PhD Defense of Mr. Georges MURR

MURR Georges PhLAM Laboratory- UMR8523 - Team DYSCO

Title: Machine Learning-assisted spatiotemporal chaos forecasting 

Jury: S. COULIBALY (PhLAM, Supervisor), B. KIBLER (Université de Bourgogne, Referee), S. RESIDORI (Directrice de recherche , Referee), A. MUSSOT (Université de Lille, PhLAM, member), M. TILDI (Université Libre de Bruxelles, member), M. CLERC (Université du Chili, Member)

Abstract:

From towering rogue waves to powerful winds, extreme events can disrupt natural systems and human activity without warning. Though seemingly unpredictable, these events often arise from the complex dynamics of chaotic systems, particularly spatiotemporal chaos, where patterns unfold across both time and space. In this thesis, we study extreme events in optical systems, focusing on an optical fiber ring resonator modeled by the Lugiato-Lefever equation. This setup provides a controlled environment to analyze the chaotic behaviors that lead to such phenomena. Recent advancements in machine learning, especially neural networks, offer new tools for predicting chaotic dynamics. However, long-term forecasting remains challenging due to chaos’s inherent unpredictability. We propose extending the prediction horizon using information theory methods, like transfer entropy, to identify local regions contributing to extreme events and improve forecast accuracy. Additionally, we examine the turbulent dynamics generated by solitons in these systems, providing explanations for their onset and evolution. Our analysis offers new insights into chaotic behavior. Finally, we propose applying these methods to real-world wind dynamics to enhance forecasting and deepen understanding of chaotic natural systems.