ED Mathématiques et Informatique
Construction of memory-optimized hierarchical matrices with rank learning for applications in electromagnetism
by Théo BRIQUET (Institut national de recherche en informatique et en automatique - Bordeaux - Sud-Ouest)
The defense will take place at 14h00 - JCA 42 Avenue Gaspard Coriolis, 31100 Toulouse
in front of the jury composed of
- Luc GIRAUD - Directeur de recherche - INRIA / Université de Bordeaux - Directeur de these
- Sandrine MOUYSSET - Maîtresse de conférences - Université de Toulouse - Rapporteur
- Paul MYCEK - Chercheur Senior - CERFACS - CoDirecteur de these
- Jérôme MONNIER - Professeur des universités - INSA Toulouse - Examinateur
- Sébastien TORDEUX - Professeur des universités - Universite de Pau et des Pays de l'Adour - Rapporteur
In the simulation of electromagnetic and acoustic wave propagation, as well as in aeroacoustic computations, the boundary element method (BEM) is commonly used as a discretisation method. This approach leads to solving very large dense linear systems, for which assembling and storing the full matrix may be infeasible. One solution is to use hierarchical matrices, specifically in this work H-matrices, built from a hierarchical partition of the computational domain. This partition defines a set of blocks, some of which can be compressed using low-rank approximation techniques, considerably reducing memory requirements. One strategy for selecting the blocks to be compressed relies on the memory footprint of their compressed representation, which depends directly on their numerical rank. When this footprint exceeds a threshold determined by the computing architecture, the block is subdivided; otherwise it is kept in compressed form. The aim of this work is to make this subdivision decision without computing the coefficients of the hierarchical blocks. To this end, we investigate supervised statistical learning techniques, predicting the numerical rank of a block from geometric information alone, and deriving the corresponding memory footprint. We build a training dataset from pairs of synthetic geometries whose shape, size, orientation and relative distance are varied so as to cover a wide diversity of interaction configurations. Each configuration is described by a set of features that are cheap to compute, characterising both geometries as well as their relative position and orientation, without assembling the corresponding matrix block. We first train linear models regularised by Elastic Net, then models based on decision trees, specifically random forests and gradient boosted trees, as well as a multi-layer perceptron (MLP) neural network. These models predict the numerical rank with high accuracy on synthetic geometries, with the tree-based models and the multi-layer perceptron achieving the best results. The trained models are then used as numerical rank estimators to build H-matrices on an industrial case based on a simplified aircraft geometry. This implementation makes it possible to assess the ability of the models to generalise to the subdomains encountered in a mesh that is more representative of the target applications. The models lead to globally accurate predictions of the numerical rank and to H-matrices whose memory footprint is better controlled. The numerical rank, and therefore the memory footprint, of some blocks nevertheless remains underestimated, highlighting the limited representativeness of the synthetic training geometries with respect to the industrial case.
ED Droit
Possession and real security
by Atta Kouassi Guy Wilfried DUA (INSTITUT DE RECHERCHE EN DROIT DES AFFAIRES ET DU PATRIMOINE)
The defense will take place at 14h30 - Salle des thèse 16 Avenue Léon Duguit 33600 Pessac
in front of the jury composed of
- Guillaume DROUOT - Professeur des universités - Université de Bordeaux - Directeur de these
- Claire SEJEAN-CHAZAL - Professeure des universités - Université Paris Nord - Rapporteur
- Charles GIJSBERS - Professeur des universités - Université Paris-Panthéon-Assas - Rapporteur
- Gaël PIETTE - Professeur des universités - Université de Bordeaux - Examinateur
Numerous recent studies have highlighted the close relationship between security interests and property law. Yet, possession, a key aspect of property law, is often overlooked in these discussions. In security law, various aspects of possession are frequently mentioned, both in the context of movable security interests, such as pledges with or without dispossession, and in the context of immovable security interests, such as mortgages or pledges of real estate. But is this truly possession in the sense of property law? Is possession not sometimes manipulated, used against the creditor or, conversely, to protect them? Starting from the traditional understanding of possession as consisting of both corpus and animus, this study examines the difficulties faced by those involved in security law in meeting the requirements of possession, and thus in being a possessor. Then, in cases where such possession is nonetheless accepted, its lack of influence on security interests can be emphasized. More broadly, the study invites us to re-examine, through the lens of possession, the relationship between security interests and property law.