Dynamics evolution prediction from time series data with recurrent neural networks in a complex system

Abstract

Time series data can be used to predict the dynamical behaviors without knowing equation model of a system. In this study, long-short term memory (LSTM) neural network is implemented to construct a complex dynamical system from data series. The network is trained through minimizing the loss function to obtain the optimal weight matrices of LSTM cells. We find that the LSTM network can well ”learn” the information of the complex system. The data series generated from periodic orbits of a nonlinear system can be exactly predicted by comparing the output of neural networks with the real complex system. For the chaotic data series, the time evolution of trajectories could exactly match the actual system in the short-term data. Moreover, the long-term ergodic behavior of the complex system remains in our prediction, although such chaotic data series are quite sensitive to the initial conditions and the ensuing increase in uncertainty.