2025Activity reportProject-Team​ASTRAL

Project-team​​ positioning:

Some topics of​​​‌ the INRIA project teams​ (STATIFY, CELESTE, MODAL, SEQUEL,​‌ CLASSIC) are close to​​ the ASTRAL objectives such​​​‌ as non parametric view​ of high dimensional data,​‌ statistical/machine learning, model selection,​​ clustering, sequential learning algorithms,​​​‌ or multivariate data analysis​ for complex data. While​‌ certain ASTRAL objectives are​​ similar to those of​​​‌ these teams, our approaches​ are significantly different. For​‌ example, in multivariate data​​ analysis of complex data​​​‌ including clustering, our team​ mainly focuses on a​‌ geometric approach for mixed​​ data. We also consider​​​‌ the case of successive​ arrivals of information in​‌ SIR both from the​​ theoretical and numerical point​​​‌ of view. Currently there​ is no direct competition​‌ between our team and​​ other INRIA project teams.​​​‌ However, interactions between ASTRAL​ and other INRIA teams​‌ exist. For instance, ASTRAL​​ and STATIFY collaborations are​​​‌ fruitful with common publications,​ in particular with S.​‌ Girard (STATIFY project team).​​

In the field of​​​‌ multivariate data analysis, the​ team have interesting discussions​‌ with Agrocampus Ouest (Rennes,​​ France) and with H.A.L.​​​‌ Kiers (Groningen University) on​ a mixed data approach​‌ for dimension reduction. Conditional​​ and regression quantiles are​​​‌ very active research fields​ in France (University of​‌ Toulouse, Toulouse School of​​ Economics, University of Montpellier)​​​‌ and around the world​ (ULB, Belgium; University of​‌ Illinois Urbana-Champaign, USA; Open​​ University, UK; Brunel University,​​​‌ UK). The ASTRAL team​ has for the last​‌ four-year period collaborated with​​ D. Paindaveine (ULB, Belgium).​​​‌ In the dimension reduction​ framework, there is a​‌ large international community in​​ Europe, America or Asia​​​‌ working on SIR and​ related methods. However, to​‌ our knowledge, the ASTRAL​​ team was the first​​​‌ to introduce importance of​ variables and recursive methods​‌ in SIR, and the​​ first to adapt the​​​‌ SIR approach to data​ stream.

Project-team‌ positioning:

In the last‌​‌ three decades, the use​​ of Feynman-Kac type particle​​​‌ models has been developed‌ in variety of scientific‌​‌ disciplines, including in molecular​​ chemistry, risk analysis, biology,​​​‌ signal processing, Bayesian inference‌ and data assimilation.

The‌​‌ design and the mathematical​​ analysis of Feynman-Kac particle​​​‌ methodologies has been one‌ of the main research‌​‌ topics of P. Del​​ Moral since the late​​​‌ 1990's 47, 44‌, 42, see‌​‌ also the books 46​​, 41, 45​​​‌, 48 and references‌ therein. These mean field‌​‌ particle sampling techniques encapsulate​​ particle filters, sequential Monte​​​‌ Carlo methods, spatial branching‌ and evolutionary algorithms, Fleming-Viot‌​‌ genetic type particles methods​​ arising in the computation​​​‌ of quasi-invariant measures and‌ simulation of non absorbed‌​‌ processes, as well as​​ diffusion Monte Carlo methods​​​‌ arising in numerical physics‌ and molecular chemistry. The‌​‌ term "particle filters" was​​​‌ first coined in the​ article 47 published in​‌ 1996 in reference to​​ branching and mean field​​​‌ interacting particle methods used​ in fluid mechanics since​‌ the beginning of the​​ 1960s. This article presents​​​‌ the first rigorous analysis​ of these mean field​‌ type particle algorithms.

The​​ INRIA project teams applying​​​‌ the particle methodology developed​ by ASTRAL include the​‌ INRIA project team SIMSMART​​ (rare event simulation as​​​‌ well as particle filters)​ and the INRIA project​‌ team Matherials (applications in​​ molecular chemistry). The project​​​‌ team ASTRAL also has​ several collaborative research projects​‌ with these, teams as​​ well as with researchers​​​‌ from international universities working​ in this subject, including​‌ Oxford, Cambridge, New South​​ Wales Sydney, UTS, Bath,​​​‌ Warwick and Singapore Universities.​

Discrete-time models.

In this​​ framework, the basic model​​​‌ can be described by​ a state space where​‌ the system evolves, an​​ action space, a stochastic​​​‌ kernel governing the dynamic​ and, depending on the​‌ state and action variables,​​ a one-step cost (reward)​​​‌ function. The distribution of​ the controlled stochastic process​‌ is defined through the​​ control policy which is​​​‌ then selected in order​ to optimize the objective​‌ function. This is a​​ very general model for​​​‌ dynamic optimization in discrete-time,​ which also goes by​‌ the name of stochastic​​ dynamic programming. For​​​‌ references, the interested reader​ may consult the following​‌ books 35, 37​​, 50, 51​​​‌, 53, 54​, 55, 56​‌, 60, 59​​, 62 and the​​​‌ references therein (this list​ of references is, of​‌ course, not exhaustive).

Continuous-time​​ models.

Most of the​​​‌ continuous-time stochastic processes consist​ of a combination of​‌ the following three different​​ ingredients: stochastic jumps, diffusion​​ and deterministic motions. In​​​‌ this project, we will‌ focus on non-diffusive models‌​‌, in other words,​​ stochastic models for which​​​‌ the randomness appears only‌ at fixed or random‌​‌ times, i.e. those combining​​ deterministic motions and random​​​‌ jumps. These stochastic processes‌ are the so-called piecewise‌​‌ deterministic Markov processes (PDMPs)​​ 36, 38,​​​‌ 39, 52,‌ 57, 58,‌​‌ 61. This family​​ of models plays a​​​‌ central role in applied‌ probability because it forms‌​‌ the bulk of models​​ in many research fields​​​‌ such as, e.g. operational‌ research, management science and‌​‌ economy and covers an​​ enormous variety of applications.​​​‌

These models can be‌ framed in several different‌​‌ forms of generality, depending​​ on their mathematical properties​​​‌ such as the type‌ of performance criterion, full‌​‌ or incomplete state information,​​ with or without constraints,​​​‌ adaptative or not, but‌ more importantly, the nature‌​‌ of the boundary of​​ the state space, the​​​‌ type of dynamic between‌ two jumps and on‌​‌ the number of decision-makers.​​ These last three characteristics​​​‌ make the analysis of‌ the controlled process much‌​‌ more involved.

Part of​​ this project will cover​​​‌ both theoretical and numerical‌ aspects of stochastic optimal‌​‌ control. It is clear​​ that stochastic problems and​​​‌ control games have been‌ extensively studied in the‌​‌ literature. Nevertheless, important challenges​​ remain to be addressed.​​​‌ From the theoretical side,‌ there are still many‌​‌ technical issues that are,​​ for the moment, still​​​‌ unanswered or at most‌ have received partial answers.‌​‌ This is precisely what​​ makes them difficult and​​​‌ requires either the creative‌ transposition of pre-existing methodologies‌​‌ or the development of​​ new approaches. It is​​​‌ interesting to note that‌ one of the feature‌​‌ of these theoretical problems​​ is that they are​​​‌ closely related to practical‌ issues. Solving such problems‌​‌ not only gives rise​​ to challenging mathematical questions,​​​‌ but also allow a‌ better insight into the‌​‌ structure and properties of​​ real practical problems. Theory​​​‌ for applications will be‌ for us the thrust‌​‌ that will guide us​​ in this project. From​​​‌ the numerical perspective, solving‌ a stochastic decision model‌​‌ remains a critical issue.​​ Indeed, except for very​​​‌ few specific models, the‌ determination of an optimal‌​‌ policy and the associated​​ value function is an​​​‌ extremely difficult problem to‌ tackle. The development of‌​‌ computational and numerical methods​​ to get quasi-optimal solutions​​​‌ is, therefore, of crucial‌ importance to demonstrate the‌​‌ practical interest of stochastic​​ decision model as a​​​‌ powerful modeling tool. During‌ the International Conference on‌​‌ Dynamic Programming and Its​​ Applications held at the​​​‌ University of British Columbia,‌ Canada in April 1977,‌​‌ Karl Hinderer, a pioneer​​ in the field of​​​‌ stochastic dynamic programming emphasized‌ that "whether or‌​‌ not our field will​​ have a lasting impact​​​‌ on science beyond academic‌ circles depends heavily on‌​‌ the success of implemented​​ applications". We believe​​​‌ that this statement is‌ still in force some‌​‌ forty years later.

The​​ objective of this project​​​‌ is to address these‌ important challenges. They are‌​‌ mainly related to models​​​‌ with general state/action spaces​ and with continuous time​‌ variables covering a large​​ field of applications. Here​​​‌ is a list of​ topics we would like​‌ to study: games, constrained​​ control problems, non additive​​​‌ types of criteria, numerical​ and computational challenges, analysis​‌ of partially observed/known stochastic​​ decision processes. This list​​​‌ is not necessarily exhaustive​ and may of course​‌ evolve over time.

Our​​ research agenda on optimal​​​‌ stochastic control is developed​ around the applied mathematical​‌ axis as well as​​ the numerical perspective, including​​​‌ concrete industrial transfers with​ a special focus on​‌ Naval Group. Our mid-term​​ objectives will focus on​​​‌ the following themes described​ above: properties of control​‌ policies in continuous-time control​​ problems, non additive types​​​‌ of criteria, numerical and​ computational challenges. Our long-term​‌ objectives will focus on​​ the analysis of partially​​​‌ observed/known stochastic control problems,​ constrained control problems and​‌ games.

Project-team positioning:

There​​ exists a large national/international​​​‌ community working on PDMPs​ and MDPs both on​‌ the theoretical, numerical and​​ practical aspects. One may​​​‌ cite A. Almudevar (University​ of Rochester, USA), E.​‌ Altman (INRIA Team NEO,​​ France), K. Avrachenkov (INRIA​​​‌ Team NEO, France), N.​ Bauerle (Karlsruhe University, Germany),​‌ D. Bertsekas (Massachusetts Institute​​ of Technology, USA), O.​​​‌ Costa (Sao Paulo University,​ Brazil), M. Davis (Imperial​‌ College London, England), E.​​ Feinberg (Stony Brook University,​​​‌ USA), D. Goreac (Université​ Paris-Est Marne-la-Vallée, France), X.​‌ Guo (Zhongshan University, China),​​ O. Hernandez-Lerma (National Polytechnic​​​‌ Institute, Mexico), S. Marcus​ (University of Maryland, USA),​‌ T. Prieto-Rumeau (Facultad de​​ Ciencias, UNED, Spain), A.​​​‌ Piunovskiy (University of Liverpool,​ England), U. Rieder (Universität​‌ Ulm, Germany), J. Tsitsiklis​​ (Massachusetts Institute of Technology,​​​‌ USA), B. Van Roy​ (Stanford University, USA), O.​‌ Vega-Amaya (Universidad de Sonora,​​ Mexico), Y. Zhang (University​​​‌ of Liverpool, England) to​ name just a few.​‌ Many of the colleagues​​ cited above are at​​​‌ the head of research​ groups which have not​‌ been described in detail​​ due to space limitation​​​‌ and so, this list​ is far from being​‌ exhaustive.

