Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network

TL;DR

This paper develops a hybrid neural network model optimized with particle swarm optimization to predict chaotic time series and assess uncertainties under noise, advancing forecasting accuracy and understanding of dynamical systems.

Contribution

The study introduces a stochastic hybrid ANN+PSO model that estimates prediction uncertainties and analyzes noise impact on chaotic system predictions.

Findings

The hybrid ANN+PSO outperforms existing models in short-term chaotic time series prediction.

Incorporating stochastic procedures enables uncertainty quantification in noisy predictions.

Noise level significantly affects the accuracy and stability of the chaotic system forecasts.

Abstract

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 ($\sigma_{N}$) from 0.01 to 0.1.