PARAMETER-IDENTIFICATION IN NOISY EXTENDED SYSTEMS - A HYDRODYNAMIC CASE

This paper is concerned with the robustness of parameter identificatio n methods with respect to the noise levels typically found in experime nts. More precisely, we fetus on the case of an extended nonlinear sys tem: a system of coupled local maps akin to a discretized complex Ginz burg-Landau equation, modeling a wake experiment. After a brief descri ption of this hydrodynamic experiment as well as of the associated cos t function and synthetic data generation, we introduce two inversion m ethods: a one-time-step approach, and a more sophisticated n-time-step optimization procedure, solved by a backpropagation method. The one-t ime-step approach reduces to a small linear system for the unknown par ameters, while the n-time-step approach involves a backpropagation equ ation for a set of Lagrange multipliers. The sensitivity of each metho d with respect to noise is then discussed. while the n-time-step metho d is very robust even with large amounts of noise, the one-time-step a pproach is shown to be affected by small noise levels.