In oil and gas drilling, the mechanical rate of penetration (ROP) is a key indicator of drilling efficiency, and its optimization is crucial for reducing drilling costs and shortening operational cycles. However, owing to the complexity and variability of formation conditions, as well as the diversity of drilling parameters and mechanical tool states, the existing ROP-prediction models often exhibit poor generalization across different regions. To address this issue, a cross-regional adaptive adjustment framework is constructed, which explicitly decouples global stable patterns from local dynamic disturbances to achieve high-precision ROP prediction. Multiregional historical drilling data are used to pretrain deep-learning models (ResNet and FTTransformer), establishing a high-accuracy offline baseline prediction. An online-trained gradient-boosting tree model (LightGBM) then captures regional variations and predicts the discrepancies between the current formation, drilling parameters, and tool conditions, in real time, relative to historical data, for residual correction. The baseline predictions and residual corrections are finally fed into a multilayer perceptron for nonlinear fusion, allowing the magnitudes of residual corrections to adapt dynamically to the real-time operating conditions, thereby enhancing the model's adaptability in new regions. This method is trained on historical data from four ultradeep wells and validated through simulations on an independent deep well. Results show that the offline model achieves a coefficient of determination (R2) of 0.9585, root mean square error (RMSE) of 5.98 m/h, and mean absolute error (MAE) of 2.90 m/h on the test well. Incorporating online residual correction further improves the performance to an R2 of 0.9695, RMSE of 5.13 m/h, and MAE of 1.67 m/h. These results demonstrate strong generalization ability under cross-regional and multicondition scenarios, providing effective technical support for real-time ROP prediction and drilling-parameter optimization.