The 13th AIMS Conference on Dynamical Systems, Differential Equations And Applications
May 31 – June 4, 2023, Wilmington, NC USA
Researchers from C2SMART attended and presented at the five day AIMS conference in Wilmington, North Carolina.
Jingqin Gao (NYU) and Bilal Thonnam Thodi (NYU Abu Dhabi) presented in the section Special Session 57: Mathematical Models for Traffic Monitoring and Control. This session was organized by Sean McQuade (Rutgers). The goal of this conference was to promote collaboration between the mathematicians and applied scientists whose work is often interconnected.
Read more about the conference here.
Leveraging connected and automated vehicle data for queue-informed and incident-aware ramp metering strategies to improve highway operations
Connected and automated vehicles (CAV) allow for the generation and sharing of enriched data. When these data are collected and utilized, it presents opportunities to enhance operational strategies aimed at better managing and improving traffic flow and safety. This study aims to develop and evaluate advanced queue-informed and incident-aware ramp metering algorithms. The queue-informed algorithm uses more accurate on-ramp queue estimation from CAV data to smooth metering rates, while the incident-aware algorithm integrates feedforward control into feedback ramp metering for distant bottlenecks. These control strategies are evaluated at both local and system-wide levels using a simulation-based approach to assess their impact on highway mobility, safety, efficiency, and reliability.
Learning inverse solver for scalar nonlinear hyperbolic PDEs: Application to the LWR traffic flow model
Presenter: Bilal Thonnam Thodi
New York University Abu Dhabi, United Arab Emirates
Collaborators: Sai Venkata Ramana Ambadipudi, Saif Eddin Jabari
First-order macroscopic traffic flow models, which are instances of nonlinear hyperbolic partial differential equations, are conventionally solved using numerical schemes which are grid-dependent and require complete knowledge of initial and boundary data. We study learning a generic inverse solver for approximating weak solutions to arbitrary input conditions, e.g., spatial boundary or random collocation points, using an operator learning framework. Under this framework, the inverse solver is a parametric operator that learns a family of weak solutions offline from data (historical simulation). Computing solution to new inputs is then a single forward evaluation of the operator. This avoids resolving the problem for every new input instance, lowering the computational cost. We also present algorithms to generate sparse training datasets and efficiently learn the essential features of the hyperbolic solutions, namely, shocks and rarefaction waves. We illustrate the proposed method for solving Lighthill-Witham-Richards (LWR) traffic flow model and discuss the generalization error growth. These fast inverse solvers can be potentially used for real-time traffic monitoring and control.