Research and Publications

My research primarily focuses on dynamics of multi agent systems with a specific focus on traffic flow and biological systems. I delve into the development and application of mathematical models to tackle complex challenges in topological data analysis of biological patterns, traffic control, traffic wave phenomena, energy efficiency optimization, and the integration of real-world data into these models with competencies in programming, simulations, numerical methods, optimization, data analysis, fitting, and visualizations.

Traffic Modeling and Control: Existing traffic models are widely used in multiple frameworks, most prominently, microscopic vehicle-scale occurring on the scale of seconds and macroscopic city-scale flow patterns that develop over the scale of hours. Practical applications usually employ either one or the other framework, and there is little overlap in the respective research communities. One aspect of my work is to develop mathematical techniques to bridge the two scales. Of particular importance are models that can capture dynamic instabilities and traveling traffic waves called phantom jams. Such models are particularly challenging to analyze, as many papers on PDE models explicitly exclude the unstable situation. Starting from existing models, my work particularly addresses the averaging of scales and the understanding of macroscopic manifestations of microscopic traffic waves with the relevance of dampening those waves in the presence of sparse control in light of the energy demand of traffic at the vehicle-scale, waves-scale, and city scale. 

Energy Modeling and Optimization: The purpose of introducing sparse control into traffic is the ability to effectively dampen waves, but more importantly, to decrease the overall energy consumption and mitigate the effects of climate change from the transportation industry. Existing energy models used in the literature are simplistic, ignoring many complicated factors that contribute to energy consumption, and are not capable of bridging between micro and macro scales. We develop a model reduction pipeline from high fidelity software to vehicle specific polynomial energy models that can allow us to estimate fuel rates instantaneously in time during simulations and without using hysteresis effects. Our simplified model was developed for six different vehicle types and validated on EPA drive cycles and is used in the training and design of controlled vehicles and in optimization problems to find optimal fuel trajectories.