Studies on transportation management systems have undergone several waves of advancement in both theory and practice, led by revolutions taking place in parallel, including automation, machine learning electrification, and sharing economy. My research focuses on a combination of two of these revolutions, control and learning methodologies and their applications in intelligent traffic systems. In this talk, I will discuss traffic state estimation problem of freeway stop-and-go traffic, also known as phantom traffic jam, a common phenomenon that has drawn a lot of research interests over the years. The congestion leads to acceleration-deceleration traffic oscillations on freeway, causing increased fuel consumption, and driving risk. Traffic state estimation problem refers to a process of inferring traffic state variables from partially observed traffic data. I will first show a methodological PDE model-based solution to predict traffic state values from boundary sensing data. Inspired by physics-informed machine learning, we develop observer-informed deep learning which integrates the PDE observer with deep learning paradigm. The observer-informed neural network forms a novel class of data-efficient function approximators that encode PDE observer as theoretical guarantee and improves the accuracy and convergence speed of spatial-temporal traffic state estimation.