Deep Euler method: solving ODEs by approximating the local truncation error of the Euler method

Understand

In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations.

• DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep neural networks which could obtain a high precision solution with a large step size.
• The deep neural network in DEM is mesh-free during training and shows good generalization in unmeasured regions.
• DEM could be easily combined with other schemes of numerical methods, such as Runge-Kutta method to obtain better solutions.