s41586-025-09962-4
On the Cutoff Phenomenon for Dyson-Jacobi Processes
- Chan-Ashing Samuel
, 2026. <div><p>We study the convergence to equilibrium of the Dyson-Jacobi process, a system of n interacting particles on the segment [0, 1] arising from Random Matrix Theory. We establish the occurence of a cutoff phenomenon for the intrinsic Wasserstein distance and provide an explicit formula for the associated mixing time.</p><p>Our approach relies on the interplay between the Riemannian geometry of the process and a flattened Euclidean representation obtained via a diffeomorphic deformation. This transformation allows us to transfer curvature-dimension inequalities from the Euclidean setting to the original space, thereby yielding sharp quantitative estimates.</p></div>
A model for a population of trees structured by phenological traits
- Boucenna Sirine
- Dakos Vasilis
- Raoul Gaël
, 2026. In the context of global warming, tree populations rely on two primary mechanisms of adaptation: phenotypic plasticity, which enables individuals to adjust their behavior in response to environmental stress, and genetic evolution, driven by natural selection and genetic diversity within the population. Understanding the interplay between these mechanisms is crucial for assessing the impacts of climate change on forest ecosystems and for informing sustainable management strategies. In this manuscript, we focus on a specific phenological adaptation: the ability of trees to enter summer dormancy once a critical temperature threshold is exceeded. Individuals are characterized by this threshold temperature and by their seed production capacity. We first establish a detailed mathematical model describing the population dynamics under these traits, and progressively reduce it to a system of two coupled ordinary differential equations. This simpler macroscopic model is then analyzed numerically, to investigate how the population reacts to a shift in its environment: an temperature increase, a drop in precipitation levels, or a combination of the two. Our results highlight contrasting effects of water stress and temperature stress on population dynamics, as well as the ambivalent effect of the plasticity.
Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
- Conforti Giovanni
- Durmus Alain
- Pham Le-Tuyet-Nhi
- Raoul Gael
, 2025. Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood, as many works have focused on their theoretical analysis. In contrast, results for diffusion models on discrete state spaces remain limited and pose significant challenges, particularly due to their combinatorial structure and their more recent introduction in generative modelling. In this work, we establish new and sharp convergence guarantees for three popular discrete diffusion models (DDMs). Two of these models are designed for finite state spaces and are based respectively on the random walk and the masking process. The third DDM we consider is defined on the countably infinite space $\mathbb{N}^d$ and uses a drifted random walk as its forward process. For each of these models, the backward process can be characterized by a discrete score function that can, in principle, be estimated. However, even with perfect access to these scores, simulating the exact backward process is infeasible, and one must rely on approximations. In this work, we study Euler-type approximations and establish convergence bounds in both Kullback-Leibler divergence and total variation distance for the resulting models, under minimal assumptions on the data distribution. In particular, we show that the computational complexity of each method scales linearly in the dimension, up to logarithmic factors. Furthermore, to the best of our knowledge, this study provides the first non-asymptotic convergence guarantees for these noising processes that do not rely on boundedness assumptions on the estimated score.
Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2 -distance
- Gentiloni-Silveri Marta
- Ocello Antonio
, 2025. Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise. Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about the data distribution. In this work, we present a novel framework for analyzing W2-convergence in SGMs, significantly relaxing traditional assumptions such as log-concavity and score regularity. Leveraging the regularization properties of the Ornstein-Uhlenbeck (OU) process, we show that weak log-concavity of the data distribution evolves into log-concavity over time. This transition is rigorously quantified through a PDE-based analysis of the Hamilton-Jacobi-Bellman equation governing the log-density of the forward process. Moreover, we establish that the drift of the time-reversed OU process alternates between contractive and noncontractive regimes, reflecting the dynamics of concavity. Our approach circumvents the need for stringent regularity conditions on the score function and its estimators, relying instead on milder, more practical assumptions. We demonstrate the wide applicability of this framework through explicit computations on Gaussian mixture models, illustrating its versatility and potential for broader classes of data distributions.
A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
- Alfaro Matthieu
- Chainais-Hillairet Claire
- Nabet Flore
, 2026. In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum.
