Hybrid solver methods for ODEs: Machine-Learning combined with standard methods

In this article, we consider combined standard and machine learning methods to solve ODEs and PDEs. We deal with the minimisation problems for the machine learning algorithms and standard discretization methods, which are related to Runge-Kutta methods and finite difference methods. We show, that we could solve the ODEs with additional ML methods, e.g., feedforward network, such that it will accelerate the solver process.