Spatially Dependent Parameter Estimation and Nonlinear Data Assimilation by Autosynchronization of a System of Partial Differential Equations

TL;DR

This paper introduces a method for estimating spatially varying parameters in reaction-diffusion PDE models using autosynchronization, demonstrated on predator-prey systems and applied to ecological modeling of marine plankton blooms.

Contribution

It presents a novel autosynchronization approach for nonlinear data assimilation of PDEs with spatially dependent parameters, validated on predator-prey models and applicable to ecological remote sensing.

Findings

Successful parameter estimation in reaction-diffusion PDEs

Effective modeling of marine plankton bloom habitats

Demonstrated robustness of autosynchronization method

Abstract

Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a 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 modelling the ecological habitat of marine plankton blooms by nonlinear data assimilation through remote sensing is discussed.