Solving a Proposed Traffic Flow Model Using Deep Learning and Physical Constraint

Abstract

First order macroscopic model such as Lighthill-Whitham-Richards (LWR) has been extensively studied and applied to various homogenous traffic problems. Although numerical methods have been widely used with good performance, researchers are still searching for new methods for solving partial differential equations. In recent years, deep learning has achieved great success in many fields, such as image classification and natural language processing. Several studies have shown that deep neural networks have powerful function-fitting capabilities and have great potential in the study of partial differential equations. In this paper, we introduce an improved Physics-Informed Neural Network (PINN) for solving one dimensional proposed macroscopic model compared to B-spline collocation method. The experimental results show that PINN is effective in solving partial differential equations and deserves further research.