The book represents the first attempt to systematically deal with the use of deep neural networks to forecast chaotic time series. Differently from most of the current literature, it implements a multi-step approach, i.e., the forecast of an entire interval of future values. This is relevant for many applications, such as model predictive control, that requires predicting the values for the whole receding horizon. Going progressively from deterministic models with different degrees of complexity and chaoticity to noisy systems and then to real-world cases, the book compares the performances of various neural network architectures (feed-forward and recurrent). It also introduces an innovative and powerful approach for training recurrent structures specific for sequence-to-sequence tasks. The book also presents one of the first attempts in the context of environmental time series forecasting of applying transfer-learning techniques such as domain adaptation.
Author(s): Matteo Sangiorgio
Series: SpringerBriefs in Applied Sciences and Technology
Publisher: Springer
Year: 2022
Language: English
Pages: 110
City: Cham
Preface
Contents
1 Introduction to Chaotic Dynamics' Forecasting
References
2 Basic Concepts of Chaos Theory and Nonlinear Time-Series Analysis
2.1 Dynamical Systems and Their Attractors
2.2 Lyapunov Exponents
2.2.1 Average Exponents
2.2.2 Local Exponents
2.3 Chaotic Systems, Predictability, and Fractal Geometry
2.3.1 Chaotic Attractors and Lyapunov Time Scale
2.3.2 Correlation and Lyapunov Dimensions
2.4 Attractor Reconstruction from Data
2.4.1 Delay-Coordinate Embedding
2.4.2 Estimation of the Largest Lyapunov Exponent
References
3 Artificial and Real-World Chaotic Oscillators
3.1 Artificial Chaotic Systems
3.1.1 Logistic Map
3.1.2 Hénon Map
3.1.3 Generalized Hénon Map
3.1.4 Time-Varying Logistic Map
3.2 Real-World Time Series
3.2.1 Solar Irradiance
3.2.2 Ozone Concentration
References
4 Neural Approaches for Time Series Forecasting
4.1 Neural Approaches for Time Series Prediction
4.1.1 FF-Recursive Predictor
4.1.2 FF-Multi-Output Predictor
4.1.3 LSTM Predictor
4.2 Performance Metrics
4.3 Training Procedure
References
5 Neural Predictors' Accuracy
5.1 Deterministic Systems
5.1.1 Performance Distribution over the System's Attractor
5.1.2 Sensitivity to the Embedding Dimension
5.2 Stochastic Time Series
5.3 Non-Stationary System
5.4 Real-World Study Cases
5.4.1 Solar Irradiance
5.4.2 Ozone Concentration
References
6 Neural Predictors' Sensitivity and Robustness
6.1 Simplicity and Robustness of the Experimental Setting
6.2 Predictors' Long-Term Behavior
6.3 Remarks on the Training Procedure
6.3.1 Backpropagation and Backpropagation Through Time
6.3.2 Training with and Without Teacher Forcing
6.4 Advanced Feed-Forward Architectures
6.5 Chaotic Dynamics in Recurrent Networks
References
7 Concluding Remarks on Chaotic Dynamics' Forecasting
References
Index
