Spatiotemporal evolution of regional innovation capacity from an open innovation perspective

This study extends the concept of open innovation from the firm level to regional innovation ecosystems by integrating social-ecological system insights and operationalizing a 3D index architecture covering basic innovation capacity, open innovation capacity, and innovation adaptability. Using a projection pursuit model optimized by a real-coded accelerating genetic algorithm (RAGA-PPM), kernel density estimation, and spatial correlation analysis, we evaluate the regional innovation capacity of 31 Chinese provinces from 2011 to 2021 and examine their spatiotemporal evolution. Results indicate that innovation adaptability carries the largest and most stable weight among Level 1 dimensions, indicating that coordination, learning, and risk absorption routines increasingly shape how inputs and openness translate into outcomes. Spatially, Beijing–Tianjin–Hebei, the Bohai Rim, the Yangtze River Delta, and the Pearl River Delta all exhibit strong capacity but heterogeneous integration, with tighter coupling in Shanghai–Jiangsu–Zhejiang–Anhui. Globally and locally, positive spatial correlations follow a pattern of initial decline and subsequent increase; local high-high clusters contract overall, with apparent weakening in the north, stronger integration in the east, and improvements around the southwest. Methodologically, RAGA-PPM improves sensitivity to nonlinear, multimodal structures and yields temporally coherent measures compared with entropy-based baselines. Furthermore, policy translation is specified along three tracks: capability formation for adaptability, orchestration of cross-regional collaboration, and demand-side measures to enhance absorption, each with concrete instruments for provincial implementation. The findings of the study advance the integration of open innovation and regional innovation systems as well as provide actionable guidance for differentiated public policies.