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This paper deals with traffic density reconstruction using measurements from Probe Vehicles (PVs). The main difficulty arises when considering a low penetration rate, meaning that the number of PVs is small compared to the total number of vehicles on the road. Moreover, the formulation assumes noisy measurements and a partially unknown first-order model. All these considerations make the use of machine learning to reconstruct the state the only applicable solution. We first investigate how the identification and reconstruction processes can be merged and how a sparse dataset can still enable a good identification. Secondly, we propose a pre-training procedure that helps the hyperparameter tuning, preventing the gradient descent algorithm from getting stuck at saddle points. Examples using numerical simulations and the SUMO traffic simulator show that the reconstructions are close to the real density in all cases.
Traffic state estimation (TSE), which reconstructs the traffic variables (e.g., density) on road segments using partially observed data, plays an important role on efficient traffic control and operation that intelligent transportation systems (ITS)
Traffic state estimation (TSE) bifurcates into two main categories, model-driven and data-driven (e.g., machine learning, ML) approaches, while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies in
We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical properties o
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate science,
Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate estimation