To some extent,​​ our team is in​​​‌ competition wit the colleagues​ and teams mentioned above.​‌ We emphasize that there​​ exists a long standing​​​‌ collaboration between our group​ and O. Costa (Sao​‌ Paulo University, Brazil) since​​ 1998. In the last​​​‌ 10 years, we have​ established very fruitful collaborations​‌ with T. Prieto-Rumeau (Facultad​​ de Ciencias, UNED, Spain)​​​‌ and A. Piunovskiy (University​ of Liverpool, England).

Inside​‌ INRIA, the team NEO​​ and in particular E.​​​‌ Altman and K. Avrachenkov​ work on discrete-time MDPs​‌ but they are mainly​​ focused on the case​​​‌ of countable (finite) state/action​ spaces MDPs. From this​‌ point of view, our​​ results on this theme​​​‌ may appear complementary to​ theirs.

6.1.1‌​‌ FracLab

• Keyword:
  Stochastic process​​
• Functional Description:

  FracLab is​​​‌ a general purpose signal‌ and image processing toolbox‌​‌ based on fractal, multifractal​​ and local regularity methods.​​​‌ FracLab can be approached‌ from two different perspectives:‌​‌ - (multi-) fractal and​​ local regularity analysis: A​​​‌ large number of procedures‌ allow to compute various‌​‌ quantities associated with 1D​​ or 2D signals, such​​​‌ as dimensions, Hölder and‌ 2-microlocal exponents or multifractal‌​‌ spectra.

  - Signal/Image processing:​​ Alternatively, one can use​​​‌ FracLab directly to perform‌ many basic tasks in‌​‌ signal processing, including estimation,​​ detection, denoising, modeling, segmentation,​​​‌ classification, and synthesis.

• URL:‌
  https://­project.­inria.­fr/­fraclab/
• Contact:
  Jacques Levy-Vehel‌​‌
• Participant:
  7 anonymous participants​​
• Partners:
  Centrale Paris, Mas​​​‌

6.1.2 PCAmixdata

• Keyword:
  Statistic‌ analysis
• Functional Description:
  Mixed‌​‌ data type arise when​​​‌ observations are described by​ a mixture of numerical​‌ and categorical variables. The​​ R package PCAmixdata extends​​​‌ standard multivariate analysis methods​ to incorporate this type​‌ of data. The key​​ techniques included in the​​​‌ package are PCAmix (PCA​ of a mixture of​‌ numerical and categorical variables),​​ PCArot (rotation in PCAmix)​​​‌ and MFAmix (multiple factor​ analysis with mixed data​‌ within a dataset). The​​ MFAmix procedure handles a​​​‌ mixture of numerical and​ categorical variables within a​‌ group - something which​​ was not possible in​​​‌ the standard MFA procedure.​ We also included techniques​‌ to project new observations​​ onto the principal components​​​‌ of the three methods​ in the new version​‌ of the package.
• URL:​​
  https://­cran.­r-project.­org/­web/­packages/­PCAmixdata/­index.­html
• Contact:
  Marie Chavent​​​‌

6.1.3 vimplclust

• Keywords:
  Clustering,​ Fair and ethical machine​‌ learning
• Functional Description:
  vimpclust​​ is an R package​​​‌ that implements methods related​ to sparse clustering and​‌ variable importance. The package​​ currently allows to perform​​​‌ sparse k-means clustering with​ a group penalty, so​‌ that it automatically selects​​ groups of numerical features.​​​‌ It also allows to​ perform sparse clustering and​‌ variable selection on mixed​​ data (categorical and numerical​​​‌ features), by preprocessing each​ categorical feature as a​‌ group of numerical features.​​ Several methods for visualizing​​​‌ and exploring the results​ are also provided.
• URL:​‌
  https://­CRAN.­R-project.­org/­package=vimpclust
• Contact:
  Marie Chavent​​

6.1.4 divdiss

• Name:
  divisive​​​‌ monothetic clustering on dissimilarity​ matrix
• Keywords:
  Clustering, Machine​‌ learning
• Functional Description:
  The​​ div_diss function implements a​​​‌ divisive monotopic hierarchical classification​ algorithm.
• URL:
  https://­github.­com/­chavent/­divdiss
• Contact:​‌
  Marie Chavent

6.1.5 pybellhop​​

• Name:
  Pybellhop
• Keywords:
  3D,​​​‌ Python, Hydroacoustics
• Scientific Description:​
  Hydroacoustic waves simulator.
• Functional​‌ Description:
  Pybellhob is exposing​​ some bellhopcuda functionalities in​​​‌ python in order to​ make them callable from​‌ any python software without​​ any disk access to​​​‌ write and read configuration​ and result files.
• Release​‌ Contributions:
  First version
• News​​ of the Year:
  Développement​​​‌ de la version v0.1.​
• Contact:
  Denis Arrivault
• Participant:​‌
  Denis Arrivault

6.1.6 pyastral​​

• Name:
  PyAstral
• Keyword:
  Python​​​‌
• Scientific Description:
  Trajectography
• Functional​ Description:
  Trajectography software
• News​‌ of the Year:
  Developments,​​ tests, documentation pour la​​​‌ version 0.1.
• Contact:
  Enzo​ Iglesis
• Participants:
  Enzo Iglesis,​‌ Denis Arrivault
• Partner:
  Naval​​ Group

6.1.7 estimation_filters

• Name:​​​‌
  Estimation Filters
• Keywords:
  Kalman​ filter, Particular filter, Bayesian​‌ estimation
• Scientific Description:
  Python​​ library offering several stochastic​​​‌ estimation filters for estimating​ and tracking the state​‌ of a dynamic system.​​
• Functional Description:
  Python library​​​‌ offering several stochastic estimation​ filters for estimating and​‌ tracking the state of​​ a dynamic system.
• News​​​‌ of the Year:
  27​ commits cette année. Divers​‌ corrections et adaptations plus​​ l'ajout de comentaires et​​​‌ de tests.
• Contact:
  Enzo​ Iglesis
• Participants:
  Enzo Iglesis,​‌ Denis Arrivault, an anonymous​​ participant

7.1.1​ Analysis of electrical features​‌ for detection of subjects​​ at risk for sudden​​​‌ cardiac death

Sudden cardiac​ death (SCD) accounts for​‌ $30\%$ of adult​​ mortality in industrialized countries.​​​‌ The majority of SCD​ cases are the result​‌ of an arrhythmia called​​ ventricular fibrillation, which itself​​​‌ results from structural abnormalities​ in the heart muscle.​‌ Despite the existence of​​ effective therapies, most individuals​​ at risk for SCD​​​‌ are not identified preventively‌ due to the lack‌​‌ of available testing. Developing​​ specific markers on electrocardiographic​​​‌ recordings would enable the‌ identification and stratification of‌​‌ SCD risk. Over the​​ past six years, the​​​‌ Liryc Institute has recorded‌ surface electrical signals from‌​‌ over 800 individuals (both​​ healthy and pathological) using​​​‌ a high-resolution 128-electrode device.‌ Features were calculated from‌​‌ these signals (signal duration​​ per electrode, frequency, amplitude​​​‌ fractionation, etc.). In total,‌ more than 1,500 electrical‌​‌ features are available per​​ patient. During the acquisition​​​‌ process using the 128-electrode‌ system in a hospital‌​‌ setting, noise or poor​​ positioning of specific electrodes​​​‌ sometimes prevents calculating the‌ intended features, leading to‌​‌ an incomplete database. This​​ thesis 24 is organized​​​‌ around two main axes.‌ First, we developed a‌​‌ method for imputing missing​​ data to address the​​​‌ problem of faulty electrodes.‌ Then, we developed a‌​‌ risk score for the​​ sudden death risk stratification.​​​‌ The most commonly used‌ family of methods for‌​‌ handling missing data is​​ imputation, ranging from simple​​​‌ completion by averaging to‌ local aggregation methods, local‌​‌ regressions, optimal transport, or​​ even modifications of generative​​​‌ models. Recently, Autoencoders (AE)‌ and, more specifically, Denoising‌​‌ AutoEncoders (DAE) have performed​​ well in this task.​​​‌ AEs are neural networks‌ used to learn a‌​‌ representation of data in​​ a reduced-dimensional space. DAEs​​​‌ are AEs that have‌ been proposed to reconstruct‌​‌ original data from noisy​​ data. In this work,​​​‌ we propose a new‌ methodology based on DAEs‌​‌ called the modified Denoising​​ AutoEncoder (mDAE) to allow​​​‌ for the imputation of‌ missing data. The second‌​‌ research axis of the​​ thesis focused on developing​​​‌ a risk score for‌ sudden cardiac death. DAEs‌​‌ can model and reconstruct​​ complex data. We trained​​​‌ DAEs to model the‌ distribution of healthy individuals‌​‌ based on a selected​​ subset of electrical features.​​​‌ Then, we used these‌ DAEs to discriminate pathological‌​‌ patients from healthy individuals​​ by analyzing the imputation​​​‌ quality of the DAE‌ on partially masked features.‌​‌ We also compared different​​ classification methods to establish​​​‌ a risk score for‌ sudden death.

Participants: Mariette‌​‌ Dupuy (ASTRAL).

