A machine learning radial basis deep neural network for solving the fractional chaotic financial system

Abstract

In this study, a machine learning radial basis deep neural network process is presented with the optimization of Bayesian regularization for solving the fractional order chaotic financial system, which is divided into four different categories. This novel designed machine learning procedure contains two hidden layers with 15 and 30 neurons in the feed-forward neural network, radial basis activation function, and optimization of Bayesian regularization. A fractional Caputo derivative is used to present more reliable solutions of the chaotic financial system as compared to integer order. The construction of the data is performed through the Adam solver to reduce the mean square error by splitting the statics into training 80 %, while 9 %, 9 % for both testing and authentication. Three different model’s cases are used to check the correctness of the deep neural network solver through the comparison and small absolute error. Moreover, the reliability of the novel designed solver is observed by using different measures based on regression coefficient, state transition, error histogram and best training values.