7 mai 2020

David Lannes (Université de Bordeaux)
Dispersive perturbations of hyperbolic initial boundary value problems

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Lieu : https://bbb2.imo.universite-paris-saclay.fr/b/nic-m3v-7dt

Résumé : We will show in this talk how some models for the description of the interactions of waves with floating structures can be formulated as hyperbolic initial boundary value problems or (depending on the model chosen for the propagation of the waves), dispersive perturbations of such problems. After recalling some classical results on hyperbolic initial boundary value problems (in particular on the nature of the admissible boundary conditions), we will explain how the presence of a dispersive perturbation in the equations drastically changes the nature of the equations. These different behaviors raise several questions, one of which being nature of the dispersionless limit. We will show that the presence of dispersive boundary layers make this limit singular, and explain how to control them on an example motivated by a model for wave-structure interactions.

Dispersive perturbations of hyperbolic initial boundary value problems  Version PDF

France Hoffmann (California Institute of Technology)
Kalman-Wasserstein Gradient Flows

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Lieu : https://bbb2.imo.universite-paris-saclay.fr/b/nic-m3v-7dt

Résumé : We study a class of interacting particle systems that may be used for optimization. By considering the mean-field limit one obtains a nonlinear Fokker-Planck equation. This equation exhibits a gradient structure in probability space, based on a modified Wasserstein distance which reflects particle correlations : the Kalman-Wasserstein metric. This setting gives rise to a methodology for calibrating and quantifying uncertainty for parameters appearing in complex computer models which are expensive to run, and cannot readily be differentiated. This is achieved by connecting the interacting particle system to ensemble Kalman methods for inverse problems. This is joint work with Alfredo Garbuno-Inigo (Caltech), Wuchen Li (UCLA) and Andrew Stuart (Caltech).

Kalman-Wasserstein Gradient Flows  Version PDF