Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network
This work addresses time series prediction for chaotic systems, which is incremental as it combines existing methods with noise analysis.
The study tackled predicting chaotic time series using a hybrid neural network optimized with particle swarm optimization, achieving performance comparable to existing literature and analyzing the impact of noise by extending the method with a stochastic procedure to compute prediction uncertainties for noise levels from 0.01 to 0.1.
In this study, an artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the short-term $x(t+6)$. The performance prediction was evaluated and compared with another studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute uncertainties of predictions for noisy Mackey--Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level ($σ_{N}$) from 0.01 to 0.1.