Research
2025: Social Distancing SIR Model
The academic setbacks my peers faced during the COVID-19 pandemic inspired me to investigate the mechanics of disease. In 2024, I used my skills in mathematics and programming to develop a custom SIR (susceptible, infected, recovered) model which incorporated the effects of social distancing to analyze its efficacy as a preventative measure.
I presented my findings at several levels of competition. My model earned 2nd place at the Florida State Science and Engineering Fair (FSEF) and was recognized as one of the top 300 projects in the nation by the Society for Science's Thermo Fisher Junior Innovator Challenge.
Simulation Video
GitHub (Click Below)
Poster (Click Below)
2025 Summer: Parameterization Method
Advised by Dr. Jason Mireles-James at FAU, I applied the Parameterization Method to numerically construct and visualize stable and unstable invariant manifolds of the Hénon map and Lorenz system. By deriving recursive equations for power-series coefficients, I computed curves and surfaces that describe how trajectories approach or move away from fixed points. I documented the mathematical derivations, implementation approach, and numerical checks in an introductory paper.
Images
GitHub (Click Below)
Paper (Click Below)
2026 - Present: DPSR + CAP
At FAU, advised by Dr. Jason Mireles-James, I developed Dense Polynomial Surrogate Reconstruction (DPSR) to recover polynomial differential equations from measurements without assuming sparsity. My Python and MATLAB work spans Lorenz, Mackey–Glass, and Kuramoto–Sivashinsky systems. I discover periodic-orbit candidates in surrogates and rigorously validate nearby true orbits using interval arithmetic, radii-polynomial bounds, and infinite-dimensional tail estimates. A manuscript is in preparation for SIADS.
