Application Of Caputo Fractional Derivative Model And BP Neural Network Model In China's GDP Growth Forecas

As a generalization of integer derivative,fractional derivative provides an excellent tool for describing the memory and heredity of various materials and processes,and can better predict and control the order of magnitude of data.As the simplest neural network model,BP neural network can flexibly solve the problem of data fluctuation.In order to combine the advantages of the two,in this paper,we study the application of Caputo fractional derivative model,BP neural network model and BP neural network model of fractional order optimization in China’s economic prediction.Firstly,principal component analysis and adaptive lasso are used to reduce the dimension of variables and remove the multicollinearity between variables.The principal component score obtained by principal component analysis is F₁,F₂ and six variables selected by adaptive lasso to establish Caputo fractional derivative model.In this paper,we use Nelder Mead algorithm to solve the parameters in the fractional derivative model,and give the predicted values of Caputo fractional derivative model under two methods.Finally,an example is given to verify the prediction accuracy of the model.Secondly,the established fractional derivative model is used to calculate the trend value of gross domestic product（GDP）.At the same time,the offset of trend value minus the actual GDP value is used as the output variable of BP neural network to carry out network training.After the training,the algebraic sum of trend value and offset is the predicted GDP value,so as to optimize BP neural network.Finally,compared with the ordinary neural network model,the experimental results show that the BP neural network model optimized by fractional derivative model further improves the fitting effect and prediction accuracy.From the comparison,the BP neural network model optimized by Caputo fractional derivative model can better predict the growth trend of China’s GDP,and provide a reference for improving the fitting and prediction accuracy,expanding the application scope of the model and China’s economic growth prediction.