Deep neural network for system of ordinary differential equations: Vectorized algorithm and simulation

Abstract

This paper is aimed at applying deep artificial neural networks for solving system of ordinary differential equations. We developed a vectorized algorithm and implemented using python code. We conducted different experiments for selecting better neural architecture. For the learning of the neural network, we utilized the adaptive moment minimization method. Finally, we compare the method with one of the traditional numerical methods-Runge–Kutta order four. We have shown that, the artificial neural network could provide better accuracy for smaller numbers of grid points.

Keywords

• Deep Neural Network
• Algorithm
• Systems of ordinary differential equation