Neural-Network-Based Calibration of Macroscopic Traffic Flow Models

Abstract

This chapter proposes a neural-network-based calibration of macroscopic traffic flow models expressed in the form of nonlinear partial differential equations (PDEs). The calibration scheme/module developed aims at improving both accuracy and stability of the nonlinear PDE models in order to make them more realistic. In essence, the macroscopic nonlinear PDE models of traffic flow (proposed in the literature) are generally inaccurate, unstable, and unlikely to describe the realistic dynamics of traffic flow. To overcome these drawbacks we exploit the artificial neural network paradigm to build a concept called NN-PDE (neural network \(+\) PDE solver), which involves the macroscopic model (in the form of a nonlinear partial differential equation) on the one hand, and the calibration scheme/module-based artificial neural network (ANN) on the other. The calibration scheme/module is used to dynamically adjust/optimize all outputs of the nonlinear “PDE” model in order to obtain a realistic set of parameters that could be used by the PDE model to describe the real/realistic dynamics of traffic flow. Overall, specific attention is devoted to some relevant issues related to the modeling concept such as accuracy, stability, and overfitting, just to name a few. These issues generally occur due to the complexity of the PDE model at stake for the sake of an accurate traffic flow model. Finally, some simulation results are shown to demonstrate the effectiveness of the NN-PDE concept developed.