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The problem of estimating the constant parameters of the Kuramoto-Sivashinsky(KS) equation has received considerable attention from researchers in physics,applied mathematics and statistics. This is motivated by the various physicalapplications of the equation and, also, because it often serves as a test modelfor the study of space-time pattern formation. Remarkably, most existinginference techniques rely on statistical or machine learning tools, which arecomputationally very costly yet do not exploit the dynamical features of thesystem. In this paper we introduce a simple, online parameter estimation methodthat relies on the synchronization properties of the KS equation. Inparticular, we describe a master-slave setup where the slave model is driven byobservations from the master system. The slave dynamics are designed tosynchronize with the master when both models have the same parameters. Weprovide a simple analysis that supports the proposed approach and also presentand discuss the results of an extensive numerical assessment of themethodology. The numerical study shows that the proposed method iscomputationally fast and also robust to initialization errors, observationalnoise and variations in the spatial resolution of the numerical scheme.

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