7.1.2​​ ClimLoco1.0: CLimate variable confidence​​​‌ Interval of Multivariate Linear‌ Observational COnstraint

Projections of‌​‌ future climate are key​​ to society's adaptation and​​​‌ mitigation plans in response‌ to climate change. Numerical‌​‌ climate models provide projections,​​ but the large dispersion​​​‌ between them makes future‌ climate very uncertain. To‌​‌ refine it, approaches called​​ observational constraints (OC) have​​​‌ been developed. They constrain‌ an ensemble of climate‌​‌ projections by some real-world​​ observations. However, there are​​​‌ many difficulties in dealing‌ with the large literature‌​‌ on OC: the methods​​ are diverse, the mathematical​​​‌ formulation and underlying assumptions‌ used are not always‌​‌ clear, and the methods​​ are often limited to​​​‌ the use of the‌ observation of only one‌​‌ variable. To address these​​ challenges, we propose in​​​‌ 18 a new statistical‌ model called ClimLoco1.0, which‌​‌ stands for "CLimate variable​​ confidence Interval of Multivariate​​​‌ Linear Observational COnstraint". It‌ describes, in a rigorous‌​‌ way, the confidence interval​​​‌ of a projected variable​ (its best guess associated​‌ with an uncertainty at​​ a confidence level) obtained​​​‌ using a multivariate linear​ OC. The article is​‌ built up in increasing​​ complexity by expressing in​​​‌ three different cases, the​ last one being ClimLoco1.0,​‌ the confidence interval of​​ a projected variable: unconstrained,​​​‌ constrained by multiple real-world​ observations assumed to be​‌ noiseless, and constrained by​​ multiple real-world observations assumed​​​‌ to be noisy. ClimLoco1.0​ thus accounts for observational​‌ noise (instrumental error and​​ climate-internal variability), which is​​​‌ sometimes neglected in the​ literature but is important​‌ as it reduces the​​ impact of the OC.​​​‌ Furthermore, ClimLoco1.0 accounts for​ uncertainty rigorously by taking​‌ into account the quality​​ of the estimators, which​​​‌ depends, for example, on​ the number of climate​‌ models considered. In addition​​ to providing an interpretation​​​‌ of the mathematical results,​ this article provides graphical​‌ interpretations based on synthetic​​ data.

Participants: Valentin Portmann​​​‌ (ASTRAL), Marie Chavent​ (ASTRAL), Didier Swingedouw​‌.

7.1.3 Détection et​​ quantification de manipulations comptables​​​‌ autour d'un seuil psychologique​ avec R.

In this​‌ work 21, we​​ study the implementation in​​​‌ R of a new​ statistical method for identifying/detecting​‌ and quantifying manipulations of​​ accounting data around psychological​​​‌ thresholds such as zero​ earnings, zero earnings variation,​‌ or earnings forecasted by​​ analysts' and investors' consensus.​​​‌ The method should also​ allow the analysis and​‌ comparison of manipulations across​​ different sub-populations. Note that​​​‌ although the current illustration​ concerns accounting-related problems and​‌ data, the code and​​ the developed methodology can​​​‌ be used in other​ fields to study behaviors​‌ in the presence of​​ psychological threshold effects. More​​​‌ specifically, an EM-type algorithm​ is proposed to estimate​‌ the underlying parameters of​​ the considered model, which​​​‌ is a mixture model​ (involving an Exponential distribution​‌ to model manipulators' behavior,​​ and a mixture of​​​‌ two Gaussian distributions to​ model the behavior of​‌ non-manipulating agents). A goodness-of-fit​​ test for assessing the​​​‌ adequacy of the model​ to the data is​‌ provided. The method also​​ delivers Bootstrap confidence intervals​​​‌ for the estimated model​ parameters. In addition, several​‌ graphical representations are available​​ via the plot function.​​​‌ After evaluating the numerical​ performance of the methodology​‌ on simulated data, the​​ proposed approach is illustrated​​​‌ on real-world data to​ study earnings management. The​‌ various R functions are​​ easy to apply to​​​‌ financial or extra-financial performance​ benchmarks, or beyond the​‌ field of accounting. An​​ R package will be​​​‌ publicly available soon.

Participants:​ Marie Chavent (ASTRAL),​‌ Delphine Féral, Jérôme​​ Saracco (ASTRAL), Véronique​​​‌ Darmendrail, Frédéric Pourtier​.

7.1.4 Algorithme de​‌ partitionnement en ligne pour​​ une compression incrémentale sans​​​‌ perte des données vibratoires​

Lossless data compression is​‌ a strategic research area​​ and a major challenge​​​‌ for data storage. In​ the context of continuous​‌ monitoring, data volumes constantly​​ increase, requiring efficient processing.​​​‌ For example, continuous compression​ for various applications such​‌ as predictive maintenance may​​ prove to be an​​​‌ effective strategy. In this​ work 22 we present​‌ an online compression method​​ that divides the signal​​ into several segments in​​​‌ order to minimize a‌ specific criterion based on‌​‌ Shannon entropy weighted by​​ the number of values​​​‌ in each partition. For‌ the compression step, the‌​‌ well-established Huffman coding method​​ is used. Furthermore, our​​​‌ approach introduces an iterative‌ process to enable online‌​‌ monitoring of the compression​​ rate. Thus, for each​​​‌ new acquisition, previously computed‌ results are reused for‌​‌ entropy calculation, which reduces​​ computational cost by avoiding​​​‌ the need to recompute‌ the criterion over the‌​‌ entire signal at each​​ iteration. In this way,​​​‌ the computation time of‌ the proposed threshold value‌​‌ remains below the sampling​​ period, allowing real-time control​​​‌ of the compression rate‌ and guaranteeing that the‌​‌ compressed file does not​​ exceed a maximum size.​​​‌ The existence of an‌ optimal value for the‌​‌ online criterion is theoretically​​ proven. To demonstrate the​​​‌ efficiency of the proposed‌ method, the approach is‌​‌ finally applied to real​​ flight data, enabling an​​​‌ optimal partitioning of the‌ signal with the smallest‌​‌ compressed file size obtained​​ at the end of​​​‌ the process. The results‌ are then compared to‌​‌ a classical Huffman-based method​​ to assess the relevance​​​‌ of the approach.

Participants:‌ Guillaume Cottin, Franck‌​‌ Cazaurang, Jérôme Saracco​​ (ASTRAL), Loïc Lavigne​​​‌, Vincent Corretja,‌ Benoît Souyri, Franck‌​‌ Tailliez.

7.1.5 Segmentation​​ and lossless compression of​​​‌ SAR data: a new‌ approach to ensure transmission‌​‌ robustness

Efficient lossless data​​ compression is essential in​​​‌ many application areas, such‌ as synthetic aperture radar‌​‌ (SAR) imaging. In addition,​​ controlling data integrity during​​​‌ the transmission process makes‌ data segmentation an attractive‌​‌ option, particularly in critical​​ applications like UAV, because,​​​‌ no preview is available.‌ In this work 23‌​‌ we present an innovative​​ method for lossless online​​​‌ data segmentation and compression,‌ based on recursive weighted‌​‌ entropy calculations and Huffman​​ coding. First, the image​​​‌ is converted into a‌ 1D signal following a‌​‌ relevant direction inspired by​​ principal component analysis. Next,​​​‌ segmentation is performed by‌ minimizing a weighted Shannon‌​‌ entropy criterion, achieving a​​ slightly higher compression ratio​​​‌ than without segmentation. The‌ approach is validated using‌​‌ opensource SAR satellite images,​​ demonstrating efficient signal partitioning​​​‌ and compression while ensuring‌ a final limit on‌​‌ compressed file size. The​​ proposed method offers a​​​‌ robust solution compatible with‌ sequential transmission and is‌​‌ particularly suited for scenarios​​ requiring reliable data flow.​​​‌

Participants: Guillaume Cottin,‌ Franck Cazaurang, Jérôme‌​‌ Saracco (ASTRAL), Loïc​​ Lavigne, Vincent Corretja​​​‌, Benoît Souyri,‌ Franck Tailliez.

7.2.1 On​​ the Particle Approximation of​​​‌ Lagged Feynman-Kac Formulae

In‌ 8, we examine‌​‌ the numerical approximation of​​ the limiting invariant measure​​​‌ associated with Feynman-Kac formulae.‌ These are expressed in‌​‌ a discrete time formulation​​ and are associated with​​​‌ a Markov chain and‌ a potential function. The‌​‌ typical application considered here​​ is the computation of​​​‌ eigenvalues associated with non-negative‌ operators as found, for‌​‌ example, in physics or​​ particle simulation of rare-events.​​​‌ We focus on a‌ novel lagged approximation of‌​‌ this invariant measure, based​​​‌ upon the introduction of​ a ratio of time-averaged​‌ Feynman-Kac marginals associated with​​ a positive operator iterated​​​‌ $l\in \mathbb{N}$ times;​ a lagged Feynman-Kac formula.​‌ This estimator and its​​ approximation using Diffusion Monte​​​‌ Carlo (DMC) have been​ extensively employed in the​‌ physics literature. In short,​​ DMC is an iterative​​​‌ algorithm involving $N\in \mathbb{N}$ particles or walkers​‌ simulated in parallel, that​​ undergo sampling and resampling​​​‌ operations. In this work,​ it is shown that​‌ for the DMC approximation​​ of the lagged Feynman-Kac​​​‌ formula, one has an​ almost sure characterization of​‌ the ${𝕃}_1$-error​​ as the time parameter​​​‌ (iteration) goes to infinity​ and this is at​‌ most of $𝒪(exp\{-\mathrm{\kappa ‌}l\}/\mathrm{N})$, for $\mathrm{\kappa ‌}>0$. In​​ addition a non-asymptotic in​​​‌ time, and time uniform​ ${𝕃}_1-$bound​‌ is proved which is​​ $𝒪(l/‌\sqrt{N})$. We​ also prove a novel​‌ central limit theorem to​​ give a characterization of​​​‌ the exact asymptotic in​ time variance. This analysis​‌ demonstrates that the strategy​​ used in physics, namely,​​​‌ to run DMC with​ $N$ and $l$ small​‌ and, for long time​​ enough, is mathematically justified.​​​‌ Our results also suggest​ how one should choose​‌ $N$ and $l$ in​​ practice. We emphasize that​​​‌ these results are not​ restricted to physical applications;​‌ they have broad relevance​​ to the general problem​​​‌ of particle simulation of​ the Feynman-Kac formula, which​‌ is utilized in a​​ great variety of scientific​​​‌ and engineering fields.

Participants:​ Elsiddig Awadelkarim, Michel​‌ Caffarel, Pierre del​​ Moral (ASTRAL), Ajay​​​‌ Jasra.

