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

Joaquín Miguez1, Harold Molina-Bulla2, Inés P Mariño3

  • 1Department of Signal Theory and Communications, <a href="https://ror.org/03ths8210">Universidad Carlos III de Madrid</a>, Avenida de la Universidad 30, 28911 Leganés (Madrid), Spain and Instituto de Investigación Sanitaria Gregorio Marañón, Calle Doctor Esquerdo 46, 28007 Madrid, Spain.

Physical Review. E
|December 18, 2024
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Summary

This study introduces a fast, online parameter estimation method for the Kuramoto-Sivashinsky (KS) equation using synchronization. The novel approach is robust to noise and initialization errors, outperforming costly statistical techniques.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Statistics

Background:

  • The Kuramoto-Sivashinsky (KS) equation models space-time pattern formation in various physical systems.
  • Estimating KS equation parameters from data is crucial but existing statistical methods are computationally expensive.
  • Current techniques often fail to leverage the inherent dynamical features of the KS system.

Purpose of the Study:

  • To develop a computationally efficient and robust online parameter estimation method for the Kuramoto-Sivashinsky equation.
  • To utilize the synchronization properties of the KS equation for parameter inference.
  • To overcome the limitations of existing costly statistical inference tools.

Main Methods:

  • A master-slave synchronization setup is employed, where a slave model's parameters are adapted based on observations from a master system.
  • The slave dynamics are data-driven, continuously adjusting parameters to achieve identical synchronization.
  • The method relies on the synchronization properties of the Kuramoto-Sivashinsky equation.

Main Results:

  • The proposed online parameter estimation method is computationally fast.
  • The method demonstrates robustness against initialization errors, observational noise, and variations in spatial resolution.
  • Extensive computer simulations validate the effectiveness and efficiency of the synchronization-based approach.

Conclusions:

  • The developed synchronization-based method offers a computationally efficient alternative for estimating Kuramoto-Sivashinsky equation parameters.
  • The approach is reliable and effective even with noisy data and imperfect initial conditions.
  • This work provides a valuable tool for analyzing complex spatio-temporal dynamics modeled by the KS equation.