Concluding Remarks on Chaotic Dynamics’ Forecasting

In this book, we compared different neural approaches in the forecasting of chaotic dynamics, which are well-known for their complex behaviors and the difficulty of their prediction. Our analysis shows that the LSTM predictor trained without teacher forcing is the most accurate approach in the forecasting of complex oscillatory time series. This predictor always provides the best accuracy in all the considered tasks, spanning a wide range of complexity and noise sources. It also demonstrates the ability to adapt to other domains with similar features without a relevant decrease of accuracy. The comparison with the real system used as predictor in a noisy environment is particularly interesting: even the complete knowledge of the system structure does not allow perfect predictions when the initial conditions are only approximately known. This allows the border between time series forecasting and system identification problems to be clearly defined.