Subadditivity and optimal matching of unbounded samples
- Caglioti Emanuele
- Goldman Michael
- Pieroni Francesca
- Trevisan Dario
, 2026. We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence for the whole range of power exponents $p$ and dimensions $d$. Moreover we identify the exact prefactor when $p\le d$. We cover in particular the Gaussian case, going far beyond the currently known bounds. Our proof technique is based on approximate sub- and super-additivity bounds along a geometric decomposition adapted to some features the density, such as its radial symmetry and its decay at infinity.
Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel modelling telomere shortening
- Olayé Jules
- Tomasevic Milica
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2026, 31. In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks individuals evolving within a continuous-time framework indexed by a binary tree, characterised by age and a multidimensional trait. Branching events occur with rates dependent on age, where offspring inherit traits from their parent with random increase or decrease in some coordinates, while the most of them are left unchanged. Exponential ergodicity is obtained at the cost of an exponential normalisation, despite the fact that we have an unbounded age-dependent birth rate that may depend on the multidimensional trait, and a non-compact transition kernel. These two difficulties are respectively treated by stochastically comparing our model to Bellman-Harris processes, and by using a weak form of a Harnack inequality. We conclude this study by giving examples where the assumptions of our main result are verified. (10.1214/25-EJP1469)
DOI : 10.1214/25-EJP1469
Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE
- Blanco Dominic
- Cadiot Matthieu
, 2026. <div><p>In this article, we extend the framework developed in [14] to allow for rigorous proofs of existence of smooth, localized solutions in semi-linear partial differential equations possessing both space and non-space group symmetries. We demonstrate our approach on the Swift-Hohenberg model. In particular, for a given symmetry group G, we construct a natural Hilbert space H l G containing only functions with G-symmetry. In this space, products and differential operators are well-defined allowing for the study of autonomous semi-linear PDEs. Depending on the properties of G, we derive a Newton-Kantorovich approach based on the construction of an approximate inverse around an approximate solution, u0. More specifically, combining a meticulous analysis and computer-assisted techniques, the Newton-Kantorovich approach is validated thanks to the computation of some explicit bounds. The strategy for constructing u0, the approximate inverse, and the computation of these bounds will depend on the properties of G and its maximal square lattice space subgroup, H. More specifically, we consider three cases: G is a space group which can be represented on the square lattice, G is not a space group which can be represented on the square lattice and the symmetry of H isolates the solution, and where G is not a space group which can be represented on the square lattice and the symmetry of H does not isolate the solution. We demonstrate the methodology on the 2D Swift-Hohenberg PDE by proving the existence of various dihedral localized patterns. The algorithmic details to perform the computer-assisted proofs can be found on Github [4].</p></div>
Existence and orbital stability proofs of traveling wave solutions on an infinite strip for the suspension bridge equation
- van der Aalst Lindsey
- Cadiot Matthieu
, 2026. <div><p>In this paper, we present a computer-assisted approach for constructively proving the existence of traveling wave solutions of the suspension bridge equation on the infinite strip Ω = R × (-d2, d2). Using a meticulous Fourier analysis, we derive a quantifiable approximate inverse A for the Jacobian DF(ū) of the PDE at an approximate traveling wave solution ū. Such approximate objects are obtained thanks to Fourier coefficient sequences and operators, arising from Fourier series expansions on a rectangle Ω0 = (-d1, d1) × (-d2, d2) for large d1. In particular, the challenging exponential nonlinearity of the equation is tackled using a rigorous control of the aliasing error when computing related Fourier coefficients. This allows to establish a Newton-Kantorovich approach, from which the existence of a true traveling wave solution of the PDE can be proven in a vicinity of ū. We successfully apply such a methodology in the case of the suspension bridge equation and prove the existence of multiple traveling wave solutions on Ω. Finally, given a proven solution ũ, a Fourier series approximation on Ω0 allows us to accurately enclose the spectrum of DF(ũ). Such a tight control provides the number of negative eigenvalues, which in turn, allows us to conclude about the orbital (in)stability of the traveling wave.</p></div>
Proving the existence of localized patterns and saddle node bifurcations in 1D activator-inhibitor type models
- Blanco Dominic
- Cadiot Matthieu
- Fassler Daniel
