Predicting solutions of the stochastic fractional order dynamical system using machine learning  

作　　者：Zi-Fei Lin Jia-Li Zhao Yan-Ming Liang Jiao-Rui Li 

机构地区：[1]School of Statistics,Xi’an University of Finance and Economics,Xi’an 710100,China [2]Xi’an University of Finance and Economics,China(Xi’an)Institute for Silk Road Research,Xi’an 710100,China

出　　处：《Theoretical & Applied Mechanics Letters》2023年第3期188-198,共11页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China(NNSFC)(Grant No.11902234);Natural Science Basic Research Program of Shaanxi(Program No.2020JQ-853);Shaanxi Provincial Department of Education Youth Innovation Team Scientific Research Project(Program No.22JP025);the Young Talents Development Support Program of Xi’an University of Finance and Economics.

摘　　要：The solution of fractional-order systems has been a complex problem for our research.Traditional methods like the predictor-corrector method and other solution steps are complicated and cumbersome to derive,which makes it more difficult for our solution efficiency.The development of machine learning and nonlinear dynamics has provided us with new ideas to solve some complex problems.Therefore,this study considers how to improve the accuracy and efficiency of the solution based on traditional methods.Finally,we propose an efficient and accurate nonlinear auto-regressive neural network for the fractional order dynamic system prediction model(FODS-NAR).First,we demonstrate by example that the FODS-NAR algorithm can predict the solution of a stochastic fractional order system.Second,we compare the FODS-NAR algorithm with the famous and good reservoir computing(RC)algorithms.We find that FODS-NAR gives more accurate predictions than the traditional RC algorithm with the same system parameters,and the residuals of the FODS-NAR algorithm are closer to 0.Consequently,we conclude that the FODS-NAR algorithm is a method with higher accuracy and prediction results closer to the state of fractional-order stochastic systems.In addition,we analyze the effects of the number of neurons and the order of delays in the FODS-NAR algorithm on the prediction results and derive a range of their optimal values.

关 键 词：Fractional-order dynamical system Gaussian white noise Deep learning FODS-NAR algorithm 

分 类 号：O19[理学—数学] TP181[理学—基础数学]