A master-slave coupling scheme for synchronization and parameter estimation in the generalized Kuramoto-Sivashinsky equation
arxiv(2023)
摘要
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 or machine learning 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.
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