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.

翻译：本文旨在开发融合机器学习技术与宏观微分模型的新方法，用于车辆交通估计与预测。众所周知，数据驱动与模型驱动方法具有（有时互补的）优势与缺陷。我们考虑一个数据集，包含高速公路上车辆的通量及速度数据，这些数据由固定传感器采集，并按车道和车辆类别分类。通过基于LSTM递归神经网络的机器学习模型，我们外推出两条重要信息：1）传感器下方是否出现拥堵，2）未来30分钟内将经过传感器下方的车辆总量。这些信息随后用于改善描述传感器间交通流动态的基于LWR的一阶多类模型的准确性。第一条信息用于反转（凹形）基本图，从而从通量数据中恢复车辆密度，并直接将密度数据注入模型。这能更精确地逼近传感器间的动态，尤其当事故发生在未监测路段时。第二条信息则用作交通模型方程的边界条件，以更准确地重构未来任意时刻道路上的车辆总量。本文还将讨论基于真实场景的若干示例。真实数据由意大利高速公路公司Autovie Venete S.p.A.提供。