Research on Solving Ordinary Differential Equations (ODEs) Based on Machine Learning

Aiming to solve the ordinary differential equations that often appear in the scientific calculation, the solution method is studied using a machine learning algorithm. A method of constructing machine learning samples from numerical solutions of ordinary differential equations is proposed, which solves the problem of mapping the model from physical to machine learning. The machine learning sample set is reconstructed from the traditional numerical solutions for the missile motion differential equations. The differential equations samples are studied using a deep feedforward network and LSTM network, and the trained network results are obtained. Good prediction accuracy of the established learning model is shown by the verification of learning results. The studies we have performed showed that it could have a very high acceleration ratio up to 2000 by using machine learning to solve the missile motion differential equations.