Master-slave coupling scheme for synchronization and parameter estimation in the generalized Kuramoto-Sivashinsky equation

Abstract

The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics, and statistics. This is motivated by the various physical applications of the equation and also because it often serves as a test model for the study of space-time pattern formation. Remarkably, most existing inference techniques rely on statistical tools, which are computationally very costly yet do not exploit the dynamical features of the system. In this paper, we introduce a simple, online parameter estimation method that relies on the synchronization properties of the KS equation. In particular, we describe a master-slave setup where the slave model is driven by observations from the master system. The slave dynamics are data-driven and designed to continuously adapt the model parameters until identical synchronization with the master system is achieved. We provide a simple analysis that supports the proposed approach and also present and discuss the results of an extensive set of computer simulations. Our numerical study shows that the proposed method is computationally fast and also robust to initialization errors, observational noise, and variations in the spatial resolution of the numerical scheme used to integrate the KS equation.