Enhancing Daily Runoff Prediction via Uniform Design and Meta-Learning Integrated Hyperparameter Optimization Embedded in Transformer

Accurate runoff prediction is an essential foundation for water resource management, flood prevention, and drought warning. Despite the superior performance of deep learning models in runoff prediction, the high-dimensional hyperparameter optimization limits their widespread application. To address this challenge, this study proposed a hyperparameter optimization strategy that integrated Uniform Design (UD) and Meta-Learning (ML) within the Transformer framework (UD-ML-Transformer) for daily runoff prediction. Performance of the proposed model was systematically evaluated against five benchmark models, including the UD-Transformer, Particle Swarm Optimization (PSO)-Transformer, and three Receptance Weighted Key Value (RWKV)-based models (PSO-RWKV, UD-RWKV, and UD-ML-RWKV), using hydroclimatic data spanning 1980 to 2014 from the Rio Pueblo de Taos watershed in USA. Results showed that the UD-ML-Transformer model performed the best in both prediction accuracy and peak flow, with the highest Nash-Sutcliffe Efficiency (NSE) of 0.906, and the lowest Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE) of 0.004, 0.062, and 0.034, respectively. The UD-Transformer ranked second in performance, followed by the PSO-Transformer. The integrated UD-ML hyperparameter optimization strategy also improved the performance of RWKV-based models. Compared with the PSO-RWKV and UD-RWKV models, the UD-ML-RWKV model exhibited an NSE improvement of 0.45–7.65% and an RMSE reduction of 1.47–21.18%, respectively. Moreover, cross-watershed validation conducted in the Ford River watershed, USA, also demonstrated the satisfactory performance of the proposed UD-ML-Transformer model, with the highest NSE of 0.890, and the lowest MSE, RMSE, and MAE of 0.088, 0.296, and 0.141, respectively. These findings highlight the superiority of integrating UD and ML for hyperparameter optimization in runoff forecasting.