Parameter identification in noisy extended systems: A hydrodynamic case

This paper is concerned with the robustness of parameter identification methods with respect to the noise levels typically found in experiments. More precisely, we fetus on the case of an extended nonlinear system: a system of coupled local maps akin to a discretized complex Ginzburg-Landau equation, modeling a wake experiment. After a brief description of this hydrodynamic experiment as well as of the associated cost function and synthetic data generation, we introduce two inversion methods: a one-time-step approach, and a more sophisticated n-time-step optimization procedure, solved by a backpropagation method. The one-time-step approach reduces to a small linear system for the unknown parameters, while the n-time-step approach involves a backpropagation equation for a set of Lagrange multipliers. The sensitivity of each method with respect to noise is then discussed. while the n-time-step method is very robust even with large amounts of noise, the one-time-step approach is shown to be affected by small noise levels.