Open AccessSolving the linear transport equation by a deep neural network approach
Author(s) -
Zheng Chen,
Liu Liu,
Lin Mu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021070
Subject(s) - artificial neural network , convergence (economics) , deep learning , computer science , partial differential equation , deep neural networks , artificial intelligence , mathematics , algorithm , mathematical analysis , economics , economic growth
In this paper, we study linear transport model by adopting deep learning method , in particular deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt it to study kinetic models, in particular the linear transport model. Moreover, theoretical analysis on the convergence of neural network and its approximated solution towards analytic solution is shown. We demonstrate the accuracy and effectiveness of the proposed DNN method in numerical experiments.