Modeling inter-city population flows: a Deep Radiation model with multisource geographic features

Due to urbanization, accurately modeling intercity population migration is vital for regional policymaking. While the radiation model provides an interpretable framework by focusing on opportunity distribution rather than physical distance, it struggles with nonlinear migration patterns and relies solely on population size as its input. To address these limitations, we propose the Deep Radiation model, which integrates the theoretical foundation of the radiation model with the nonlinear capabilities of neural networks. By replacing linear equations with a feedforward neural network, our model predicts migration flows based on an expanded set of features across four dimensions: economic development, urbanization, infrastructure, and environmental factors. Testing on 295 Chinese cities demonstrates that the Deep Radiation model significantly outperforms the original in capturing human mobility patterns, particularly the push–pull effects of cities and their surrounding regions. This study advances migration modeling and provides actionable insights for regional planning.