This is part 1 of the video series on my doctoral research. In this video, I will cover the research plan for my doctoral dissertation, and the relevant mathematical concepts such as scalar conservation laws and the method of characteristics. 

Part 2 of this video series on my doctoral research focuses on developing a physics-informed deep learning (PIDL) paradigm for traffic state estimation (TSE). 

In this video, PIDL is presented with LWR and CTM formulations, and case studies are provided for the validation of the PIDL application approach for TSE. 

I will highlight in this video the challenges and limitations of PIDL in the traffic state estimation setting and discuss mitigation strategies. I will also present the integration of nonlocal physics in training PIDL for improved performance. 

Physics-informed deep learning (PIDL) incorporates the law of physics into the optimization process of training a neural network to achieve fast convergence and precise learning outcomes. 

This part 1 of my presentation covers the topic of flow conservation laws and applying PIDL for traffic state estimation (TSE). 

Part 2 of my presentation on PIDL presents the two case studies using (1) synthetic connected vehicle data, (2) Next Generation Simulation (NGSIM) vehicle data. 

It also discusses the limitation of PIDL method with the hyperbolic LWR partial differential equation (PDE).