Hybrid forecasting of chaotic dynamical systems

• Main Author: Zhu, Yicheng
• Other Authors: Juan-Pablo Ortega Lahuerta
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Mathematical Sciences
• Online Access: https://hdl.handle.net/10356/175572
• Institution: Nanyang Technological University

We work on prediction methods for chaotic dynamical systems by integrating knowledge-based models (KBM) and reservoir computing (RC) techniques within the framework of physics-informed machine learning. The study focuses primarily on the Kuramoto-Sivashinsky (KS) equation, a model emblematic of chaotic systems prevalent in various physical sciences. We investigate the effectiveness of traditional numerical prediction methods alongside the hybrid Method of Experts (MoE) approaches. Our results show that while the stand-alone RC model and the hybrid model with static weights provide valuable predictive capacity, the integrated MoE model, which incorporates a hybrid of KBM and RC using dynamic weight adjustments based on real-time performance evaluations, provides more accurate predictions over longer periods and maintains a high level of distributional accuracy. This provides a novel approach to predicting chaotic behaviour with potential applications in climate science, epidemiology and fluid dynamics.