Title: Inverse state and parameter estimation: optimal algorithms and applications
Author: Olga Mula (TU Eindhoven)

In this talk, I will present an overview of recent works aiming at solving inverse problems (state and parameter estimation) by combining measurement observations and physical PDE models. After defining a notion of optimal performance in terms of the smallest possible reconstruction error that any reconstruction algorithm can achieve, I will present practical numerical algorithms based on nonlinear reduced models for which we can prove that they can deliver a performance close to optimal. The performance of the approach will be illustrated on simple benchmark examples and also on non trivial applications such as urban pollution, and some biomedical problems. Finally, I will outline certain intrinsic limitations arising in inverse problems for transport dominated PDEs, and discuss some possible remedies.