7.2.2 On​ the Mathematical foundations of​‌ Diffusion Monte Carlo

The​​ Diffusion Monte Carlo method​​​‌ with constant number of​ walkers, also called Stochastic​‌ Reconfiguration as well as​​ Sequential Monte Carlo, is​​​‌ a widely used Monte​ Carlo methodology for computing​‌ the ground-state energy and​​ wave function of quantum​​​‌ systems. In 9,​ we present the first​‌ mathematically rigorous analysis of​​ this class of stochastic​​​‌ methods on non necessarily​ compact state spaces, including​‌ linear diffusions evolving in​​ quadratic absorbing potentials, yielding​​​‌ what seems to be​ the first result of​‌ this type for this​​ class of models. We​​​‌ present a novel and​ general mathematical framework with​‌ easily checked Lyapunov stability​​ conditions that ensure the​​​‌ uniform-in-time convergence of Diffusion​ Monte Carlo estimates towards​‌ the top of the​​ spectrum of Schrödinger operators.​​​‌ For transient free evolutions,​ we also present a​‌ divergence blow up of​​ the estimates w.r.t. the​​​‌ time horizon even when​ the asymptotic fluctuation variances​‌ are uniformly bounded. We​​ also illustrate the impact​​​‌ of these results in​ the context of generalized​‌ coupled quantum harmonic oscillators​​ with non necessarily reversible​​​‌ nor stable diffusive particle​ and a quadratic energy​‌ absorbing well associated with​​ a semi-definite positive matrix​​​‌ force.

Participants: Michel Caffarel​, Pierre del Moral​‌ (ASTRAL), Luc de​​ Montella (ASTRAL).

7.2.3​​​‌ On time uniform Wong-Zakai​ approximation theorems

In 17​‌, we consider the​​ long time behavior of​​ Wong-Zakai approximations of stochastic​​​‌ differential equations. These piecewise‌ smooth diffusion approximations are‌​‌ of great importance in​​ many areas, such as​​​‌ those with ordinary differential‌ equations associated to random‌​‌ smooth fluctuations; e.g. robust​​ filtering problems. In many​​​‌ examples, the mean error‌ estimate bounds that have‌​‌ been derived in the​​ literature can grow exponentially​​​‌ with respect to the‌ time horizon. We show‌​‌ in a simple example​​ that indeed mean error​​​‌ estimates do explode exponentially‌ in the time parameter,‌​‌ i.e. in that case​​ a Wong-Zakai approximation is​​​‌ only useful for extremely‌ short time intervals. Under‌​‌ spectral conditions, we present​​ some quantitative time-uniform convergence​​​‌ theorems, i.e. time-uniform mean‌ error bounds, yielding what‌​‌ seems to be the​​ first results of this​​​‌ type for Wong-Zakai diffusion‌ approximations.

Participants: Pierre del‌​‌ Moral (ASTRAL), Shulan​​ Hu, Ajay Jasra​​​‌, Hamza Ruzayqat,‌ Xinyu Wang.

7.2.4‌​‌ Study of particle methods​​ in nonlinear filtering :​​​‌ application to passive trajectography‌

This thesis 25 presents‌​‌ a theoretical and applied​​ study of particle filtering​​​‌ methods, with the aim‌ of increasing confidence in‌​‌ their use for critical​​ applications, such as in​​​‌ the military or underwater‌ domains. First, we focus‌​‌ on the Diffusion Monte​​ Carlo (DMC) method, a​​​‌ variant of particle methods‌ used in physics to‌​‌ compute the ground state​​ of quantum systems. We​​​‌ establish assumptions that guarantee‌ the uniform-in-time convergence of‌​‌ this method on non-compact​​ state spaces while ensuring​​​‌ that the conditions remain‌ flexible enough to include‌​‌ Gaussian linear models. This​​ work is the first​​​‌ result of its kind‌ for particle methods. In‌​‌ order to provide a​​ concrete example that satisfies​​​‌ our assumptions and to‌ study the implications of‌​‌ our theorem, we perform​​ a detailed analysis of​​​‌ the coupled harmonic oscillator.‌ This study allows us‌​‌ to highlight cases in​​ which the DMC exhibits​​​‌ asymptotic convergence properties, even‌ though its error diverges‌​‌ for any finite number​​ of particles. This result​​​‌ underscores the importance of‌ establishing uniform-in-time convergence guarantees.‌​‌ Furthermore, we show that​​ this divergence is not​​​‌ inevitable : a modification‌ of DMC can be‌​‌ sufficient to ensure its​​ convergence, thereby opening new​​​‌ perspectives for its application‌ to more complex systems.‌​‌ Following on from our​​ theoretical work, we explore​​​‌ the question of passive‌ trajec- tography, with the‌​‌ aim of improving the​​ performance of particle-based methods.​​​‌ To this end, we‌ propose first to integrate‌​‌ sound pressure level measurements​​ with the angle measurements​​​‌ traditionally used for tracking.‌ Our numerical studies show‌​‌ that this approach significantly​​ improves tracking accuracy. In​​​‌ addition, we demonstrate that‌ combining this new data‌​‌ with a more realistic​​ conical angle measurement and​​​‌ a Doppler frequency shift‌ measurement enhances the robustness‌​‌ and efficiency of our​​ method. This encouraging result​​​‌ opens promising prospects for‌ future applications, but the‌​‌ study presented here is​​ only a first step​​​‌ before the method can‌ be fully operational in‌​‌ real-world conditions. In order​​ to propose an immediately​​​‌ applicable solution, we perform‌ an in-depth analysis of‌​‌ the quality of information​​​‌ in the context of​ passive bearing-based localization. During​‌ this analysis, we study​​ the Fisher information associated​​​‌ with the bearing-based localization​ problem, as well as​‌ the convergence properties of​​ the position estimators. This​​​‌ work leads to the​ definition of a ma-​‌ neuvering protocol that allows​​ an observer to localize​​​‌ a target with precision​ and efficiency.

Participants: Luc​‌ de Montella (ASTRAL).​​

7.2.5 On the contraction​​​‌ properties of Sinkhorn semigroups​

We develop in 26​‌ a novel semigroup stability​​ analysis based on Lyapunov​​​‌ techniques and contraction coefficients​ to prove exponential convergence​‌ of Sinkhorn equations on​​ weighted Banach spaces. This​​​‌ operator-theoretic framework yields exponential​ decays of Sinkhorn iterates​‌ towards Schrödinger bridges with​​ respect to general classes​​​‌ of $\Phi$-divergences and​ Kantorovich-type criteria, including the​‌ relative entropy, squared Hellinger​​ integrals, $\alpha$-divergences as​​​‌ well as weighted total​ variation norms and Wasserstein​‌ distances. To the best​​ of our knowledge, these​​​‌ contraction inequalities are the​ first results of this​‌ type in the literature​​ on entropic transport and​​​‌ the Sinkhorn algorithm. We​ also provide Lyapunov contractions​‌ principles under minimal regularity​​ conditions that allow to​​​‌ provide quantitative exponential stability​ estimates for a large​‌ class of Sinkhorn semigroups.​​ We apply this novel​​​‌ framework in a variety​ of situations, ranging from​‌ polynomial growth potentials and​​ heavy tailed marginals on​​​‌ general normed spaces to​ more sophisticated boundary state​‌ space models, including semi-circle​​ transitions, Beta, Weibull, exponential​​​‌ marginals as well as​ semi-compact models. Last but​‌ not least, our approach​​ also allows to consider​​​‌ statistical finite mixture of​ the above models, including​‌ kernel-type density estimators of​​ complex data distributions arising​​​‌ in generative modeling.

Participants:​ Deniz Akyildiz, Pierre​‌ del Moral (ASTRAL),​​ Joaquin Miguez.

7.2.6​​​‌ Particle Filtering for Non-Deterministic​ Electrocardiographic Imaging

Electrocardiographic imaging​‌ (ECGI) aims to non-invasively​​ reconstruct activation maps of​​​‌ the heart from temporal​ body surface potentials. While​‌ most existing approaches rely​​ on inverse and optimization​​​‌ techniques that may yield​ satisfactory reconstructions, they typically​‌ provide a single deterministic​​ solution, overlooking the inherent​​​‌ uncertainty of the problem​ stemming from its very​‌ ill-posed nature, the poor​​ knowledge of biophysical features​​​‌ and the unavoidable presence​ of noise in the​‌ measurements. The Bayesian framework,​​ which naturally incorporates uncertainty​​​‌ while also accounting for​ temporal correlations across time​‌ steps, can be used​​ to address this limitation.​​​‌ In 30, we​ propose a low-dimensional representation​‌ of the activation sequence​​ that enables the use​​​‌ of particle filtering, a​ Bayesian filtering method that​‌ does not rely on​​ predefined assumptions regarding the​​​‌ shape of the posterior​ distribution, in contrast to​‌ approaches like the Kalman​​ filter. This allows to​​​‌ produce not only activation​ maps but also probabilistic​‌ maps indicating the likelihood​​ of activation at each​​​‌ point on the heart​ over time, as well​‌ as pseudo-probability maps reflecting​​ the likelihood of a​​​‌ point being part of​ an earliest activation site.​‌ Additionally, we introduce a​​ method to estimate the​​​‌ probability of the presence​ of a conduction lines​‌ of block on the​​ heart surface. Combined with​​ classical reconstruction techniques, this​​​‌ could help discriminate artificial‌ from true lines of‌​‌ block in activation maps.​​ We support our approach​​​‌ with a numerical study‌ based on simulated data,‌​‌ demonstrating the potential of​​ our method.

Participants: Emma​​​‌ Lagracie, Luc de‌ Montella (ASTRAL).

7.2.7‌​‌ Entropic continuity bounds for​​ conditional covariances with applications​​​‌ to Schrödinger and Sinkhorn‌ bridges

In 31,‌​‌ we present new entropic​​ continuity bounds for conditional​​​‌ expectations and conditional covariance‌ matrices. These bounds are‌​‌ expressed in terms of​​ the relative entropy between​​​‌ different coupling distributions. Our‌ approach combines Wasserstein coupling‌​‌ with quadratic transportation cost​​ inequalities. We illustrate the​​​‌ impact of these results‌ in the context of‌​‌ entropic optimal transport problems.​​ The entropic continuity theorem​​​‌ presented in the article‌ allows to estimate the‌​‌ conditional expectations and the​​ conditional covariances of Schrödinger​​​‌ and Sinkhorn transitions in‌ terms of the relative‌​‌ entropy between the corresponding​​ bridges. These entropic continuity​​​‌ bounds turns out to‌ be a very useful‌​‌ tool for obtaining remarkably​​ simple proofs of the​​​‌ exponential decays of the‌ gradient and the Hessian‌​‌ of Schrödinger and Sinkhorn​​ bridge potentials.

