The state reconstruction problem of a heterogeneous dynamic system under sporadic measurements is considered. This system consists of a conversation flow together with a multi-agent network modeling particles within the flow. We propose a partial-state reconstruction algorithm using physics-informed learning based on local measurements obtained from these agents. Traffic density reconstruction is used as an example to illustrate the results and it is shown that the approach provides an efficient noise rejection.

This article investigates the use of a model-based neural network for the traffic reconstruction problem using noisy measurements coming from Probe Vehicles (PV). The traffic state is assumed to be the density only, modeled by a partial differential equation. There exist various methods for reconstructing the density in that case. However, none of them perform well with noise and very few deal with lagrangian measurements. This paper introduces a method that can reduce the processes of identification, reconstruction, prediction, and noise rejection into a single optimization problem. Numerical simulations, based either on a macroscopic or a microscopic model, show good performance for a moderate computational burden. Copyright

We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model used 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 aids 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.