  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.
