Discovering Epidemiological ODE Models from Data: This project seeks to discover governing differential equations directly from data to determine the overall course of an epidemic. The two methodologies used to accomplish this will be the popular SINDy algorithm, developed by Brunton and Kutz et al. as well as the symbolic regression model applied to the derivative of the model. The group successfully used both methods to recover the SIR model from synthetic data with noise artificially added and to predict COVID-19 data. The PySR model, when effectively regularized showed promise in being able to robustly recover governing differential equations in the presence of noisy data.

Dynamic Traffic Network Simulation and Modeling the Impact of Pluvial Flash Flooding: In contemporary transportation systems, the management of traffic flow under heavy load and unpredictable events such as flash floods are a critical challenge. The conventional static traffic assignment, where routes are fixed at the onset, is insufficient in addressing real-time variations in trip volumes, accidents, work zones, and weather conditions. Dynamic Traffic Assignment (DTA) is a pragmatic solution, adapting routing strategies continuously to evolving traffic conditions. Existing navigation services, while adept at adapting to incidents like accidents and road closures, often neglect unreported events like flash floods, posing a significant threat to both drivers and system integrity. By simplifying the traffic network setting, we will replicate diverse flooding intensities, enabling comprehensive evaluation of our dynamic traffic assignment strategy. By systematically analyzing these simulations, our research aims to establish a robust and adaptive framework for rerouting under flash flood conditions, thereby enhancing the resilience and safety of modern transportation networks.

Using Physics Informed Neural Networks (PINNs) to Solve the Heat Equation: This paper examines the use of a novel technique that uses the auto-differentiation ca- pability of neural networks to solve the heat equation. This is a method that was proposed in Raissi, 2019 et al. This method makes use of neural networks as universal function approximators to match the solution to a partial differential equation.

Dopamine, Mimicry, and Value Alignment: Artificial Intelligence and Addiction: Computer scientists, philosophers, economists, and many others have voiced concerns about Artificial Intelligence (AI) for decades. This paper provides a framework and a review of how AI can be addictive by mimicking neuropleasurable stimuli for humans. It argues that this problem is exacerbated when the values of the humans interacting with AI and the values of the AI are poorly aligned. The paper examines the role of the dopaminergic reward system in powerful behavior reinforcement, what economic gains and externalities this causes, and how this may disproportionately affect certain subsets of the population. This paper also proposes a model to illustrate how, when considering factors of time, effort, and expected reward, the magnitude of the reward is not deterministic of human action. Lastly, the paper examines ethical frameworks and contemporary theories governing the use of AI to produce large-scale addiction, big-nudging, and general manipulation.