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JDNN: Jacobi Deep Neural Network for Solving Telegraph Equation

Maryam BabaeeiKimia Mohammadi MohammadiZeinab HajimohammadiKoroush Paranda
Dec 2022
摘要
In this article, a new deep learning architecture, named JDNN, has beenproposed to approximate a numerical solution to Partial Differential Equations(PDEs). The JDNN is capable of solving high-dimensional equations. Here, JacobiDeep Neural Network (JDNN) has demonstrated various types of telegraphequations. This model utilizes the orthogonal Jacobi polynomials as theactivation function to increase the accuracy and stability of the method forsolving partial differential equations. The finite difference timediscretization technique is used to overcome the computational complexity ofthe given equation. The proposed scheme utilizes a Graphics Processing Unit(GPU) to accelerate the learning process by taking advantage of the neuralnetwork platforms. Comparing the existing methods, the numerical experimentsshow that the proposed approach can efficiently learn the dynamics of thephysical problem.
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