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Gaussian Processes: from knowledge-informed Machine Learning to optimization
No full textNational audienceMany situations lead to sparse data or uncertain data. Gaussian processes (GPs) offer a mathematically funded framework for learning, optimizing,and other decision-making activities. This poster, presented at the HCERES* audit of the LIMOS laboratory in 2025, summarizes several contributions of the St-Etienne applied mathematics team of the LIMOS made between 2023 and 2025. * HCERES : Haut Conseil de l'Evaluation de la Recherche et de l'Enseignement Supérieu
Action matters for object representation learning from sequences
No full textInternational audienceAccording to the sensorimotor contingencies theory, building from developments in cognitive sciences, action, and especially the rules governing the changes in sensations caused by action, are essential to construct meaningful representation of the environment. However, most of current approaches to self-supervised learning are currently learning static representations from large datasets. In this article, we study how state-of-the-art deep learning methods can learn sensorimotor representations from sequences of interactions in a simplified deterministic Tetris-like environment, partially observable by the model. Especially, we emphasize the role of action to facilitate the emergence of representations related to objects present in the environment (here Tetris manipulable shapes). To that purpose, several model configurations were compared: a multi-task Transformer, a multi-task State Space Model, and ablated variants omitting action either in the input and/or in the pretext tasks. All models were trained in a self-supervised setting using predictive tasks of a masked subpart of the input sequence. Results show that explicitly including actions in the input and in the pretext tasks significantly improves the quality of learned representations, particularly in ambiguous situations. These findings support the relevance of the sensorimotor framework for structuring representation learning
Open-Loop Paralleling of Class E2 resonant DC-DC Converters
No full textInternational audienceIn view of investigating new strategies to cope with the limitation of high output power of very high frequency power converters, this paper describes the implementation of Class E2 parallel resonant DC-DC converters which is suitable candidate topology for the experiment as it can maintain ZVS over a wide load range naturally in open-loop. Consequently, several 10W elementary prototypes were gathered which maintain an overall efficiency >80% for a load range variation of 2-10W at a switching frequency of 10MHz. Subsequently, multiple paralleling configurations are investigated experimentally which allowed the construction of a predictive model for untested parallel converter configurations. A maximum output power of 42.78W was achieved with 5 parallel converters.
Des détections aux décisions : une approche d'apprentissage profond multi-instances guidé par l'attention pour l'inspection visuelle des pneumatiques
No full textInternational audienceThis paper proposes a data-driven methodology within the "detect-repair" strategy of zero-defect manufacturing (ZDM) for quality assessment of tires at the end of the production line. By integrating a decision support system (DSS) based on multiple instance learning (MIL) with an existing defect detection system, our approach marks a significant step forward in automating accurate tire quality assessment. This enables informed decisions regarding repair or delivery to be made without manual intervention. Our proposed method extends its utility across any manufacturing sectors needing to ensure its product quality based on tacit knowledge. Notably, the proposed DSS leverages historical data to outperform rule-based systems through an attention-based deep learning neural network, improving decision-making accuracy and reducing false positives. Moreover, the attention scores are used to obtain explainable predictions for each detected defect. The achieved area under the curve (AUC) value of 0.837 demonstrates the proposed system's strong predictive performance. This innovative data-driven methodology not only represents progress in ZDM but also allows to make a step further towards more efficient, adaptive decision support systems in industrial quality control
Remanent deformation and local stiffening induced by electric field in low glass transition epoxy-amine polymer network doped with ionic liquid
No full textInternational audienceRoom temperature ionic liquids (RTILs) can behave like solids as the result of their ordering in the vicinity of substrates or confining in porous membranes. In this work, we have used this specific property to fabricate soft electroactuators in which deformation can be maintained after removal of the electric field. Epoxy-amine doped with 5 %wt of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIM TFSI) was processed. The study of bending under a constant electric field of E = 0.1 MV/m shows slow deformation kinetics as a function of time. Interestingly, when the electric field is removed, around 80 % of the displacement is maintained for at least a day. The reversibility of this phenomenon was checked by successively applying positive and negative electric fields. It shows that complex successive electro-mechanical cycles can be performed without performance degradation (i.e. the sample reaches the same bending amplitude). Besides, energy dispersive X-ray spectroscopy was used to map the bis(trifluoromethylsulfonyl)imide counter anion before and after the application of the electric field and revealed the presence of a persistent anionic rich layer near the positive electrode after removing the electric field. This result was also supported by atomic force microscopy, which revealed an improvement in sample stiffness near the positive electrode. It explains the observed remanent deformation and opens up prospects for the processing of materials whose stiffness can be controlled by applying an electric field
