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Data Assimilation: a deterministic vision, theory and applications. Lecture 1: Least-square estimation

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Authors : Moireau, Philippe (Author of the conference)
CIRM (Publisher )

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Abstract : The question of using the available measurements to retrieve mathematical models characteristics (parameters, boundary conditions, initial conditions) is a key aspect of the modeling objective in biology or medicine. In a stochastic/statistical framework this question is seen as an estimation problems. From a deterministic point of view, we classical talk about inverse problems as we recover classical model inputs from outputs. When considering evolution problems,this question falls in the realm of data assimilation that can be seen from a deterministic of statistical point of view. Our objective in this course is to introduce the mathematical principles and numerical aspects behind data assimilation strategies with an emphasis on the deterministic formalism allowing to understand why data assimilation is a specific inverse problem. Our presentation will include considerations on finite dimensional problems but also on infinite dimensional problems such as the ones arising from PDE models. And we will illustrate the course with numerous examples coming from cardiovascular applications and biology.

MSC Codes :
35L05 - Wave equation (hyperbolic PDE)
35R30 - Inverse problems for PDE
93B07 - Observability
93B30 - System identification
93E10 - Estimation and detection in stochastic control
93E11 - Filtering

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 30/07/2018
    Conference Date : 19/07/2018
    Subseries : Research School
    arXiv category : Optimization and Control
    Mathematical Area(s) : PDE ; Control Theory & Optimization
    Format : MP4 (.mp4) - HD
    Video Time : 01:33:10
    Targeted Audience : Researchers ; Graduate Students
    Download : https://videos.cirm-math.fr/2018-07-19_Moireau_Part1.mp4

Information on the Event

Event Title : CEMRACS - Summer school: Numerical and mathematical modeling for biological and medical applications: deterministic, probabilistic and statistical descriptions / CEMRACS - École d'été : Modélisation numérique et mathématique pour la biologie et la médecine : descriptions déterministes, probabilistes et statistiques
Event Organizers : Calvez, Vincent ; Grandmont, Céline ; Löcherbach, Eva ; Poignard, Clair ; Ribot, Nathalie ; Vauchelet, Nicolas
Dates : 16/07/2018 - 24/08/2018
Event Year : 2018
Event URL : https://conferences.cirm-math.fr/1834.html

Citation Data

DOI : 10.24350/CIRM.V.19423103
Cite this video as: Moireau, Philippe (2018). Data Assimilation: a deterministic vision, theory and applications. Lecture 1: Least-square estimation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19423103
URI : http://dx.doi.org/10.24350/CIRM.V.19423103

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