Attractor Inspired Deep Learning for Modelling Chaotic Systems

Abstract

Predicting and understanding the behavior of dynamic systems have driven advancements in various approaches, including physics-based models and data-driven techniques like deep neural networks. Chaotic systems, with their stochastic nature and unpredictable behavior, pose challenges for accurate modeling and forecasting, especially during extreme events. In this paper, we propose a novel deep learning framework called Attractor-Inspired Deep Learning (AiDL), which seamlessly integrates actual statistics and mathematical models of system kinetics. AiDL combines the strengths of physics-informed machine learning and data-driven methods, offering a promising solution for modeling nonlinear systems. By leveraging the intricate dynamics of attractors, AiDL bridges the gap between physics-based models and deep neural networks. We demonstrate the effectiveness of AiDL using real-world data from various domains, including catastrophic weather mechanics, El Niño cycles, and disease transmission. Our empirical results showcase AiDL’s ability to substantially enhance the modeling of extreme events. The proposed AiDL paradigm holds promise for advancing research in Time Series Prediction of Extreme Events and has applications in real-world chaotic system transformations.