Analysis of traffic density dynamics under varied noise conditions using data-driven partial differential equations

The paper illustrates traffic flow dynamics using partial differential equations derived from data using the Physics-Informed Information Criterion technique [1]. Thus, the aim is to explain the effect of various noise levels by varying the convection term and diffusion coefficients over time. First, we analyze the model using the Lie symmetry approach and also obtain an optimal system. Using these optimized systems, traffic flow densities are calculated to study the effect of noisy data on the results. In addition, the flow of traffic densities is obtained via a traveling wave. Kink-type graphical representations are obtained, which aid in traffic congestion prediction. By understanding and predicting traffic behavior under certain noise levels, this approach significantly contributes to traffic management strategy development.