A neural network-based method for solving a class of high-order nonlinear partial differential equations*

In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one-dimensional stationary form of Cahn-Hilliard/Allen-Cahn equation and its time-dependent derivative term is numerically calculated by using this method. The results of numerical examples show that the method has high accuracy in solving these problems.