基于深度LSTM的高维混沌系统混合预测模型
A hybrid model based on deep LSTM for predicting high-dimensional chaotic systems
摘要：
提出了一种结合深度长短期记忆（LSTM）模型和动力系统的不精确经验模型的混合方法来预测高维混沌系统。通过叠加多个递归神经网络层将深层结构编码到LSTM中，并使用Adam优化算法训练混合模型。在均方根误差（RMSE）和异常相关系数（ACC）准则下，分别采用单层LSTM、多层LSTM和相应的混合方法，得到了Mackey-Glass系统和Kuramoto-Sivashinsky系统的统计结果.数值实验结果表明，该方法能有效避免多层LSTM模型在重构混沌吸引子时的快速发散，证明了基于梯度下降法的深度学习与经验模型相结合的可行性。
英文摘要：
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.
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