Introduction to Chaotic Dynamics’ Forecasting

Chaotic dynamics are the paradigm of complex and unpredictable evolution due to their built-in feature of amplifying arbitrarily small perturbations. The forecasting of these dynamics has attracted the attention of many scientists since the discovery of chaos by Lorenz in the 1960s. In the last decades, machine learning techniques have shown a greater predictive accuracy than traditional tools from nonlinear time-series analysis. In particular, artificial neural networks have become the state of the art in chaotic time series forecasting. However, how to select their structure and the training algorithm is still an open issue in the scientific community, especially when considering a multi-step forecasting horizon. We implement feed-forward and recurrent architectures, considering different training methods and forecasting strategies. The predictors are evaluated on a wide range of problems, from low-dimensional deterministic cases to real-world time series.