Learning-based State Reconstruction for a Scalar Hyperbolic PDE under noisy Lagrangian Sensing

Abstract

The state reconstruction problem of a heterogeneous dynamic system under sporadic measurements is considered. This system consists of a conversation flow together with a multi-agent network modeling particles within the flow. We propose a partial-state reconstruction algorithm using physics-informed learning based on local measurements obtained from these agents. Traffic density reconstruction is used as an example to illustrate the results and it is shown that the approach provides an efficient noise rejection.

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.…”