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

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.