Math-Modeling

Finalist Award — Top ~7% globally at the 2023 High School Mathematical Contest in Modeling. The Model We constructed a Dandelion Spread PDE Model (DSM) — a system of four coupled partial differential equations that model population densities of: Settled dandelion seeds Dandelion plants Puffballs Drifting seeds We corrected the Fisher model by multiplying a logistic term to obtain a logistic population growth that depicts the effect of intraspecific competition on the dandelion population. ...

Advanced to Final Defense — Top 26 among 900+ teams at the IMMC Greater China International Round. Approach Applied machine learning methods — Entropy Weight and K-Means clustering — to evaluate different development plans for a 5-square-kilometer land area. The model considered three key dimensions: Environmental impacts — ecological footprint and sustainability metrics Economic profits — projected returns and cost-benefit analysis Community utilities — social infrastructure and quality of life factors The optimization framework balanced these competing objectives to find the most effective land development strategy. ...

Advanced to International Round at the IMMC Greater China National Round. Approach Applied machine learning classification methods to classify lizards into 26 species: Logistic Regression — baseline linear classifier Decision Tree — interpretable tree-based model Random Forest — ensemble method for improved accuracy The models were trained on morphological and behavioral features to achieve reliable multi-class species identification. Download Full Paper (PDF)

Global Meritorious Winner — Top ~10% among 11,296 teams. The only high school team to achieve this on Problem B (among 728 teams). Methodology We first built an optimization model by subtracting the predicted economic profit using the modeled negative impacts, and conducted simulated annealing to obtain the value of each variable for the optimized policy. To account for changes in animal populations and propose an alternative policy that preserves these populations, we developed our animal population model using the logistic model framework. This model includes the additional mortality rate resulting from policies that permit hunting. ...