Sensitivity of Chaotic Dynamics Prediction to Observation Noise

Recent advances in nonlinear time-series prediction demonstrated the ability of recurrent neural network to forecast chaotic time series on a multi-step horizon, outperforming previous approaches. Researches considered chaotic systems with different degree of complexity, but the analysis was mainly limited to the noise-free case. In this work, we extend the analysis to a noisy environment, in order to fill the gap between deterministic and real-world time series. We consider four archetypal deterministic chaotic systems each with different levels of additive noise, representing the observation uncertainty always affecting practical applications. A time series of solar irradiance is also taken into account as a real-world case study. Various neural architectures, including feed-forward and recurrent networks, are adopted as predictors. LSTM cells are used as recurrent neurons, with a special focus on the training approach. As in the noise-free case, LSTM trained without the traditional teacher forcing, i.e., with a training that replicates the forecasting conditions, proved to be the best architecture. The experiments on the archetypal systems also shows that the error due to the model identification is negligible if compared to the one caused by a small observation noise. In other words, system identification and predictions are well distinct tasks.