Modélisation mathématique de l'inflammation
No full textInflammation is a fundamental defense mechanism of the human body in response to various external stimuli. It plays an important role in the development and progression of numerous diseases, including cardiovascular disorders, and neurodegenerative diseases. Although each type of inflammatory disease has its own characteristic stimuli, the inflammatory response mechanism is generic. It begins with the recognition of harmful agents by pattern recognition receptors on cell surfaces, followed by the activation of inflammatory signaling pathways. This leads to the release of inflammatory mediators and the subsequent recruitment of immune cells to the region of inflammation. This thesis focuses on the mathematical modeling of the inflammatory process. In particular, it aims to develop a generalized models that capture the key phases of inflammation, namely initiation, development, and resolution, using a system of reaction-diffusion and integro-differential equations. We also demonstrate its applicability to a range of diseases, such as atherosclerosis, Alzheimer's disease, skin diseases, and auto-immune diseases.L’inflammation est un mécanisme de défense fondamental de l’organisme en réponse à divers stimuli externes. Elle joue un rôle important dans le développement et la progression de nombreuses maladies, notamment les troubles cardiovasculaires et les maladies neurodégénératives. Bien que chaque type d’inflammation soit déclenché par des stimuli spécifiques, le mécanisme de réponse inflammatoire reste globalement générique. Il débute par la reconnaissance des agents nuisibles par les récepteurs situés à la surface des cellules, suivie de l’activation de voies de signalisation inflammatoires. Cela conduit à la libération de médiateurs inflammatoires et au recrutement subséquent de cellules immunitaires dans la région affectée. Ce travail de thèse porte sur la modélisation mathématique du processus inflammatoire. En particulier, il vise à développer des modèles généralisés capables de décrire les phases clés de l’inflammation, notamment les phases d’initiation, de développement et de résolution, à l’aide d’un système d’équations de réaction-diffusion et d’équations intégro-différentielles. Nous démontrons également l’applicabilité de cette approche à plusieurs maladies, telles que l’athérosclérose, la maladie d’Alzheimer, les maladies de la peau et les maladies auto-immunes
BSP-OT: Sparse transport plans between discrete measures in loglinear time
No full textInternational audienceTo solve the optimal transport problem between two uniform discrete measures of the same size, one seeks a bijective assignment that minimizes some matching cost. For this task, exact algorithms are intractable for large problems, while approximate ones may lose the bijectivity of the assignment. We address this issue and the more general cases of non-uniform discrete measures with different total masses, where partial transport may be desirable. The core of our algorithm is a variant of the Quicksort algorithm that provides an efficient strategy to randomly explore many relevant and easy-to-compute couplings, by matching BSP trees in loglinear time. The couplings we obtain are as sparse as possible, in the sense that they provide bijections, injective partial matchings or sparse couplings depending on the nature of the matched measures. To improve the transport cost, we propose efficient strategies to merge k sparse couplings into a higher quality one. For k = 64, we obtain transport plans with typically less than 1% of relative error in a matter of seconds between hundreds of thousands of points in 3D on the CPU. We demonstrate how these high-quality approximations can drastically speed-up usual pipelines involving optimal transport, such as shape interpolation, intrinsic manifold sampling, color transfer, topological data analysis, rigid partial registration of point clouds and image stippling
Effective regions and kernels in continuous sparse regularisation, with application to sketched mixtures
No full textThis paper advances the general theory of continuous sparse regularisation on measures with the Beurling-LASSO (BLASSO). This TV-regularised convex program on the space of measures allows to recover a sparse measure using a noisy observation from a measurement operator. While previous works have uncovered the central role played by this operator and its associated kernel in order to get estimation error bounds, the latter requires a technical local positive curvature (LPC) assumption to be verified on a case-by-case basis. In practice, this yields only few LPC-kernels for which this condition is proved. In this paper, we prove that the ``sinc-4'' kernel, used for signal recovery and mixture problems, does satisfy the LPC assumption. Furthermore, we introduce the kernel switch analysis, which allows to leverage on a known LPC-kernel as a pivot kernel to prove error bounds. Together, these results provide easy-to-check conditions to get error bounds for a large family of translation-invariant model kernels. Besides, we also show that known BLASSO guarantees can be made adaptive to the noise level. This improves on known results where this error is fixed with some parameters depending on the model kernel. We illustrate the interest of our results in the case of mixture model estimation, using band-limiting smoothing and sketching techniques to reduce the computational burden of BLASSO
