JDNN: Jacobi Deep Neural Network for Solving Telegraph Equation

TL;DR

The paper introduces JDNN, a novel deep neural network architecture using Jacobi polynomials, designed to efficiently solve high-dimensional telegraph equations with improved accuracy and computational speed.

Contribution

The paper presents JDNN, a new neural network architecture employing Jacobi polynomials as activation functions for solving high-dimensional PDEs, demonstrating enhanced accuracy and efficiency.

Findings

Successfully solves high-dimensional telegraph equations.

Utilizes GPU acceleration for faster training.

Outperforms existing methods in accuracy and efficiency.

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.