The nonlinear relationship between urban design form and energy efficiency

Optimizing urban form is a critical pathway for achieving low-carbon development, yet existing research often relies on linear assumptions, failing to capture the complex, stage-dependent dynamics of urban systems. This study constructs an Integrated Urban Form Index based on multidimensional indicators—compactness, connectivity, and complexity—and employs econometric models to investigate the non-linear impact of urban form on Total Factor Energy Efficiency. Empirical results confirm that the relationship follows a distinct S-shaped trajectory characterized by threshold effects, rather than a simple linear progression. The evolution of urban form is delineated into three dynamic regimes: a latent stage with limited impact, an acceleration stage with increasing marginal returns, and a saturation stage with diminishing benefits. Mechanism analysis reveals that transportation structure optimization and agglomeration economies serve as the dual drivers underpinning this evolution. Consequently, this study advocates for stage-adaptive planning strategies, suggesting that small and medium-sized cities focus on breaking through development thresholds, while large cities prioritize stock optimization and resilience enhancement to avoid high-carbon lock-in.