LMBP

Jeudi 29 janvier 2026 - Charlie Sire
Spline Interpolation on Compact Riemannian Manifolds

Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches focus on Euclidean domains or the sphere, relying on the spectral properties of the Laplacian, this work introduces a method for spline interpolation on general manifolds by exploiting its equivalence with kriging. Specifically, the proposed approach uses finite element approximations of random fields defined over the manifold, based on Gaussian Markov Random Fields and a discretization of the Laplace-Beltrami operator on a triangulated mesh. This framework enables the modeling of spatial fields with local anisotropies through domain deformation. The method is first validated on the sphere using both analytical test cases and a pollution-related study, and is compared to the classical spherical harmonics-based method. Additional experiments on the surface of a cylinder further illustrate the generality of the approach.

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Jeudi 04 décembre 2025 - Susovan Pal
Manifold learning with non-smooth boundaries, and asymptotics of the graph Laplacian

Manifold learning algorithms often assume that data lie on or near a smooth lower-dimensional manifold M embedded in a higher dimensional Euclidean space, and that the Laplace–Beltrami operator of M can be approximated by graph Laplacian constructed from the data. However, analogous results for singular geometric spaces (for instance, spaces with boundaries or cusps) remain largely unexplored. In this talk, I will present recent work analyzing the asymptotic behavior of the unnormalized graph Laplacian on manifolds with non-smooth boundaries, which we refer to as manifolds with kinks, corners or cusps being special cases. In contrast with the smooth case—where convergence is to the Laplace–Beltrami operator—we show that the limiting behavior involves a first-order boundary operator, namely a generalized normal derivative, giving rise to generalized Neumann Laplacian. Numerical simulations support and illustrate the theoretical results. Aside from the usual motivation of nonlinear dimensionality reduction, we also show one application on edge detection in image processing.

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Jeudi 27 novembre 2025 - rémi Vaucher
Infering hypergraphs on set of time series using the signature transform.

Topological data analysis (TDA) has emerged in recent years as a rapidly developing area within statistics. Its central challenge lies in equipping a dataset with a suitable topological structure, typically via the construction of simplicial complexes, which can be viewed as a particular class of hypergraphs. For temporal data, however, the absence of an intrinsic metric constitutes a major obstacle to building such structures. To address this issue, we propose the use of rough path signatures.

By design, signatures extract a temporal summary of the geometric features of a path. In this work, we introduce two approaches: the first constructs a hypergraph that captures explainability relationships, while the second relies on kernel-based methods.

These contributions aim to bridge the gap between geometric representations of temporal processes and topological modelling, thereby enabling a richer structural understanding of time-dependent data.

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Mardi 18 novembre 2025 - 18 novembre 2025 : Issam Falih + Julien Hautot
GT IA 14h-16h

Jeudi 06 novembre 2025 - HCERES

ne pas prévoir de séminaire ? HCERES

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Jeudi 23 octobre 2025 - Jonathan Husson
Grandes deviations et spectres de matrices aléatoires

Jeudi 16 octobre 2025 - fete de la science
fete de la science

éviter de prévoir un séminaire : fête de la science

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Jeudi 02 octobre 2025 - Gauthier Thurin
Quantiles multivariés, transport optimal et applications

On introduira une définition de quantiles multivariés fondée sur le transport de mesures depuis une loi de référence fixée. Une application à la prédiction conforme sera détaillée, ce qui permettra de mettre en perspective ses principales propriétés par rapport à d’autres alternatives.

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Jeudi 25 septembre 2025 - réunion d'équipe
réunion d'équipe et séminaire GT IA (par Julien et Boris)

Pas de séminaire : réunion d'équipe
Info : a 14h séminaire du GT IA

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