Unlocking the Psychology Behind Effective Mathematical Modeling

(1) Problem Perception Stage

This stage focuses on correctly understanding the real problem, preparing mentally for its complexity, and gathering all relevant background information, variables, and conditions. It emphasizes re‑expressing the problem in visual or simplified forms to highlight main factors and clarify contradictions.

(2) Model Brewing Stage

Here necessary and reasonable simplifications are made by drawing on interdisciplinary knowledge and imaginative thinking. Assumptions are based on recognizing intrinsic patterns and analyzing data, ensuring essential factors are retained while irrelevant ones are discarded, and determining the model type (deterministic, stochastic, discrete, continuous, static, or dynamic).

(3) Modeling Inspiration Stage

After the first two stages, inspiration is sparked by selecting mature mathematical relationships, analogizing existing models, or using computer simulations. Strategies include leveraging known laws, drawing parallels with similar models (e.g., population growth vs. epidemic spread), and employing simulations when analytical solutions are infeasible.

Overall, these three phases form the beginning of a modeling project, requiring iterative validation, parameter adjustment, and refinement to produce a practical, accurate model that reflects the real problem.

Source: Shen Wenxuan, Yang Qingtiao – "Mathematical Modeling Attempts"