, 2026. <div><p>In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activatorinhibitor systems using computer-assisted proofs. Specifically, we develop the necessary analysis to compute explicit upper bounds required in a Newton-Kantorovich approach. Given an approximate solution ū, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood ū. For this matter, we construct an approximate inverse of the linearization around ū, and establish sufficient conditions under which the contraction is achieved. This provides a framework for which computer-assisted analysis can be applied to verify the existence and local uniqueness of solutions in a vicinity of ū, and control the linearization around ū. Furthermore, we extend the method to rigorously establish saddle-node bifurcations of localized solutions for the same type of models, by considering a well-chosen zero-finding problem. This depends on the rigorous control of the spectrum of the linearization around the bifurcation point. Finally, we demonstrate the effectiveness of the framework by proving the existence and stability of multiple steady-state patterns in various activatorinhibitor systems, as well as a saddle-node bifurcation in the Glycolysis model.</p></div>
Finite element modelling for the reproduction of dynamic OCE measurements in the cornea
- Merlini Giulia
- Imperiale Sébastien
- Allain Jean-Marc
Journal of the Mechanics and Physics of Solids, Elsevier, 2026, 206, pp.106363. Recent advances in dynamic elastography, particularly through optical coherence tomography combined with transient excitations have enabled rapid, localized, and non-invasive mechanical data acquisition of the cornea. This dataopens the path to early-detection of pathologies and more accurate treatment. However, the analysis of the wave propagation is a complex mechanical problem: the cornea is a structure under pressure, with non-linear material behavior. Thus, computational analysis are needed to extract mechanical parameters from the data. In this study, we present a time-dependent finite element model for the reproduction of transient shear wave elastographic measurements in the cornea. The mechanical problem consists in a smallamplitude wave propagating in the cornea, largely deformed by intraocular pressure in physiological conditions. The model accounts for anisotropic, hyperelastic, and incompressible behavior of the cornea, as well as its accurate geometry, and the preloaded condition. We have implemented two different numerical approaches to solve first the static non-linear inflation of the cornea and then the linear wave propagation problem to reproduce the measurements. We investigate the impact of material anisotropy and prestress on wave propagation and demonstrate that intraocular pressure critically influences shear wave velocity. Additionally, by introducing a localized mechanical defect to simulate a pathological defect, we show that simulated shear wave can detect and quantify mechanical weaknesses, suggesting potential as a diagnostic tool to assess corneal health. (10.1016/j.jmps.2025.106363)
DOI : 10.1016/j.jmps.2025.106363
Self-interacting approximation to McKean-Vlasov long-time limit: a Markov chain Monte Carlo method
- Du Kai
- Ren Zhenjie
- Suciu Florin
- Wang Songbo
Journal de Mathématiques Pures et Appliquées, Elsevier, 2026, 205, pp.103782. For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we demonstrate the ergodicity of the self-interacting dynamics, under broad conditions, by applying the reflection coupling method. Second, in scenarios where the drifts are negative intrinsic gradients of convex mean-field potential functionals, we use entropy and functional inequalities to demonstrate that the stationary measures of the self-interacting processes approximate the invariant measures of the corresponding McKean-Vlasov processes. As an application, we show how to learn the optimal weights of a two-layer neural network by training a single neuron. (10.1016/j.matpur.2025.103782)
DOI : 10.1016/j.matpur.2025.103782
On the simulation of extreme events with neural networks
- Allouche Michaël
- Girard Stéphane
- Gobet Emmanuel
, 2026. This article aims at investigating the use of generative methods based on neural networks to simulate extreme events. Although very popular, these methods are mainly invoked in empirical works. Therefore, providing theoretical guidelines for using such models in extreme values context is of primal importance. To this end, we propose an overview of most recent generative methods dedicated to extremes, giving some theoretical and practical tips on their tail behaviour thanks to both extreme-value and copula tools.
A REMARK ON SELF-ADJOINT PROBLEMS IN THE OPTIMIZATION OF NON-LINEAR MODELS
- Égoire Allaire G R
- Cherrière Théodore
- Gauthey Thomas
- Hage Hassan Maya
- Mininger Xavier
Journal of Optimization Theory and Applications, Springer Verlag, 2026, 208, pp.100. This article considers optimization problems under nonlinear partial differential equation (p.d.e.) constraints. It is assumed that the p.d.e. arises from minimizing a convex energy. We prove that the optimization problem is self-adjoint when the objective function is the dual energy. In other words, the differential of the objective function with respect to the optimization variable does not involve any adjoint state. This result generalizes the well-known fact that the so-called compliance is self-adjoint in the linear case. We also prove that in a large class of objective functions the dual energy is the only one which is self-adjoint.