Participants: Pierre​​​‌ del Moral (ASTRAL).‌

7.2.8 On the Kantorovich‌​‌ contraction of Markov semigroups​​

In 32, we​​​‌ develop a novel operator‌ theoretic framework to study‌​‌ the contraction properties of​​ Markov semigroups with respect​​​‌ to a general class‌ of Kantorovich semi-distances, which‌​‌ notably includes Wasserstein distances.​​ The rather simple contraction​​​‌ cost framework developed in‌ this article, which combines‌​‌ standard Lyapunov techniques with​​ local contraction conditions, helps​​​‌ to unifying and simplifying‌ many arguments in the‌​‌ stability of Markov semigroups,​​ as well as to​​​‌ improve upon some existing‌ results. Our results can‌​‌ be applied to both​​ discrete time and continuous​​​‌ time Markov semigroups, and‌ we illustrate their wide‌​‌ applicability in the context​​ of (i) Markov transitions​​​‌ on models with boundary‌ states, including bounded domains‌​‌ with entrance boundaries, (ii)​​ operator products of a​​​‌ Markov kernel and its‌ adjoint, including two-block-type Gibbs‌​‌ samplers, (iii) iterated random​​ functions and (iv) diffusion​​​‌ models, including overdampted Langevin‌ diffusion with convex at‌​‌ infinity potentials.

Participants: Pierre​​ del Moral (ASTRAL),​​​‌ Mathieu Gerber.

7.2.9‌ Stability of Schrödinger bridges‌​‌ and Sinkhorn semigroups for​​ log-concave models

In 33​​​‌ we obtain several new‌ results and developments in‌​‌ the study of entropic​​ optimal transport problems (a.k.a.​​​‌ Schrödinger problems) with general‌ reference distributions and log-concave‌​‌ target marginal measures. Our​​ approach combines transportation cost​​​‌ inequalities with the theory‌ of Riccati matrix difference‌​‌ equations arising in filtering​​ and optimal control theory.​​​‌ This methodology is partly‌ based on a novel‌​‌ entropic stability of Schrödinger​​ bridges and closed form​​​‌ expressions of a class‌ of discrete time algebraic‌​‌ Riccati equations. In the​​ context of regularized entropic​​​‌ transport these techniques provide‌ new sharp entropic map‌​‌ estimates. When applied to​​ the stability of Sinkhorn​​​‌ semigroups, they also yield‌ a series of novel‌​‌ contraction estimates in terms​​ of the fixed point​​​‌ of Riccati equations. The‌ strength of our approach‌​‌ is that it is​​​‌ applicable to a large​ class of models arising​‌ in machine learning and​​ artificial intelligence algorithms. We​​​‌ illustrate the impact of​ our results in the​‌ context of regularized entropic​​ transport, proximal samplers and​​​‌ diffusion generative models as​ well as diffusion flow​‌ matching models

Participants: Pierre​​ del Moral (ASTRAL).​​​‌

7.2.10 Target motion analysis​ using angular measurements and​‌ underwater sound pressure levels​​

In 16 we address​​​‌ the problem of target​ motion analysis using data​‌ acquired by sonars operating​​ in passive mode. Most​​​‌ theoretical and applied studies​ rely solely on bearing​‌ information, and various filtering​​ algorithms, especially particle filter​​​‌ methods, have demonstrated strong​ performance in this context.​‌ To improve upon existing​​ approaches, bearing information is​​​‌ combined with received underwater​ sound pressure levels. This​‌ method requires no additional​​ sensors compared to bearings-only​​​‌ trackings, as hydrophones—already used​ for beamforming—can also measure​‌ sound pressure levels. Additionally,​​ underwater transmission losses can​​​‌ be estimated through simulations​ based on commonly available​‌ environmental data. The effectiveness​​ of the proposed method​​​‌ is demonstrated using simulated​ data, showing improved performance—especially​‌ in scenarios without observer​​ maneuvers. To increase realism,​​​‌ the impact of replacing​ bearing measurements with conical​‌ angle measurements is also​​ investigated. These measurements account​​​‌ for both elevation and​ bearing angles, thereby providing​‌ a fairly comprehensive characterization​​ of bottom-bounce paths commonly​​​‌ encountered under real-world conditions.​ This enables exploration of​‌ scenarios with different immersion​​ levels for both target​​​‌ and observer. The results​ further emphasize the benefits​‌ of incorporating sound pressure​​ levels measurements into the​​​‌ tracking process.

Participants: Enzo​ Iglésis, Luc de​‌ Montella (ASTRAL).

7.3.1 Non-stationary value iteration​ for adaptive average control​‌ of piecewise deterministic Markov​​ processes

The main goal​​​‌ of 10 is to​ present a non-stationary value​‌ iteration adaptive average control​​ for Piecewise Deterministic Markov​​​‌ Processes (PDMPs), introduced by​ M.H.A. Davis, as a​‌ family of continuous-time Markov​​ processes punctuated by random​​​‌ jumps and with inter-jump​ movement driven by a​‌ deterministic flow. It is​​ assumed in this paper​​​‌ that there are no​ boundary jumps. We study​‌ the adaptive average optimal​​ control problem of PDMPs,​​​‌ considering that the jump​ intensity $\lambda$, the​‌ post-jump transition kernel $\mathrm{Q}$, as well as​​​‌ the cost $C$ depend​ on an unknown parameter​‌ ${\beta }^{*}$. For​​ a sequence of strongly​​​‌ consistent estimators $\left\{{\mathrm{\beta }}_n^{*}\right\}$ of​‌ ${\beta }^{*}$ (that is,​​ ${\beta }_n^{*}$ converge​​​‌ to ${\beta }^{*}$ almost​ surely) a non-stationary value​‌ iteration (depending on the​​ current estimate ${\beta }_{\mathrm{n‌}}^{*}$) is shown​ to be optimal for​‌ the long-run average control​​ problem. We assume a​​​‌ total variation norm condition​ on the parameters $\mathrm{\lambda ‌}$ and $Q$ of the​​ process (which generalizes the​​​‌ minorization condition considered in​ the literature), resulting in​‌ a span-contraction operator. The​​ paper concludes with a​​​‌ numerical example.

Participants: O.L.V​ Costa, François Dufour​‌ (ASTRAL), Alexandre Genadot​​ (ASTRAL).

7.3.2 Minimum​​​‌ Contrast Estimators for Piecewise​ Deterministic Markov Processes

The​‌ main goal of this​​ paper 11 is to​​ study the minimum contrast​​​‌ estimator (MCE) approach for‌ the parameter estimation problem‌​‌ of piecewise deterministic Markov​​ processes (PDMPs), associated to​​​‌ adaptive control problems. It‌ is assumed that the‌​‌ control acts continuously on​​ the jump intensity $\mathrm{\lambda ‌}$ and on the transition‌ measure $Q$ of the‌​‌ process, as well as​​ on the costs, and​​​‌ that these parameters depend‌ on an unknown parameter‌​‌ ${\beta }^{*}$. One​​ of our objective is​​​‌ to introduce a minimum‌ contrast estimator ${\left({\mathrm{\beta ‌‌}}_n\right)}_{n\in \mathbb{N}}$ for the family​​​‌ of PDMPs. Sufficient conditions‌ are then presented to‌​‌ ensure that ${\left({\mathrm{\beta }}_n\right)}_{n\in ‌\mathbb{N}}$ is a strongly‌ consistent estimator of ${\mathrm{\beta ‌‌}}^{*}$. It should​​ be noticed that PDMPs​​​‌ are characterized by a‌ deterministic motion punctuated by‌​‌ random jumps (either spontaneous​​ or due to the​​​‌ flow touching a boundary),‌ which brings new challenges‌​‌ in the analysis of​​ the problem. The paper​​​‌ is concluded with a‌ numerical example for the‌​‌ adaptive discounted control of​​ PDMPs.

Participants: O.L.V Costa​​​‌, François Dufour (ASTRAL)‌, Alexandre Genadot (ASTRAL)‌​‌.

7.3.3 Absorbing Markov​​ decision processes and their​​​‌ occupation measures.

In 13‌, we consider an‌​‌ absorbing Markov decision process​​ with Borel state and​​​‌ action spaces. We study‌ conditions under which the‌​‌ MDP is uniformly absorbing​​ and the set of​​​‌ occupation measures of the‌ MDP is compact in‌​‌ the usual weak topology.​​ These include suitable continuity​​​‌ requirements on the transition‌ kernel and conditions on‌​‌ the dynamics of the​​ system at the boundary​​​‌ of the absorbing set.‌ We generalize previously known‌​‌ results and give an​​ answer to some conjectures​​​‌ that have been mentioned‌ in the related literature.‌​‌

Participants: François Dufour (ASTRAL)​​, Tomas Prieto-Rumeau.​​​‌

7.3.4 The bearing only‌ localization problem via partially‌​‌ observed Markov decision process​​

In 12, We​​​‌ consider the classical problem‌ of localization of a‌​‌ target from an observer​​ from bearing measurements. We​​​‌ reformulate this problem within‌ the framework of the‌​‌ theory of partially observed​​ Markov decision processes and​​​‌ propose a method for‌ numerically solving this problem.‌​‌ Theoretical convergence of this​​ numerical solution scheme is​​​‌ obtained and numerical investigations‌ are also carried out,‌​‌ enabling us to recover​​ optimal curves already suggested​​​‌ in the literature via‌ other techniques.

Participants: François‌​‌ Dufour (ASTRAL), Alexandre​​ Genadot (ASTRAL), Romain​​​‌ Namyst.

7.3.5 Asymptotic‌ optimality of a class‌​‌ of controlled non-Markov processes​​

Motivated by applications in​​​‌ power systems and problems‌ arising in simulation of‌​‌ large scale complex system​​ optimizations, this work is​​​‌ concerned with controlled stochastic‌ switching systems. The system‌​‌ of interest displays a​​ multi-time scale structure. In​​​‌ contrast to the so-called‌ singularly perturbed diffusions and‌​‌ multi-scale Markov decision processes,​​ controlled non-Markov processes (also​​​‌ known as non-Markov decision‌ processes) are treated. The‌​‌ novelty of this work​​ 14 is the treatment​​​‌ of the non-Markov controlled‌ processes and the time-scale‌​‌ used. The fast and​​ slow processes are coupled​​​‌ through a stochastic differential‌ equation. Using averaging, it‌​‌ is first shown that​​​‌ the non-Markov switching process​ has a weak limit​‌ that is a Markov​​ decision process. Then asymptotic​​​‌ optimal control of the​ non-Markov process is obtained​‌ by using the limit​​ process.

