Physics-informed Learning for Identification and State Reconstruction of Traffic Density

Abstract

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 firstorder 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.

A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation

“…Huang et al [38] studied the use of PIDL to encode the Greenshields-based LWR and validated it in the loop detector scenarios using SUMO simulated data. Barreau et al [39], [40], [41] studied the probe vehicle sensors and developed coupled micro-macro models for PIDL to perform TSE. Shi et al [42] extended the PIDL-based TSE to the second-order ARZ with observed data from both loop detectors and probe vehicles.…”

“…As to model identification, which is another feature of PIDL-based TSE, this paper only assumes a traffic flow conservation equation and optionally, a momentum equation for the velocity field, without specifying any mathematical relation between traffic quantities. The aforementioned related studies in [39], [41] directly fit a velocity function using measured density and velocity from probe vehicles before or during the PIDL training. In contrast, we focus on a more general case, where the output of the FD function is unobserved from sensors, and the end-to-end FD relation is to be learned directly using ML surrogates under the PIDL framework.…”

Physics-informed neural networks for modelling power transformer’s dynamic thermal behaviour

“…However, the use of these libraries is out of the scope of the presented study. An insightful aspect that will be one of the main targets of implementing the PINN algorithm is given by [21], where the physics-informed approach is applied to the traffic density reconstruction; however, it also describes an investigation applicable to our case. It introduces the ''first-order physics'' term, which is a term that also includes measurements in its implementation.…”

PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation

“…The innovative work of the network is to integrate the PDE residual into the loss function, which only requires the labeled data about the initial value and boundary conditions [17,18] or no labeled data [19][20][21] during the training process. PINN achieves good results in PDE and has a wide range of applications in other disciplines, including temperature modeling [22,23], traffic flow evaluation [24], and partial differential equation mining [25,26]. Despite the great success and wide application, there are still some problems in the application of the deep leaning method in the solution of PDE.…”