  In this paper, we aim at developing new methods to join machine learning
techniques and macroscopic differential models for vehicular traffic estimation
and forecast. It is well known that data-driven and model-driven approaches
have (sometimes complementary) advantages and drawbacks. We consider here a
dataset with flux and velocity data of vehicles moving on a highway, collected
by fixed sensors and classified by lane and by class of vehicle. By means of a
machine learning model based on an LSTM recursive neural network, we
extrapolate two important pieces of information: 1) if congestion is appearing
under the sensor, and 2) the total amount of vehicles which is going to pass
under the sensor in the next future (30 min). These pieces of information are
then used to improve the accuracy of an LWR-based first-order multi-class model
describing the dynamics of traffic flow between sensors. The first piece of
information is used to invert the (concave) fundamental diagram, thus
recovering the density of vehicles from the flux data, and then inject directly
the density datum in the model. This allows one to better approximate the
dynamics between sensors, especially if an accident happens in a not monitored
stretch of the road. The second piece of information is used instead as
boundary conditions for the equations underlying the traffic model, to better
reconstruct the total amount of vehicles on the road at any future time. Some
examples motivated by real scenarios will be discussed. Real data are provided
by the Italian motorway company Autovie Venete S.p.A.
