Abstract In this paper a time-varying state transition matrix of Tschauner-Hempel equations is designed by learning an analytical solution of the true anomaly using machine learning techniques. The problem of solving the true anomaly which is an necessary issue for calculate the state transition matrix of Tschauner-Hempel equations is transformed into a supervised learning problem. Then, a nearly analytical state transition matrix with time as the independent variable is designed. Based on the universal approximation theorem the feedforward neural network is used to infer a high-precision analytical solution. Finally, the feedforward neural network is trained based on the backpropagation by using the labeled data which are generated by presented data generation algorithm. It is demonstrated that the designed state transition matrix has high accuracy and is computationally highly efficient.


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    Titel :

    Feedforward neural network based time-varying state-transition-matrix of Tschauner-Hempel equations


    Beteiligte:
    Zheng, Maozhang (Autor:in) / Luo, Jianjun (Autor:in) / Dang, Zhaohui (Autor:in)

    Erschienen in:

    Advances in Space Research ; 69 , 2 ; 1000-1011


    Erscheinungsdatum :

    2021-10-05


    Format / Umfang :

    12 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch






    Best Forms of Solution of the Tschauner-Hempel Differential Equations

    Carter, T. E. / American Astronautical Society / American Institute of Aeronautics and Astronautics | British Library Conference Proceedings | 1997