Interval Prediction of Total Nitrogen Using a Hybrid BiLSTM-Res Model and Bayesian Optimization: A Case Study in the Pearl River Delta

This study develops a hybrid deep learning framework for point and interval prediction of Total Nitrogen (TN) concentrations in the Pearl River Delta, China. To address the inherent stochasticity of water quality systems, Bidirectional Long Short-Term Memory (BiLSTM) networks are integrated with residual learning blocks (Res) and Bayesian Optimization (BO). The resulting BiLSTM-Res-BO framework is evaluated within a comparative analysis of eight forecasting models that combine BiLSTM and BiGRU architectures with two uncertainty quantification approaches: Quantile Regression (QR) and Monte Carlo Dropout (MCD). Results from 37 monitoring stations demonstrate that the effectiveness of residual learning is highly context-dependent. For point forecasting, BiLSTM-Res achieves substantial performance gains (12.5–15% RMSE reduction) at complexity-sensitive sites, while providing negligible or slightly degraded performance under hydrologically stable conditions. For interval forecasting, QR-based residual models—particularly Q-BiLSTM-Res—produce notably narrower prediction intervals, with interval width reductions of 16.7–27.3% relative to the baseline BiLSTM model, under comparable levels of empirical coverage. In contrast, MC-dropout-based methods tend to yield wider intervals with different coverage–width trade-offs, reflecting distinct uncertainty propagation behaviors across modeling frameworks.