Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Herr Professor Dr. Jean-Frederic Gerbeau (Inria Paris & Laboratoire J.L. Lions (UPMC & CNRS))

Diese Veranstaltung ist Teil der Veranstaltungsreihe „Schwerpunktskolloquium Analysis und Numerik“.

Abstract: Many phenomena are modeled by deterministic differential equations, whereas the observation of these phenomena, in particular in life science, exhibit an important inter-subject variability. We will address the following question: how the model can be adapted to reflect the variability observed in a population? We will present a non-parametric and non-intrusive procedure based on oine computations of the deterministic model. The algorithm infers the probability density function of uncertain parameters from the matching of the observable statistical moments at different points in the physical domain. This inverse procedure is improved by incorporating a point selection algorithm that both reduces its computational cost and increases its robustness. The method will be illustrated for dierent models, based on Ordinary or Partial Dierential Equations. In particular, applications to experimental data sets in cardiac electrophysiology will be presented. In biophysics and medicine, the system of interest is often studied by monitoring quantities, called biomarkers, extracted from measurements. These biomarkers convey some information about relevant hidden quantities, which can be seen as parameters of an underlying model. We propose a strategy to automatically design biomarkers to estimate a given parameter. Such biomarkers are chosen as the solution of a sparse optimization problem. We will show applications in electrophysiology where our algorithm provides composite biomarkers which improve the parameter estimation and the classication problems.