Chaotic time series prediction of nonlinear systems based on various neural network models

This paper discusses the chaos prediction of nonlinear systems using various neural networks based on the modified substructure data-driven modeling architecture. In the modeling step, we construct two-coefficient loss functions according to the linear multi-step method to improve the prediction accuracy of neural networks. Then, the predicted response data of the system is given by the forward Euler method and neural networks. Under such architecture, chaos forecasting is carried out on a five-degree-of-freedom duffing oscillator system via the feedforward neural network (FNN), long short-term memory (LSTM) network and LSTM encoder-decoder (LSTM ED). The numerical simulation results show that the model can predict chaotic time series even if a small amount of information and samples are known, and the prediction window is twice that of the observation window. Among these models, LSTM ED exhibits the highest accuracy in both short-term and long-term chaos prediction. Furthermore, the prediction results mainly involve three evaluation indicators: absolute error, mean absolute error, normalized root mean square error. Through error analysis and noise processing, LSTM ED shows superior stability, robustness and extrapolation ability. Its prediction error is about half of FNN and the maximum increase in accuracy is 71.3 %.