University of Paris and Institut Univesitaire de France
Inverse problems have been solved by least squares for decades in the field of control with applications to industrial processes. It has been used also extensively by the petroleum industries and more recently for intial data assimilation in meteorology. The new aspects of these problems is that the data are modified in real time within the simulation process.
Optimal control and the Calculus of Variation is a powerful method for solving these complex and computer intensive problems. There are intrinsic difficulties due to non-uniqueness and non-differentiabilities which we will also review in this talk and for which parameter reductions or topological embedding are important tools.
Finally we will show on a few examples how numerical implementations are spectacularly simplified by the use of automatic differentiation.