A hybrid model based on deep LSTM for predicting high-dimensional chaotic systems

Understand

We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems.

• The deep hierarchy is encoded into the LSTM by superimposing multiple recurrent neural network layers and the hybrid model is trained with the Adam optimization algorithm.
• The statistical results of the Mackey-Glass system and the Kuramoto-Sivashinsky system are obtained under the criteria of root mean square error (RMSE) and anomaly correlation coefficient (ACC) using the singe-layer LSTM, the multi-layer LSTM, and the corresponding hybrid method, respectively.
• The numerical results show that the proposed method can effectively avoid the rapid divergence of the multi-layer LSTM model when reconstructing chaotic attractors, and demonstrate the feasibility of the combination of deep learning based on the gradient descent method and the empirical model.