4B. Mathematical Model (Mô hình toán học)

Mathematical Model – Abstract

This subsection presents the Mathematical Model of V-Planning, establishing the quantitative framework for representing, analyzing, and optimizing urban value within the Urban Value Field (UVF). It formalizes urban value as a continuous spatiotemporal field governed by mathematical equations, state variables, and computational models that describe the dynamics of complex urban systems. The framework introduces the Urban Value Field Equation, reaction–diffusion models, network models, and optimization techniques to simulate value propagation, spatial interactions, and urban development processes. Advanced mathematical methods, including Hamiltonian optimization, Fredholm integral equations, and multi-objective optimization, are incorporated to support predictive modeling and planning optimization under complex spatial constraints. By integrating mathematics, spatial economics, Geographic Information Systems (GIS), and computational science, this model provides a rigorous analytical foundation for scenario simulation, infrastructure planning, and evidence-based urban decision-making.

Keywords: V-Planning; Mathematical Modeling; Urban Value Field (UVF); Multi-Objective Optimization; Computational Urban Science

4B.1. Mathematical Representation

4B.2. State Variables

4B.3. Continuous Field

4B.4. Urban Value Field Equation

4B.5. Reaction–Diffusion Model

4B.6. Network Model

4B.7. Hamiltonian Optimization

4B.8. Fredholm Integral Equation

4B.9. Dynamic System

4B.10. Multi-objective Optimization

4B.11. Model Stability

4B.12. Chapter Summary