| 20/11/2025 | | | | 11:00 | | | | Salle de conférence | | |
| | David Ryckelynck (Mines Paris - PSL - CEMEF) | | | | Self supervised machine learning for mechanics of materials | | | | We propose a general framework for projection-based model order
reduction using self-supervised machine learning. For parametric elliptic equations this approach is theoretically based on Céa's Lemma. The proposed methodology, called
ROM-net, consists in using deep learning techniques to adapt the reduced-order model to a stochastic input tensor whose nonparametrized variabilities strongly influence the quantities of interest for a given physics problem. In particular, we introduce the concept of dictionary-based ROM-nets, where deep neural networks recommend a suitable local reduced-order model from a dictionary. The dictionary of local reduced-order models is constructed from a clustering of vector subspaces in a Grassmann manifold.
It enables the identification of the local low-dimensional subspace in which the solutions evolve for different input tensors. This methodology is applied to an anisothermal elastoplastic problem in structural mechanics coupled to a stochastic thermal field. When using deep neural networks, the
selection of the best reduced-order model for a given thermal loading is 60 times faster than when following the clustering procedure used in the training phase. The implementation of local hyper-reduction schemes using a dictionary-based ROM-net is straightforward. The extension to variational inequalities will be addressed at the end of the lecture.
| | | | Gestion: Francesca |
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| 27/11/2025 | | | | 11h | | | | Salle de conférence | | |
| | Mickaël Latocca (Université d'Évry) | | | | | | | | | | | | Gestion: Isabelle |
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| 04/12/2025 | | | | 11h | | | | Salle de conférence | | |
| | Helge Dietert (Université Paris Cité) | | | | | | | | | | | | Gestion: Isabelle |
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| 11/12/2025 | | | | 11h | | | | Salle de conférence | | |
| | Remy Rodiac (LJAD) | | | | Limite de champ-moyen de vortex pour l'énergie de Ginzburg-Landau sans champ magnétique | | | | On s'intéresse aux minimiseurs d'une énergie de Ginzburg-Landau sans champ magnétique avec une donnée au bord dont le degré topologique tend vers l'infini. Cela force l'apparition d'un nombre de vortex de plus en plus grand et on se pose alors la question de la distribution en moyenne de ces vortex. On montre, dans le cas d'un domaine simplement connexe ou d'un anneau circulaire, que les vortex s'accumulent près du bord du domaine. Pour cela on est conduit à étudier une fonctionnelle définie sur l'espace des mesures de Radon. Ceci est un travail en commun avec Amandine Aftalion (Orsay). | | | | Gestion: Joris |
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| 18/12/2025 | | | | 11:00 | | | | Salle de conférence | | |
| | Ana Alonso Rodriguez (Universita' di Trento) | | | | | | | | | | | | Gestion: Francesca |
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| 29/01/2026 | | | | 11h | | | | Salle de conférence | | |
| | Paola Goatin (INRIA Université Côte d'Azur) | | | | | | | | | | |
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| 12/02/2026 | | | | 11h | | | | Salle de conférence | | |
| | Ayman Moussa (Sorbonne Université) | | | | | | | | | | | | Gestion: Isabelle |
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| 26/03/2026 | | | | 11h | | | | Salle de conférence | | |
| | Raphaël Danchin (Université Paris-Est Créteil) | | | | | | | | | | | | Gestion: Isabelle |
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