A Hybrid Optimization Framework Integrating Spatial Dependency Modeling and Nonlinear Feature Learning for Complex System Prediction

Abstract

This study proposes a spatial-nonlinear two-layer ensemble framework based on the Spatial Durbin Model (SDM) and XGBoost to address the dual challenges of spatial dependency and spatial dependence. challenges of spatial dependence and nonlinear driving mechanisms in complex systems. The framework employs a residual enhancement strategy to The framework employs a residual enhancement strategy to decouple spatial spillover effects from high-dimensional nonlinear features, and it uses an adaptive spatial weight matrix based on economic distance and Bayesian optimization to enhance the spatial dependence and nonlinear driving mechanisms in complex systems. And Bayesian optimization to enhance the ability to analyze spatial effects. Additionally, the framework constructs a comprehensive workflow of " Additionally, the framework constructs a comprehensive workflow of " feature dimensionality reduction-spatial modeling-nonlinear residual fitting-ensemble optimization. that the ensemble model achieves the lo this articlest RMSE (0.085), MAE (0.062), and AIC (402.5) values and the highest Pearson's R (0.87) and residual Moran's I (0.03) values close to 0. The ensemble model significantly outperforms OLS, SAR, SDM, and single machine learning models, effectively improving the ensemble model significantly outperforms OLS, SAR, SDM, and single machine learning models, effectively improving prediction accuracy and robustness while demonstrating good engineering transferability.