Développement d'un outil pour l'optimisation du dimensionnement et de la gestion des systèmes multi-sources avec batteries : application aux tours de télécommunication (OSETTA)
No full textThe telecommunications industry faces a dual challenge: democratizing digital access while reducing its environmental impact. This sector accounts for 3% of global energy consumption and generates 430 MtCO₂ annually. Base stations, essential for connectivity, are responsible for 57% of this consumption.The digital divide persists, particularly in Canada where only 64% of rural households have access to 50/10 Mbps Internet connections, compared to 99% in urban areas. This disparity is even more pronounced in Indigenous communities, where 5G access concerns only 41.53% of the population.The sector's energy supply relies on various sources: 46% renewable energy, 43% from the conventional grid, and 11% from diesel generators. However, less than 1% of renewable energy is produced directly on-site. By 2030, the number of sites with unstable network or off-grid is expected to increase by 22%.Facing these challenges, telecom operators aim to reduce their emissions by 50% by 2030 and achieve carbon neutrality by 2050. Major players like Rogers and Bell Canada have already begun this shift by deploying stations powered by renewable energy in remote areas.This research project proposes the development of an optimization tool for hybrid nanogrids combining photovoltaic panels, batteries, and diesel generators to power isolated base stations. The approach targets optimal sizing and economic and environmental management of these systems.The study integrates innovations such as bifacial photovoltaic panels, which offer 10-20% higher efficiency and are expected to represent 20% of the global market by 2030. It also addresses the critical impact of snow accumulation, which can reduce energy yield from 3.5% to 100%.The main contributions revolve around three axes: detailed system modeling, optimization of energy management in the face of uncertainties, and coordination between modeling and management to maximize the integration of renewable energy.The result will be an optimized sizing tool facilitating the planning and management of stations powered by nanogrids, thus contributing to emission reduction policies and the goal of carbon neutrality by 2050.L'industrie des télécommunications affronte un double défi : démocratiser l'accès numérique tout en réduisant son impact environnemental. Ce secteur représente 3% de la consommation énergétique mondiale et génère 430 MtCO₂ annuellement. Les stations de base, essentielles à la connectivité, sont responsables de 57% de cette consommation.La fracture numérique persiste, notamment au Canada où seulement 64% des ménages ruraux accèdent à une connexion Internet 50/10 Mbps, contre 99% en zones urbaines. Cette disparité s'accentue dans les communautés autochtones, où l'accès à la 5G ne concerne que 41,53% de la population.L'approvisionnement énergétique du secteur repose sur des sources variées : 46% d'énergies renouvelables, 43% du réseau conventionnel et 11% de générateurs diesel. Toutefois, moins de 1% des énergies renouvelables est produit directement sur site. D'ici 2030, le nombre de sites en réseau instable ou hors réseau devrait augmenter de 22%.Face à ces enjeux, les opérateurs télécoms visent à réduire leurs émissions de 50% d'ici 2030 et atteindre la neutralité carbone en 2050. Des acteurs majeurs comme Rogers et Bell Canada ont déjà entamé ce virage en déployant des stations alimentées par énergies renouvelables dans les zones éloignées.Ce projet de recherche propose le développement d'un outil d'optimisation des nanoréseaux hybrides associant panneaux photovoltaïques, batteries et générateurs diesel pour alimenter les stations de base isolées. L'approche cible le dimensionnement optimal et la gestion économique et environnementale de ces systèmes.L'étude intègre des innovations comme les panneaux photovoltaïques bifaciaux, qui offrent un rendement supérieur de 10-20% et devraient représenter 20% du marché mondial d'ici 2030. Elle aborde également l'impact critique de l'accumulation de neige, qui peut réduire le rendement énergétique de 3,5% à 100%.Les contributions principales s'articulent autour de trois axes : la modélisation détaillée du système, l'optimisation de la gestion énergétique face aux incertitudes, et la coordination entre modélisation et gestion pour maximiser l'intégration des énergies renouvelables.Le résultat sera un outil de dimensionnement optimisé facilitant la planification et la gestion des stations alimentées par nanoréseaux, contribuant ainsi aux politiques de réduction des émissions et à l'objectif de neutralité carbone d'ici 2050
Optimal sub-Gaussian variance proxy for 3-mass distributions
No full textWe investigate the problem of characterizing the optimal variance proxy for sub-Gaussian random variables, whose moment-generating function exhibits bounded growth at infinity. We apply a general characterization method to discrete random variables with equally spaced atoms. We thoroughly study 3-mass distributions, thereby generalizing the well-studied Bernoulli case. We also prove that the discrete uniform distribution over N points is strictly sub-Gaussian. Finally, we provide an open-source Python package that combines analytical and numerical approaches to compute optimal sub-Gaussian variance proxies across a wide range of distributions