JDNN: Jacobi Deep Neural Network for Solving Telegraph Equation

Abstract: In this article, a new deep learning architecture, named JDNN, has been proposed to approximate a numerical solution to Partial Differential Equations (PDEs). The JDNN is capable of solving high-dimensional equations. Here, Jacobi Deep Neural Network (JDNN) has demonstrated various types of telegraph equations. This model utilizes the orthogonal Jacobi polynomials as the activation function to increase the accuracy and stability of the method for solving partial differential equations. The finite difference time discretization technique is used to overcome the computational complexity of the given equation. The proposed scheme utilizes a Graphics Processing Unit (GPU) to accelerate the learning process by taking advantage of the neural network platforms. Comparing the existing methods, the numerical experiments show that the proposed approach can efficiently learn the dynamics of the physical problem.