Deep Learning in Multi-step Forecasting of Chaotic Dynamics

Abstract

The prediction of chaotic dynamical systems’ future evolution is widely debated and represents a hot topic in the context of nonlinear time series analysis. Recent advances in the field proved that machine learning techniques, and in particular artificial neural networks, are well suited to deal with this problem. The current state-of-the-art primarily focuses on noise-free time series, an ideal situation that never occurs in real-world applications. This chapter provides a comprehensive analysis that aims at bridging the gap between the deterministic dynamics generated by archetypal chaotic systems, and the real-world time series. We also deeply explore the importance of different typologies of noise, namely observation and structural noise. Artificial intelligence techniques turned out to provide robust predictions, and potentially represent an effective and flexible alternative to the traditional physically-based approach for real-world applications. Besides the accuracy of the forecasting, the domain-adaptation analysis attested the high generalization capability of the neural predictors across a relatively heterogeneous spatial domain.