The traffic delay due to congestion cost the U.S. economy $ 81 billion in 2022, and on average, each worker lost 97 hours each year during commute due to longer wait time. Traffic management and control strategies that serve as a potent solution to the congestion problem require accurate information on prevailing traffic conditions. However, due to the cost of sensor installation and maintenance, associated sensor noise, and outages, the key traffic metrics are often observed partially, making the task of estimating traffic states (TSE) critical. The challenge of TSE lies in the sparsity of observed traffic data and the noise present in the measurements. The central research premise of this dissertation is whether and how the fundamental principles of traffic flow theory could be harnessed to augment machine learning in estimating traffic conditions. This dissertation develops a physics-informed deep learning (PIDL) paradigm for traffic state estimation. The developed PIDL framework equips a deep learning neural network with the strength of the governing physical laws of the traffic flow to better estimate traffic conditions based on partial and limited sensing measurements. First, this research develops a PIDL framework for TSE with the continuity equation Lighthill-Whitham-Richards (LWR) conservation law - a partial differential equation (PDE). The developed PIDL framework is illustrated with multiple fundamental diagrams capturing the relationship between traffic state variables. The framework is expanded to incorporate a more practical, discretized traffic flow model - the cell transmission model (CTM). Case studies are performed to validate the proposed PIDL paradigm by reconstructing the velocity and density fields using both synthetic and realistic traffic datasets, such as the next-generation simulation (NGSIM). The case studies mimic a multitude of application scenarios with pragmatic considerations such as sensor placement, coverage area, data loss, and the penetration rate of connected autonomous vehicles (CAVs). The study results indicate that the proposed PIDL approach brings exceedingly superior performance in state estimation tasks with a lower training data requirement compared to the benchmark deep learning (DL) method. Next, the dissertation continues with an investigation of the empirical evidence which points to the limitation of PIDL architectures with certain types of PDEs. It presents the challenges in training PIDL architecture by contrasting PIDL performances in learning the first-order scalar hyperbolic LWR conservation law and its second-order parabolic counterpart. The outcome indicates that PIDL experiences challenges in incorporating the hyperbolic LWR equation due to the non-smoothness of its solution. On the other hand, the PIDL architecture with the parabolic version of the PDE, augmented with the diffusion term, leads to the successful reassembly of the density field even with the shockwaves present. Thereafter, the implication of PIDL limitations for traffic state estimation and prediction is commented upon, and readers' attention is directed to potential mitigation strategies. Lastly, a PIDL framework with nonlocal traffic flow physics, capturing the driver reaction to the downstream traffic conditions, is proposed. In summary, this dissertation showcases the vast capability of the developed physics-informed deep learning paradigm for traffic state estimation in terms of efficiently utilizing meager observation for precise reconstruction of the data field. Moreover, it contemplates the practical ramification of PIDL for TSE with the hyperbolic flow conservation law and explores the remedy with sampling strategies of training instances and adding the diffusion term. Ultimately, it paints the picture of potent PIDL applications in TSE with nonlocal physics and suggests future research directions in PIDL for traffic state predictions.


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Graduation Date





Agarwal, Shaurya


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Civil, Environmental, and Construction Engineering

Degree Program

Civil Engineering


CFE0009538; DP0027545





Release Date

May 2023

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)