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

TL;DR

This paper introduces a hybrid deep LSTM model combined with empirical dynamical models to improve the prediction accuracy of high-dimensional chaotic systems, demonstrating enhanced stability and effectiveness.

Contribution

It presents a novel hybrid approach integrating deep LSTM networks with empirical models, addressing divergence issues in chaotic system prediction.

Findings

Hybrid model outperforms single-layer LSTM in chaotic prediction

Deep LSTM effectively captures complex dynamics of chaotic systems

Method reduces divergence and improves stability in high-dimensional systems

Abstract

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.