Dynamical approximations for parameter and time dependent partial differential equations

Abstract: 

Partial differential equations (PDEs) are used to model complex physical systems and evolving phenomena. In some situations, these equations may depend on parameters, which may be unknown, related to physical quantities or the geometry of the domain.

Model order reduction (MOR) techniques have been extensively developed to compute an approximation of the solution to these equations that is cheap to evaluate, which is crucial in a multi-query context, e.g. for parameter studies, uncertainty quantification, inverse problems, etc. To this end, the numerical methods developed over the last few decades aim to calculate linear approximation in a low-rank format. The main idea behind these approaches is to approximate the set of parameter-dependent solutions with a well-chosen finite-dimensional linear subspace of small dimension.

A first objective of this presentation is to give a brief overview and illustration of these approaches, with a particular focus on dynamical low-rank approximation (DLRA). Then, we will then discuss new MOR methods that have recently emerged combining either nonlinearity in the approximation format or random linear algebra (RLA).

‼️ Le séminaire peut être suivi en ligne via le lien : https://univ-amu-fr.zoom.us/j/95011527683?pwd=bTeNvaaZY75buaa7bRL0pcucXSASm7.1

Le mardi 5 mai 2026 à 11h00 / Amphithéâtre François Canac, LMA

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