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, The, 2026. 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
Nonlinear model calibration through bifurcation curves
- Mélot Adrien
- Denimal Goy Enora
- Renson Ludovic
Mechanical Systems and Signal Processing, Elsevier, 2026, 242, pp.113589. Nonlinear systems exhibit a plethora of complex dynamic behaviours that are difficult to model and predict accurately. This difficulty often arises from a lack of knowledge of the physics that induces the nonlinear behaviours and the strong sensitivity of the nonlinear dynamics to parameter variation. We introduce in this paper a methodology to carry out nonlinear model updating based on bifurcations. The proposed approach involves minimising the distance between experimental and numerical bifurcation curves, which are key dynamic features that define stability boundaries and regions of multi-stability. For the model, bifurcation curves are computed via standard numerical bifurcation tracking analyses. In the experiment, we use control-based continuation to obtain the data. The approach is first demonstrated on a Duffing and a beam system using synthetic data, before being applied to experimental data collected on a base-excited energy harvester with magnetic nonlinearity.
Improved well-posedness for the limit flow of differentiation of roots of polynomials
- Bertucci Charles
- Pesce Valentin
, 2026. In this paper, we study the partial differential equation on the circle that was heuristically obtained by Steinerberg [32] on the real line and which represents the evolution of the density of the roots of polynomials under differentiation. After integrating the partial differential equation in question, we observe that it can be treated with the theory of viscosity solutions. This equation at hand is a non linear parabolic integro-differential equation which involves the elliptic operator called the half-Laplacian. Due to the singularity of the equation, we restrict our study to strictly positive initial condition. We obtain a comparison principle for solutions of the primitive equation which yields uniqueness, existence, continuity with respect to initial condition. We also present heuristics to justify that the system of particles indeed approximates the solution of the equation.
A stochastic use of the Kurdyka-Lojasiewicz property: Investigation of optimization algorithms behaviours in a non-convex differentiable framework
- Fest Jean-Baptiste
- Repetti Audrey
- Chouzenoux Emilie
Foundations of Data Science, American Institute of Mathematical Sciences, 2026, 9, pp.164-191. Asymptotic analysis of generic stochastic algorithms often relies on descent conditions. In a convex setting, some technical shortcuts can be considered to establish asymptotic convergence guarantees of the associated scheme. However, in a non-convex setting, obtaining similar guarantees is usually more complicated, and relies on the use of the Kurdyka-Łojasiewicz (KŁ) property. While this tool has become popular in the field of deterministic optimization, it is much less widespread in the stochastic context and the few works making use of it are essentially based on trajectory-by-trajectory approaches. In this paper, we propose a new framework for using the KŁ property in a non-convex stochastic setting based on conditioning theory. We show that this framework allows for deeper asymptotic investigations on stochastic schemes verifying some generic descent conditions. We further show that our methodology can be used to prove convergence of generic stochastic gradient descent (SGD) schemes, and unifies conditions investigated in multiple articles of the literature. (10.3934/fods.2025016)
DOI : 10.3934/fods.2025016
Spatio-temporal thermalization and adiabatic cooling of guided light waves
- Zanaglia Lucas
- Garnier Josselin
- Carusotto Iacopo
- Doya Valérie
- Michel Claire
- Picozzi Antonio
Physical Review Letters, American Physical Society, 2026, 136, pp.053802. We propose and theoretically characterize three-dimensional spatio-temporal thermalization of a continuous-wave classical light beam propagating along a multi-mode optical waveguide. By combining a non-equilibrium kinetic approach based on the wave turbulence theory and numerical simulations of the field equations, we anticipate that thermalizing scattering events are dramatically accelerated by the combination of strong transverse confinement with the continuous nature of the temporal degrees of freedom. In connection with the blackbody catastrophe, the thermalization of the classical field in the continuous temporal direction provides a novel intrinsic mechanism for adiabatic cooling and spatial beam condensation. This process of adiabatic cooling is distinct from other mechanisms of thermalization and provides new insights into the dynamics of far-from-equilibrium closed systems and their route to thermalization. (10.1103/mqzh-w2gh)
DOI : 10.1103/mqzh-w2gh

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