Hybrid CA–deep learning model for 3D urban growth simulation

Abstract

Accurate three-dimensional (3D) urban growth simulation is essential for sustainable planning, yet most models separate horizontal expansion from vertical intensification and lack uncertainty quantification. We present a unified framework that integrates an entropy-based cellular automata (CA) model for horizontal growth with a deep neural network (DNN) for vertical prediction. A key innovation is the pixel-wise linkage of vertical growth to newly urbanized cells identified by the CA, enabling targeted, cell-level height forecasts, reducing computational noise, and overcoming the conventional decoupling of horizontal and vertical growth. Shannon entropy quantifies transition uncertainty, enhancing model transparency and interpretability. The framework flexibly simulates diverse urbanization scenarios, including compact, business-as-usual, and suburban patterns by adjusting development pressure and constraints. Empirical results show robust performance: the CA achieves 93.2% precision and 92.85% F1-score, while the DNN attains an R2 of 0.92 for height prediction. This interpretable, scenario-driven approach provides planners with rigorous, scalable tools for 3D urban growth analysis in rapidly changing regions.