Spatially dependent parameter estimation and nonlinear data assimilation by autosynchronization of a system of partial differential equations.

Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a partial differential equation (PDE) model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A two-component system of predator-prey reaction-diffusion PDEs is used with spatially dependent parameters to benchmark the methods described. Applications to modeling the ecological habitat of marine plankton blooms by nonlinear data assimilation through remote sensing are discussed.