A macroscopic traffic flow modelling and collision avoidance using B-spline and Physics-Informed Neural Network approaches

The macroscopic model, such as the Lighthill-Whitham-Richards (LWR), has been extensively studied and applied to various homogeneous traffic problems. However, numerical methods have been widely used with good performance. The outcome of this work is the proposal of a one-dimensional speed-density model. We applied both the B-spline collocation and the Physics-Informed Neural Network (PINN) methods to solve this model. The results clearly demonstrated that the B-spline method outperforms the PINN method in terms of accuracy. These results were then used firstly to compare it with thus obtained with a microscopic urban mobility simulator (SUMO) and secondly to visualize collision phenomena which are crucial for public safety. To manage collisions, the Intelligent Driver Model (IDM) was implemented. This integrated approach highlights the effectiveness of our density-speed model, coupled with advanced solving and control techniques, in enhancing the understanding and management of traffic.