Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction

Junsheng Zhao, Yongmin Li, Xingjiang Yu, Xingfang Zhang
2014 Discrete Dynamics in Nature and Society  
For decades, Mackey-Glass chaotic time series prediction has attracted more and more attention. When the multilayer perceptron is used to predict the Mackey-Glass chaotic time series, what we should do is to minimize the loss function. As is well known, the convergence speed of the loss function is rapid in the beginning of the learning process, while the convergence speed is very slow when the parameter is near to the minimum point. In order to overcome these problems, we introduce the
more » ... troduce the Levenberg-Marquardt algorithm (LMA). Firstly, a rough introduction is given to the multilayer perceptron, including the structure and the model approximation method. Secondly, we introduce the LMA and discuss how to implement the LMA. Lastly, an illustrative example is carried out to show the prediction efficiency of the LMA. Simulations show that the LMA can give more accurate prediction than the gradient descent method.
doi:10.1155/2014/193758 fatcat:whtybk7vqnf2jfbdtv3git7e6u