Session A6 - Mathematical Foundations of Data Assimilation and Inverse Problems
July 12, 14:30 ~ 15:00 - Room T1
Estimation for front propagation models with front level-set data using observers. Applications in medicine and in fire propagation.
Inria, Université Bordeaux, Bordeaux INP, France - email@example.com
In this presentation, we present a sequential — observer based — data assimilation strategy for front propagation models (as reaction-diffusion, eikonal or reaction-transport equations), and for data corresponding to propagation isochrones. First, an original similarity measure between the computed front and the observed front is introduced. Then an efficient feedback adapted to this similarity measure is presented based on shape derivatives leading in fine to a so-called Luenberger observer. This shape observer can be completed with the introduction of the topological derivative of the measure in order to take into account the breakthrough of new fronts. Mathematical justifications of the stabilization property brought by the feedback are detailed. We also discuss the extension to joint state-parameter estimation by using a Kalman based strategy such as RO-UKF. Finally, numerical illustrations are presented on synthetic data and on real data in three applications domains (cardiac electrophysiology, tumor growth and fire propagation) revealing the potential of the approach.
Joint work with Dominique Chapelle (Inria, Université Paris Saclay) and Philippe Moireau (Inria, Université Paris Saclay).