Appears in collections : 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, Ecoles de recherche

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.