deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations
Machine Learning
2023-09-15 v1 Artificial Intelligence
Numerical Analysis
Numerical Analysis
Abstract
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a discretization technique are used in the proposed design. In each equation, a deep neural network is used to approximate the unknown function. Three forms of fractional differential equations have been examined to highlight the method's versatility: a fractional ordinary differential equation, a fractional order integrodifferential equation, and a fractional order partial differential equation. The results show that the proposed architecture solves different forms of fractional differential equations with excellent precision.
Cite
@article{arxiv.2309.07684,
title = {deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations},
author = {Ali Nosrati Firoozsalari and Hassan Dana Mazraeh and Alireza Afzal Aghaei and Kourosh Parand},
journal= {arXiv preprint arXiv:2309.07684},
year = {2023}
}