Research
Transportation Modeling
My primary research interests are in the analysis and simulation of transportation systems. I specialize in multiscale modeling for traffic flow as well building discrete-event simulation models. From individual vehicle interactions to system-wide behavior, I study how microscopic behaviors aggregate to create large-scale patterns.
Ultimately, my goal is to contribute to the development of smarter, more sustainable transportation systems by optimizing routes, improving decision-making algorithms, and minimizing resource usage.
Theoretical Fluid Dynamics
My doctoral thesis research was primarily in analytical fluid dynamics. The main focus was on the theory of traffic flow, in which the motion of cars on a roadway is compared to that of a fluid stream. I am also interested more broadly in hyperbolic conservation laws and collective dynamics. Common examples of continuum models of traffic flow include the first order Lighthill-Whitham-Richards (LWR) model or the second order Aw-Rascle-Zhang (ARZ) model, in which the density and velocity of traffic each have their own (coupled) dynamics. The advancements I have made in this area of research focus upon the incorporation of nonlocal effects which represent the anticipation of downstream traffic conditions. Click below to read some papers I co-authored with my advisor, Dr. Changhui Tan, regarding analysis of first and second order nonlocal macroscopic models.
(Scientific) Machine Learning
I also have an interest in applying machine learning for transportation problems. Deep learning in particular is well suited for analyzing the differential equations arising from traffic flow- in particular those models which are physics-informed. ML can be used in this respect both for traffic state estimation (TSE) or equation discovery.
I'm also interested in the prospect of leveraging machine learning to improve exploration algorithms for very large traffic networks. Graph embedding techniques such as Node2Vec can be used to train heuristic functions that accelerate A* searches on known graphs representing multimodal transportation networks.
Computational Fluid Dynamics
During summer 2023, I served as a graduate student intern at UMD ARLIS. With guidance from Dr. James Baeder, our team used machine learning to improve CFD solvers for the Spalart Allmaras (SA) turbulence closure model for Reynolds-Averaged-Navier-Stokes (RANS) equations. While turbulence models for RANS are attractive compared to computationally intractable direct numerical simulation (DNS), current turbulence models perform poorly when adverse pressure gradients (e.g. separated flow) is present. We used Field-Inversion-Machine-Learning (FIML) to produce a neural network correction to the SA model by modifying the turbulence production term. In house mesh generation and flow solvers were computed using the UMD Zaratan HPC cluster (80 Nvidia A100 GPUs!). For the FIML step, adjoint methods are used to compute gradients.
Figure: One sees a recirculating flow in the separated flow region. The nlf-0416 airfoil is experiencing stall due to high angle of attack (20 degrees). SA turbulence model is inaccurate in quantifying loss of lift owing to this phenomenon.
Conferences, Workshops, and Seminars
09/18/2021 44TH SIAM-SEAS conference, Auburn University
Contributed presentation: On a Class of Nonlocal Macroscopic Traffic Models.
WINNER: Best Presentation Award.
09/24/2021 ACM Student Seminar, University of South Carolina
Talk: Hyperbolic Conservation Laws and Nonlocal Traffic Flow Theory
04/22/2022 ACM Student Seminar, University of South Carolina
Talk: Uniqueness of Entropy Solutions for Scalar Conservation Laws.
06/28/2022-06/29/2022 Partners for Minorities in Engineering and Computer Science
Senior precalculus workshop
09/28/2022 ACM Student Seminar, University of South Carolina
Talk: Traffic flow - Nonlocal to Local Solutions
10/25/2022 PME and Gamecock Math Club (undergraduate math club), University of South Carolina
Talk: A 'Crash' Course on the Mathematics of Traffic Flow
11/12/2022 40th Southeastern-Atlantic Regional Conference on Differential Equations, NC State University
Contributed presentation: Sharp Critical Thresholds for a Class of Nonlocal Traffic Flow Models
01/25/2023 Graduate Colloquium, University of South Carolina
Talk: Fluid Dynamics: Scalar Balance Laws for Traffic Flow
03/17/2023 AMS Sectional Meeting, Georgia Tech
08/04/2023 UMD ARLIS Research Conference
Poster presentation: Neural Networks for Improved Turbulence Models
03/18/2024 University of South Carolina
Doctoral thesis defense: Global Well-Posedness of Nonlocal Conservation Laws Arising from Traffic Flow