Participants: François Dufour​​​‌ (ASTRAL), Ky Tran​, Le Yi Wang​‌, George Yin.​​

7.3.6 About Fisher Information​​​‌ Matrix and Self-Optimizing Control​ in Bearing Only Localization​‌

In 29, we​​ revisit the results of​​​‌ Optimal observer motion for​ localization with bearing measurements​‌ from Hammel, Liu, Hilliard,​​ and Gong concerning the​​​‌ lower bound associated with​ the determinant of the​‌ Fisher information matrix for​​ bearing only localization. We​​​‌ specify this bound and​ use the associated optimality​‌ curves to construct an​​ adaptive control for locating​​​‌ the position of a​ target using only noisy​‌ bearing measurements. For this​​ self-optimizing control, the target​​​‌ position estimate is updated​ using a contrast miminmum​‌ estimator whose strong consistency​​ is proved. Numerical simulations​​​‌ allow us to discuss​ the effectiveness of the​‌ proposed method.

Participants: Alexandre​​ Genadot (ASTRAL), Enzo​​​‌ Iglésis (ASTRAL), Luc​ de Montella (ASTRAL).​‌

7.4.1 Multiscale entropy rates:​ a study on different​‌ stochastic processes

Participants: Eric​​ Grivel, Pierrick Legrand​​​‌ (ASTRAL), Bastien Berthelot​.

In 15,​‌ we propose to analyze​​ the behavior of the​​​‌ entropy rate (ER) when​ applied to a signal​‌ and its coarse-grained versions.​​ The “multiscale entropy rate”​​​‌ (MSER) is deduced by​ storing in a vector​‌ the resulting ERs. Our​​ contribution consists in studying​​​‌ the MSER calculated on​ different stochastic processes. When​‌ dealing with Gaussian complex​​ or real moving average​​​‌ (MA) processes or autoregressive​ (AR) processes, which can​‌ be seen as the​​ filtering of a white​​​‌ Gaussian driving process, the​ MSER depends on the​‌ variances of the driving​​ processes of the corresponding​​​‌ minimum-phase ARMA process at​ each scale. More particularly,​‌ we derive the analytical​​ expression of the MSER​​​‌ for 1st -order​ MA or AR processes​‌ using different approaches. This​​ study allows us to​​​‌ better understand what each​ scale brings in and​‌ to describe the behavior​​ of the MSER for​​​‌ these types of processes.​ We also show that​‌ there is a mapping​​ between the stochastic-process parameters​​​‌ and the ER computed​ at different scales. Finally,​‌ we show that the​​ multiscale procedure is not​​​‌ relevant for a sum​ of complex exponentials disturbed​‌ by an additive white​​ Gaussian noise.

7.4.2 Empirical​​​‌ Results for Adjusting Truncated​ Backpropagation Through Time while​‌ Training Neural Audio Effects​​

In 19 we investigate​​​‌ the optimization of Truncated​ Backpropagation Through Time (TBPTT)​‌ for training neural networks​​ in digital audio effect​​​‌ modeling, with a focus​ on dynamic range compression.​‌ The study evaluates key​​ TBPTT hyperparameters – sequence​​​‌ number, batch size, and​ sequence length – and​‌ their influence on model​​ performance. Using a convolutional-recurrent​​​‌ architecture, we conduct extensive​ experiments across datasets with​‌ and without conditionning by​​ user controls. Results demonstrate​​​‌ that carefully tuning these​ parameters enhances model accuracy​‌ and training stability, while​​ also reducing computational demands.​​ Objective evaluations confirm improved​​​‌ performance with optimized settings,‌ while subjective listening tests‌​‌ indicate that the revised​​ TBPTT configuration maintains high​​​‌ perceptual quality.

Participants: Yann‌ Bourdin (ASTRAL), Pierrick‌​‌ Legrand (ASTRAL), Fanny​​ Roche.

7.4.3 Multiscale​​​‌ cross entropy rate as‌ a way to compare‌​‌ signals: application to Gaussian​​ ARMA processes

The entropy​​​‌ rate of a stochastic‌ process corresponds to the‌​‌ asymptotic difference between the​​ entropies of consecutive sample​​​‌ blocks as their size‌ increases. Widely used in‌​‌ information theory, it also​​ serves as a key​​​‌ marker for signal characterization‌ in classification tasks. Recently,‌​‌ we studied the entropy​​ rate of a signal​​​‌ at different scales using‌ a multiscale approach. The‌​‌ latter generates a set​​ of signals from the​​​‌ original one either (i)‌ by applying a coarse-graining‌​‌ (CG) procedure —where the​​ signal is filtered with​​​‌ an average filter of‌ order equal to the‌​‌ scale and then decimated​​ by a factor equal​​​‌ to the scale— or‌ (ii) by directly decimating‌​‌ the original signal. In​​ 20, we extend​​​‌ the multiscale framework to‌ the cross-entropy rate, introducing‌​‌ the multiscale cross-entropy rate​​ (MCER). MCER can be​​​‌ defined either as the‌ sum of cross-entropy rates‌​‌ across scales or as​​ a vector storing these​​​‌ values. By applying it‌ to Gaussian ARMA processes,‌​‌ we aim to understand​​ the insights provided by​​​‌ the multiscale procedure and‌ to define the influence‌​‌ of the process parameters​​ on the cross-entropy rate​​​‌ at each scale. To‌ this end, we present‌​‌ the properties of ARMA​​ processes after applying the​​​‌ multiscale procedure, provide analytical‌ expressions for the MCER,‌​‌ and outline a practical​​ method for deriving it.​​​‌ The MCER is a‌ potential alternative to multiscale‌​‌ cross-sample entropy and its​​ variants, which have been​​​‌ used in biomedical applications‌ and finance to quantify‌​‌ joint synchrony between signals.​​

Participants: Eric Grivel,​​​‌ Pierrick Legrand (ASTRAL),‌ Bastien Berthelot.

7.4.4‌​‌ Time-Varying Audio Effect Modeling​​ by End-to-End Adversarial Training​​​‌

Deep learning has become‌ a standard approach for‌​‌ the modeling of audio​​ effects, yet strictly black-box​​​‌ modeling remains problematic for‌ time-varying systems. Unlike time-invariant‌​‌ effects, training models on​​ devices with internal modulation​​​‌ typically requires the recording‌ or extraction of control‌​‌ signals to ensure the​​ time-alignment required by standard​​​‌ loss functions. In 27‌ we introduce a Generative‌​‌ Adversarial Network (GAN) framework​​ to model such effects​​​‌ using only input-output audio‌ recordings, removing the need‌​‌ for modulation signal extraction.​​ We propose a convolutional-recurrent​​​‌ architecture trained via a‌ two-stage strategy: an initial‌​‌ adversarial phase allows the​​ model to learn the​​​‌ distribution of the modulation‌ behavior without strict phase‌​‌ constraints, followed by a​​ supervised fine-tuning phase where​​​‌ a State Prediction Network‌ (SPN) estimates the initial‌​‌ internal states required to​​ synchronize the model with​​​‌ the target. Additionally, a‌ new objective metric based‌​‌ on chirp-train signals is​​ developed to quantify modulation​​​‌ accuracy. Experiments modeling a‌ vintage hardware phaser demonstrate‌​‌ the method's ability to​​ capture time-varying dynamics in​​​‌ a fully black-box context.‌

Participants: Yann Bourdin (ASTRAL)‌​‌, Pierrick Legrand (ASTRAL)​​​‌, Fanny Roche.​

7.4.5 Epidemic Forecasting: Lessons​‌ Learned from the SARS-CoV-2​​ Pandemic to Balance Accuracy,​​​‌ Feasibility, and Impact

The​ COVID-19 pandemic highlighted the​‌ importance of reliable, real-time​​ hospital forecasting. At Bordeaux​​​‌ University Hospital, we developed​ models to predict SARS-CoV-2-related​‌ hospitalizations 14 days in​​ advance using integrated data​​​‌ sources. We identified six​ key lessons to guide​‌ future epidemic response: (1)​​ Multimodal data improves accuracy;​​​‌ (2) Simple baseline models​ are essential for benchmarking​‌ and building trust; (3)​​ Model and metric choices​​​‌ must align with decision​ goals which often means​‌ prioritizing absolute over relative​​ metrics and beginning with​​​‌ simple models; (4) Prediction​ intervals should be provided​‌ to communicate the uncertainty​​ associated with forecasts; (5)​​​‌ Real-world constraints such as​ computational cost, maintainability, and​‌ required expertise should guide​​ model selection; (6) Forecasts​​​‌ must be contextualized and​ commu- nicated carefully to​‌ policymakers. In 28 we​​ advocate for a systems-level​​​‌ forecasting approach that balances​ accuracy, feasibility, and impact.​‌

Participants: Thomas Ferté,​​ Vincent Thevenet, Xavier​​​‌ Hinaut, Pierrick Legrand​ (ASTRAL), Dan Dutartre​‌, Romain Griffier,​​ Viannet Jouhet, Boris​​​‌ Hejblum, Rodolphe Thiébaut​.

7.4.6 L'IA se​‌ met au rock.

Advances​​ in computing power and​​​‌ AI now make it​ possible to faithfully reproduce​‌ the sound of the​​ legendary tube amplifiers that​​​‌ delighted generations of guitarists.​ In this paper 34​‌, published in french,​​ we examine how these​​​‌ digital breakthroughs are already​ reshaping the landscape of​‌ music.

Participants: Hugo Leroux​​, Tara Vanhatalo (ASTRAL)​​​‌, Pierrick Legrand (ASTRAL)​.

Naval Group

Participants:​ Denis Arrivault, Pierre​‌ del Moral, François​​ Dufour, Alexandre Genadot​​​‌, Enzo Iglésis,​ Dann Laneuville, Adrien​‌ Nègre.

In the​​ application domain, an important​​​‌ research focus of the​ team is the tracking​‌ of passive underwater targets​​ in the context of​​​‌ passive underwater acoustic warfare.​ This is a very​‌ complicated practical problem that​​ combines both filtering and​​​‌ stochastic control issues. This​ research topic is addressed​‌ in collaboration with Naval​​ Group. We refer the​​​‌ reader to the section​ 4.1 for a more​‌ detailed description of this​​ theme.

Thales AVS

Participants:​​​‌ Bastien Berthelot, Pierrick​ Legrand.

The collaboration​‌ is centered around some​​ contributions to the estimation​​​‌ of the Hurst coefficient​ and his application on​‌ biosignals in the domain​​ of crew monitoring.

Case​​​‌ Law Analytics

Participants: Pierrick​ Legrand.

Pierrick Legrand​‌ is a consultant for​​ the startup Pyxiscience. The​​​‌ object of the consulting​ is confidential.

