Solving the linear transport equation by a deep neural network approach

Abstract

<p style='text-indent:20px;'>In this paper, we study linear transport model by adopting <i>deep learning method</i>, 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.</p>