Predictions by classical and recurrent neural networks of time series with pseudo-periodic behaviour

Time series predictions are one of the main topics of current researches. For this purpose, I worked with the Cosmogeophysics group of the University of Turin to develop a new robust methodology based on deep neural networks to be applied to time series forecasting. We designed and implemented a classical Feed Forward Neural Network (FFNN), as well as two Long-Short Term Memory (LSTM) recurrent networks, to predict with high performances the future behaviour of time series containing pseudo-periodic components. The first LSTM network (1-STEP LSTM) and the classical one predict one-time step value at a time; to extend the prediction further in time an iterated procedure is adopted, in which the prediction for a time step is used, in place of the corresponding unmeasured value, to predict the value at the following time step. The other LSTM network (MULTISTEP LSTM) was designed to predict values at multiple time steps, thus avoiding the possible issue of error accumulation, often affecting iterated schemes. I tested the performances of these networks on the sunspot number time series (SSN) since it is characterized by a high signal-to-noise ratio and two dominant periodicities of different time scales, namely the 11-year-cycle (Schwabe cycle) and the centennial modulation (Gleissberg cycle). I used these numerical models to predict sunspot numbers for the next 10 years (Solar Cycle 25). The amplitude of the sunspot cycle itself, which determines its space weather consequences, is highly variable and difficult to predict. The LSTMs networks performed better than the classical FFNN in predicting sunspot number time series. FFNN prediction of the next solar cycle is smoother than the ones obtained by the recurrent networks. The 1-STEP LSTM and the FFNN both predict a slightly smaller cycle that the current one, while the MULTISTEP LSTM predicts a solar cycle 25 similar or somewhat stronger than the 24th cycle. The forecasting approach employing deep learning techniques is purely numerical: it relies solely on time series values. The preliminary comparison of our predictions with those obtained by physical models, available in the literature, provides a pretty good agreement between the two approaches. The approach adopted in my thesis work should allow understanding which deep learning forecasting technique matches physics-based predictions best, when they are available, and therefore to shed light onto the contribution that deep learning can give to the forecasting of geophysical time series. It could be particularly interesting to make similar predictions for climate time series which are generally characterized by lower levels of the signal-to-noise ratio.