Thales DMS​‌

Participants: Jérôme Saracco.​​

The aim of this​​​‌ collaboration is to develop​ lossless data compression methodologies​‌ for vibration data from​​ Rafale flights and SAR​​​‌ radar images.

It has​ resulted in a patent​‌ entitled "Procédé de prise​​ de décision rapide utilisant​​​‌ une décomposition en plans​ de bits pour une​‌ compression sans perte des​​ images radar".

The results​​​‌ obtained were presented at​ two conferences (DASC 2025​‌ and SAGIP 2025).

Orosys

Participants:‌​‌ Tara Vanhatalo, Pierrick​​ Legrand.

Within the​​​‌ framework of Tara Vanhatalo’s‌ Cifre PhD thesis on‌​‌ the stochastic modeling of​​ guitar amplifiers, a strong​​​‌ collaboration was established between‌ the company Orosys and‌​‌ the ASTRAL team.

Arturia​​

Participants: Yann Bourdin,​​​‌ Pierrick Legrand.

Within‌ the framework of Yann‌​‌ Bourdin’s Cifre PhD thesis​​ on the stochastic modeling​​​‌ of audio compressor and‌ nonlinear audio effects, a‌​‌ strong collaboration was established​​ between the company Arturia​​​‌ and the ASTRAL team.‌

9.1.1 Participation in‌​‌ other International Programs

Participants:​​ Francois Dufour.

Scientific​​​‌ cooperation with Spain funded‌ by the Spanish Ministry‌​‌ of Science and Innovation​​ (reference number PID2021-122442NB-I00). This​​​‌ project focuses on the‌ analysis and control of‌​‌ deterministic/stochastic dynamic systems and​​ on game theory (2022-2025).​​​‌

9.2.1 Visits of international‌​‌ scientists

Naval Group

Astral is‌ a joint INRIA team‌​‌ project with Naval Group.​​ The topic of this​​​‌ collaboration is described in‌ section 4.1.

QuAMProcs‌​‌ of the program Project​​ Blanc of the ANR​​​‌

The mathematical analysis of‌ metastable processes started 75‌​‌ years ago with the​​ seminal works of Kramers​​​‌ on Fokker-Planck equation. Although‌ the original motivation of‌​‌ Kramers was to «​​ elucidate some points in​​​‌ the theory of the‌ velocity of chemical reactions‌​‌ », it turns out​​ that Kramers’ law is​​​‌ observed to hold in‌ many scientific fields: molecular‌​‌ biology (molecular dynamics), economics​​ (modelization of financial bubbles),​​​‌ climate modeling, etc. Moreover,‌ several widely used efficient‌​‌ numerical methods are justified​​ by the mathematical description​​​‌ of this phenomenon.

Recently,‌ the theory has witnessed‌​‌ some spectacular progress thanks​​ to the insight of​​​‌ new tools coming from‌ Spectral and Partial Differential‌​‌ Equations theory.

Semiclassical methods​​ together with spectral analysis​​​‌ of Witten Laplacian gave‌ very precise results on‌​‌ reversible processes. From a​​ theoretical point of view,​​​‌ the semiclassical approach allowed‌ to prove a complete‌​‌ asymptotic expansion of the​​ small eigen values of​​​‌ Witten Laplacian in various‌ situations (global problems, boundary‌​‌ problems, degenerate diffusions, etc.).​​ The interest in the​​​‌ analysis of boundary problems‌ was rejuvenated by recent‌​‌ works establishing links between​​ the Dirichlet problem on​​​‌ a bounded domain and‌ the analysis of exit‌​‌ event of the domain.​​ These results open numerous​​​‌ perspectives of applications. Recent‌ progress also occurred on‌​‌ the analysis of irreversible​​ processes (e.g. on overdamped​​​‌ Langevin equation in irreversible‌ context or full (inertial)‌​‌ Langevin equation).

The above​​​‌ progresses pave the way​ for several research tracks​‌ motivating our project: overdamped​​ Langevin equations in degenerate​​​‌ situations, general boundary problems​ in reversible and irreversible​‌ case, non-local problems, etc.​​

10.1.1 Journal​‌

10.2.1 Teaching

• J.​​​‌ Saracco is the head​ of the engineering department​‌ of ENSC, Graduate School​​ of Cognitics (applied cognitive​​​‌ science and technology), which​ is a Bordeaux INP​‌ engineering school.
• Alexandre Genadot​​ is the head of​​​‌ the MIASHS Licence of​ the Université de Bordeaux.​‌
• Pierrick Legrand is in​​ charge of the IBM​​​‌ Chair at ENSC.
• Licence:​ P. Legrand, Espaces Euclidiens​‌, 46.5h, L2, Université​​ de Bordeaux, France.
• Licence:​​​‌ P. Legrand, Informatique pour​ les mathématiques, 30h,​‌ L3, Université de Bordeaux,​​ France.
• DU: P. Legrand,​​​‌ Évolution Artificielle, Big Data​, 8h, DU, Bordeaux​‌ INP, France.
• Engineer School:​​ Signal Processing, ENSC,​​​‌ Bordeaux, 1A, France.
• Engineer​ School: Signal Processing,​‌ 54 hours, ENSC, Bordeaux,​​ 2A, France.
• Master: Scientific​​​‌ courses, 10 hours, Université​ de Bordeaux, France.
• Licence:​‌ A. Genadot, Bases en​​ Probabilités, 18h, L1,​​​‌ Université de Bordeaux, France.​
• Licence: A. Genadot, Projet​‌ Professionnel de l'Étudiant,​​ 8h, L1, Université de​​​‌ Bordeaux, France.
• Licence: A.​ Genadot, Probabilité, 30h,​‌ L2, Université de Bordeaux,​​ France.
• Licence: A. Genadot,​​​‌ Techniques d'Enquêtes, 10h,​ L2, Université de Bordeaux,​‌ France.
• Licence: A. Genadot,​​ Modélisation Statistique, 16.5h,​​​‌ L3, Université de Bordeaux,​ France.
• Licence: A. Genadot,​‌ Préparation Stage, 15h,​​ L3, Université de Bordeaux,​​​‌ France.
• Licence: A. Genadot,​ TER, 5h, L3,​‌ Université de Bordeaux, France.​​
• Licence: A. Genadot, Processus​​​‌, 16.5h, L3, Université​ de Bordeaux, France.
• Licence:​‌ A. Genadot, Statistiques,​​ 20h, L3, Bordeaux INP,​​ France.
• Master: A. Genadot,​​​‌ Savoirs Mathématiques, 81h,‌ M1, Université de Bordeaux‌​‌ and ESPE, France.
• Master:​​ A. Genadot, Martingales,​​​‌ 29h, M1, Université de‌ Bordeaux, France.
• Licence: F.‌​‌ Dufour, Probabilités et Statistiques​​, 70h, first year​​​‌ of ENSEIRB-MATMECA engineering school,‌ Bordeaux INP, France.
• Master:‌​‌ F. Dufour, Probabilistic Approach​​ and Monte Carlo Methods​​​‌, 24h, third year‌ of ENSEIRB-MATMECA engineering school,‌​‌ Bordeaux INP, France.
• Licence:​​ J. Saracco, Probabilités et​​​‌ Statistique, 27h, first‌ year of ENSC Graduate‌​‌ School of Engineering, Bordeaux​​ INP, France.
• Licence: J.​​​‌ Saracco, Statistique inférentielle et‌ analyse des données,‌​‌ 45h, first year of​​ ENSC Graduate School of​​​‌ Engineering, Bordeaux INP, Institut‌ Polytechnique de Bordeaux, France.‌​‌
• Licence: J. Saracco, Statistique​​ pour l'ingénieur, 16h,​​​‌ first year of ENSPIMA‌ Graduate School of Engineering,‌​‌ Bordeaux INP, Institut Polytechnique​​ de Bordeaux, France.
• Master:​​​‌ J. Saracco, Modélisation statistique‌, 81h, second year‌​‌ of ENSC Graduate School​​ of Engineering, Bordeaux INP,​​​‌ Institut Polytechnique de Bordeaux,‌ France.
• DU: J. Saracco,‌​‌ Statistique et Big Data​​, 45h, DU BDSI​​​‌ (Big Data et Statistique‌ pour l'Ingénieur), Bordeaux INP,‌​‌ France.
• Licence: M. Chavent,​​ Statistique inférentielle, 18h,​​​‌ L2, Université de Bordeaux,‌ France.
• Licence: M. Chavent,‌​‌ Techniques d'Enquêtes, 10h,​​ L2, Université de Bordeaux,​​​‌ France.
• Master: M. Chavent,‌ Data Mining, 43h,‌​‌ M2, Université de Bordeaux,​​ France.
• Master: M. Chavent,​​​‌ Machine Learning, 58h,‌ Université de Bordeaux, France.‌​‌
• DU: M. Chavent, Apprentissage​​, 12h, DU BDSI,​​​‌ Bordeaux INP, France.

10.2.2‌ Supervision

• The members of‌​‌ the team have been​​ involved in the supervision​​​‌ of various Master's internships,‌ final-year projects (PFE), individual‌​‌ computer science projects, etc.​​
• The members of the​​​‌ team supervise PhD theses,‌ Master theses and engineers‌​‌ internships

10.2.3 Juries

• Alexandre​​ Génadot served as a​​​‌ reviewer for Orlane Rossini's‌ PhD thesis entitled “Model-based‌​‌ reinforcement learning for the​​ control of partially observable​​​‌ piecewise deterministic semi-Markov decision‌ processes”, which was defended‌​‌ on November 28, 2025,​​ at the University of​​​‌ Montpellier II.
• Jérôme Saracco‌ was chair of the‌​‌ thesis committee for Daphné​​ AUROUET's PhD thesis entitled​​​‌ Predictive recursive nonparametric methods‌ for modelling banknotes circulation,‌​‌ defended at ENSAI in​​ Rennes in October 2025.​​​‌
• Jérôme Saracco was chair‌ of the thesis committee‌​‌ for Valentin Portmann's PhD​​ thesis entitled "Développement de​​​‌ nouveaux algorithmes d’apprentissage statistique‌ pour coupler projections climatiques‌​‌ et observations passées en​​ vue de réduire les​​​‌ incertitudes du changement climatique‌ à venir" defended at‌​‌ Bordeaux University in November​​ 2025.
• Jérôme Saracco was​​​‌ a member of the‌ jury for the John‌​‌ ALBECHAALANY's PhD thesis, entitled​​ “Modulation et optimisation des​​​‌ pratiques d'élevage pour améliorer‌ la qualité de la‌​‌ viande bovine et de​​ volaille,” defended in March​​​‌ 2025 at INRAE in‌ Clermont-Ferrand, as co-supervisor of‌​‌ the thesis work.
• Pierrick​​ Legrand was chair of​​​‌ the thesis committee for‌ Luc De Montella's entitled‌​‌ "Etude de méthodes particulaires​​ en filtrage non linéaire​​​‌ : application à la‌ trajectographie passive" defended in‌​‌ May 2025 at Bordeaux​​ University.
• Pierrick Legrand was​​​‌ chair of the thesis‌ committee for Alexis Boffet's‌​‌ PhD thesis entiled "Évaluation​​​‌ de la charge mentale​ du pilote en condition​‌ opérationnelle induisant des niveaux​​ élevés de vigilance et/ou​​​‌ stress par intégration du​ bio signal d'activité électrodermale​‌ dans un système intégrateur​​ multi signaux" defended in​​​‌ November 2025 at Bordeaux​ University.
• Pierrick Legrand was​‌ chair of the thesis​​ committee for Zheng Fang's​​​‌ PhD thesis entiled "Study​ of functional changes in​‌ cerebral networks associated with​​ cognitive control dysfunctions in​​​‌ Parkinson's disease" defended in​ June 2025 at Rennes​‌ University.

