In this talk, we investigate the inverse problem of approximating the solution of an equation from measurements, with a focus on the placement of the sensors. If we know a reduced model for the equation, that is, a linear space of reduced dimension providing a good approximation to the set of all solutions, then the reconstruction can be obtained by a least-squares fit of the data. However the stability of this method depends on the choice of measurements, and we will consider various strategies for achieving near-optimal accuracy with a limited number of sensors.

[L'exposé sera précédé par un "pré-exposé" à 13h30 dans la même salle, par Hugo Leclerc.]