The problem of estimating the constant parameters of the Kuramoto--Sivashinsky (KS) equation from observed data has attracted considerable interest in physics, applied mathematics and statistics. This interest arises from the wide range of physical phenomena described by the KS equation and its role as a benchmark model for studying spatio-temporal pattern formation. Most existing inference methods rely on statistical techniques, which are often computationally expensive and do not explicitly exploit the dynamical structure of the system.

In this work we show a simple online parameter estimation method based on the synchronization properties of the KS equation. Specifically, we consider a master--slave framework in which the slave model is driven by observations of the master system. The slave dynamics are designed to adapt the model parameters continuously until identical synchronization with the master system is achieved. We present a basic theoretical analysis supporting the method and illustrate its performance through extensive numerical simulations. The results show that the approach is computationally efficient and robust with respect to initialization errors, observational noise and changes in the spatial resolution used to integrate the KS equation.