Abstract
Traffic congestion remains the biggest challenge in modern cities, influencing travel time,
fuel consumption and air quality. Understanding and forecasting traffic behavior and
patterns is a crucial element of transportation planning. This dissertation explores two
different but complementary approaches to model traffic flow: traditional mathematical
models based on diffusion equations, and modern data-driven models using Physics-
Informed Neural Networks (PINNs). By embedding the diffusion equation during the
training process, PINNs offer a powerful tool that can handle noisy or incomplete traffic
data, making them especially useful in real-world applications. The observed historical
data, diffusion equation, and boundary conditions were used to train PINNs.
The experimental findings demonstrate that important traffic dynamics can be captured
by both PINNs and the classical diffusion model. This shows that combining
mathematical understanding with machine learning techniques can lead to more accurate
and practical traffic flow models, paving the way for smarter transport systems
in the future. The strong performance of PINNs prediction output, especially during
afternoon peak hours confirms that such a model is not only mathematically sound
but also operationally relevant. The study’s accuracy is evaluated using the standard
error metrics: mean squared error (MSE), root mean squared error (RMSE) and mean
absolute error (MAE). The error values for the test set are MSE= 0.0089, RMSE=
0.3943, MAE = 0.2766 and R2 = 0.8153. Furthermore, the model shows low MSE on
the test set (0.0089) compared to the validation set (0.1054), indicating good predictive
accuracy on the sampled Mondays.
This research laid a basic foundation for hybrid modeling, focusing on one-dimensional
traffic flow using diffusion based of partial differential equations (PDEs). Future research
should consider expanding both the scope and depth of the hybrid model, such as multilane,
feeding the model with live sensor or GPS data, incorporating additional real-world
factors such as weather conditions, traffic incidents. The expansion could result in more
valuable real-time traffic management systems.