06/30/2026
Algebra, MathBio, and Numerical PDE Group Presentations: On Wednesday July 1st 11AM-2:15PM in GP227 the local REU groups will present the projects they have worked on during the summer.
The schedule is as follows:
11AM-11:50AM Algebra group: Vu Minh Khang Ho, Hans Laren, and Nathan McWilliams (Mentors: Dr. Perlman and Dr. Polstra)
11:50 – 12:15 PM Break/pizza
12: 15 – 1:05 MathBio/Numerical PDE: Spence Hanegan (Mentors: Dr. S. Shao and Dr. Zhao)
1:15- 2:05 Computational Modeling: Warren Chen, Levi Maxwell, and Jonathan Wisnoff (Mentors: Dr. Wang and Dr. J. Zhao)
You can find (two of) the abstracts below.
The abstract for the MathBio/Numerical PDE group:
Title: Physics-informed Neural Networks for the Poisson-Boltzmann Equation
Abstract: The electrostatic potential of proteins is necessary for computing the solvation free energy used for biomolecular modeling and drug discovery. However, the widely used Poisson-Boltzmann Equation (PBE) for solving electrostatic potential presents significant numerical challenges such as singular atomic charges, nonlinear terms, and sharp dielectric interfaces. Applying Physics-Informed Neural Networks (PINN) to the PBE provides a promising alternative to traditional mesh-based schemes. Existing PINN approaches address the PBE’s piecewise-defined nature by using cPINN or xPINN architectures; however, the resulting loss functions are complex and can lead to training instability and poor computational efficiency. We developed a PINN method that employs a Sobolev extension to represent a piecewise continuous function in $\mathbb{R}^n$ as a continuous function in $\mathbb{R}^{n+1}$. This reformulates the PBE as a continuous problem, a setting more suited to neural network approximation. We analyze and validate this approach against the Kirkwood Sphere PBE benchmark and a diverse set of proteins.
The abstract for the Computational Modeling group:
Title: Mathematical Modeling of Human Behavior in Epidemics Using Population Networks, Game Theory, and Digital Twins
Abstract: Human behavior strongly shapes epidemic transmission and the impact of public health interventions. This REU project examines this issue through three related projects focused on social contacts, behavioral responses, and campus-scale simulation.
(1) The first project reconstructs realistic population contact networks from previously collected contact data. Using simulated annealing and network rewiring, it produces network structures that preserve important features of empirical contact patterns and can be used in epidemic simulations. (2) The second project develops a game-theoretic model of behavioral decision-making during an epidemic. Individuals choose between compliance and noncompliance with public health guidance according to a logit equilibrium that accounts for perceived infection risk, economic burden, government mandates, peer influence, and restriction fatigue. (3) The third project develops an interactive digital twin of the University of Alabama campus for simulating epidemic scenarios and evaluating intervention strategies. The simulator provides a campus-scale platform incorporating epidemic dynamics, behavioral assumptions, and policy interventions.
Overall, these projects offer complementary approaches to modeling human behavior in epidemics and provide building blocks for a future integrated framework combining contact networks, behavioral decision-making, and digital twin simulation.
