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