Spatio-temporal evolution of industrial R&D productivity in China

New quality productivity (NQP) is an important force for economic and social progress, and in the industrial sector—the core of the real economy—its transformation bears directly on national competitiveness and high-quality, sustainable growth. Focusing on the R&D-innovation core of industrial NQP, this paper constructs an evaluation system of seven indicators along the “R&D investment–activity–output” chain for 31 Chinese provinces over 2015–2023. Using the entropy method and grey relational analysis, it identifies each province's core driving indicator and proposes the concept of “heterogeneity of core driving indicators”; a PSO-optimized fractional grey multivariate model, FGM(1,2), is then used to forecast NQP for 2024–2028, outperforming ARIMA, conventional grey models and machine-learning benchmarks. The results reveal an overall upward but regionally uneven trend: the East advances rapidly and is primarily R&D-investment-driven, the Central region grows fastest, the Northeast lags, and the West achieves localized, policy-supported breakthroughs with output-driven features. These findings support differentiated, region-specific strategies for sustained NQP growth and high-quality regional development.