International journals​

• 8 articleE.Elsiddig​‌ Awadelkarim, M.Michel​​ Caffarel, P. D.​​​‌Pierre Del Moral and​ A.Ajay Jasra.​‌ On the Particle Approximation​​ of Lagged Feynman-Kac Formulae​​​‌.Stochastic Processes and​ their Applications188October​‌ 2025, 104690HAL​​DOIback to text​​​‌
• 9 articleM.Michel​ Caffarel, P.Pierre​‌ del Moral and L.​​Luc de Montella.​​​‌ On the Mathematical foundations​ of Diffusion Monte Carlo​‌.Journal of Mathematical​​ Physics661January​​​‌ 2025, 013301HAL​DOIback to text​‌
• 10 articleO.O.L.V.​​ Costa, F.François​​​‌ Dufour and A.A.​ Genadot. Non-stationary value​‌ iteration for adaptive average​​ control of piecewise deterministic​​ Markov processes.Nonlinear​​​‌ Analysis: Hybrid Systems58‌November 2025, 101622‌​‌HALDOIback to​​ text
• 11 articleF.​​​‌François Dufour, A.‌Alexandre Genadot and O.‌​‌ L.Oswaldo Luiz Do​​ Valle Costa. Minimum​​​‌ Contrast Estimators for Piecewise‌ Deterministic Markov Processes.‌​‌Numerical Algebra, Control and​​ Optimization1512025​​​‌, 1-14HALDOI‌back to text
• 12‌​‌ articleF.François Dufour​​, A.Alexandre Genadot​​​‌ and R.Romain Namyst‌. The bearing only‌​‌ localization problem via partially​​ observed Markov decision process​​​‌.Mathematical Methods of‌ Operations Research1012‌​‌March 2025, 219-257​​HALDOIback to​​​‌ text
• 13 articleF.‌François Dufour and T.‌​‌Tomás Prieto-Rumeau. Absorbing​​ Markov decision processes and​​​‌ their occupation measures.‌SIAM Journal on Control‌​‌ and Optimization631​​2025, 676-698In​​​‌ press. HALDOIback‌ to text
• 14 article‌​‌F.François Dufour,​​ K.Ky Tran,​​​‌ L. Y.Le Yi‌ Wang and G.George‌​‌ Yin. Asymptotic optimality​​ of a class of​​​‌ controlled non-Markov processes.‌Applicable Analysis10411‌​‌2025, 2005-2017HAL​​DOIback to text​​​‌
• 15 articleE.Eric‌ Grivel, P.Pierrick‌​‌ Legrand and B.Bastien​​ Berthelot. Multiscale entropy​​​‌ rates: a study on‌ different stochastic processes.‌​‌Digital Signal ProcessingMay​​ 2025HALDOIback​​​‌ to text
• 16 article‌E.Enzo Iglésis and‌​‌ L.Luc de Montella​​. Target motion analysis​​​‌ using angular measurements and‌ underwater sound pressure levels‌​‌.Journal of the​​ Acoustical Society of America​​​‌1583September 2025‌, 2590-2601HALDOI‌​‌back to text
• 17​​ articleP.Pierre del​​​‌ Moral, S.Shulan‌ Hu, A.Ajay‌​‌ Jasra, H.Hamza​​ Ruzayqat and X.Xinyu​​​‌ Wang. On time‌ uniform Wong-Zakai approximation theorems‌​‌.Mathematics of Computation​​661June 2025​​​‌HALDOIback to‌ text
• 18 articleV.‌​‌Valentin Portmann, M.​​Marie Chavent and D.​​​‌Didier Swingedouw. ClimLoco1.0:‌ CLimate variable confidence Interval‌​‌ of Multivariate Linear Observational​​ COnstraint.Geoscientific Model​​​‌ Development1822November‌ 2025, 9015-9038HAL‌​‌DOIback to text​​

International peer-reviewed conferences

• 19​​​‌ inproceedingsY.Yann Bourdin‌, P.Pierrick Legrand‌​‌ and F.Fanny Roche​​. Empirical Results for​​​‌ Adjusting Truncated Backpropagation Through‌ Time while Training Neural‌​‌ Audio Effects.DAFx​​ 2025 - 28th International​​​‌ Conference on Digital Audio‌ EffectsAncona, ItalySeptember‌​‌ 2025HALback to​​ text
• 20 inproceedingsE.​​​‌Eric Grivel, P.‌Pierrick Legrand and B.‌​‌Bastien Berthelot. Multiscale​​ cross entropy rate as​​​‌ a way to compare‌ signals: application to Gaussian‌​‌ ARMA processes.2025​​ 33rd European Signal Processing​​​‌ Conference (EUSIPCO)EUSIPCO 2025‌ - 33rd European Signal‌​‌ Processing ConferencePalerme, Italy​​September 2025HALback​​​‌ to text

Conferences without‌ proceedings

• 21 inproceedingsM.‌​‌Marie Chavent, D.​​Delphine Féral, J.​​​‌Jérôme Saracco, V.‌Véronique Darmendrail and F.‌​‌Frédéric Pourtier. Détection​​ et quantification de manipulations​​​‌ comptables autour d’un seuil‌ psychologique avec R.‌​‌11èmes Rencontres RMons,​​​‌ BelgiumMay 2025HAL​back to text
• 22​‌ inproceedingsG.Guillaume Cottin​​, F.Franck Cazaurang​​​‌, J.Jérôme Saracco​, L.Loïc Lavigne​‌, V.Vincent Corretja​​, B.B. Souyri​​​‌ and F.Franck Tailliez​. Algorithme de partitionnement​‌ en ligne pour une​​ compression incrémentale sans perte​​​‌ des données vibratoires.​3ème congrès annuel de​‌ la SAGIP (SAGIP 2025)​​Mulhouse (FR), FranceMay​​​‌ 2025HALback to​ text
• 23 inproceedingsG.​‌Guillaume Cottin, F.​​Franck Cazaurang, J.​​​‌Jérôme Saracco, L.​Loïc Lavigne, V.​‌Vincent Corretja, B.​​B. Souyri and F.​​​‌Franck Tailliez. Segmentation​ and lossless compression of​‌ SAR data: a new​​ approach to ensure transmission​​​‌ robustness.44th Digital​ Avionics Systems Conference (DASC​‌ 2025)Montréal (Québec), Canada​​September 2025HALback​​​‌ to textback to​ text

Doctoral dissertations and​‌ habilitation theses

• 24 thesis​​M.Mariette Dupuy.​​​‌ Analysis of electrical features​ for detection of subjects​‌ at risk for sudden​​ cardiac death.Université​​​‌ de BordeauxJanuary 2025​HALback to text​‌
• 25 thesisL.Luc​​ de Montella. Study​​​‌ of particle methods in​ nonlinear filtering : application​‌ to passive trajectography.​​Université de BordeauxMay​​​‌ 2025HALback to​ text

Reports & preprints​‌

• 26 miscO. D.​​O. Deniz Akyildiz,​​​‌ P.Pierre del Moral​ and J.Joaquin Miguez​‌. On the contraction​​ properties of Sinkhorn semigroups​​​‌.2025HALback​ to text
• 27 misc​‌Y.Yann Bourdin,​​ P.Pierrick Legrand and​​​‌ F.Fanny Roche.​ Time-Varying Audio Effect Modeling​‌ by End-to-End Adversarial Training​​.December 2025HAL​​​‌back to text
• 28​ miscT.Thomas Ferté​‌, V.Vincent Thevenet​​, X.Xavier Hinaut​​​‌, P.Pierrick Legrand​, D.Dan Dutartre​‌, R.Romain Griffier​​, V.Viannet Jouhet​​​‌, B. P.Boris​ P Hejblum and R.​‌Rodolphe Thiébaut. Epidemic​​ Forecasting: Lessons Learned from​​​‌ the SARS-CoV-2 Pandemic to​ Balance Accuracy, Feasibility, and​‌ Impact.November 2025​​HALDOIback to​​​‌ text
• 29 miscA.​Alexandre Genadot, E.​‌Enzo Iglésis and L.​​Luc de Montella.​​​‌ About Fisher Information Matrix​ and Self-Optimizing Control in​‌ Bearing Only Localization.​​January 2025HALback​​​‌ to text
• 30 misc​E.Emma Lagracie and​‌ L.Luc de Montella​​. Particle Filtering for​​​‌ Non-Deterministic Electrocardiographic Imaging.​September 2025HALback​‌ to text
• 31 misc​​P.Pierre del Moral​​​‌. Entropic continuity bounds​ for conditional covariances with​‌ applications to Schrödinger and​​ Sinkhorn bridges.2025​​​‌HALback to text​
• 32 miscP.Pierre​‌ del Moral and M.​​Mathieu Gerber. On​​​‌ the Kantorovich contraction of​ Markov semigroups.2025​‌HALback to text​​
• 33 miscP.Pierre​​​‌ del Moral. Stability​ of Schrödinger bridges and​‌ Sinkhorn semigroups for log-concave​​ models.2025HAL​​​‌back to text

Other​ scientific publications

• 34 misc​‌H.Hugo Leroux,​​ T.Tara Vanhatalo and​​​‌ P.Pierrick Legrand.​ L'IA se met au​‌ rock.March 2025​​HALback to text​​