Deep learning of flood forecasting by considering interpretability and physical constraints

Deep learning models show promise for flood forecasting but often lack interpretability and physical realism. To bridge this gap, we enhance traditional Long Short-Term Memory (LSTM) networks by integrating: (1) a feature-time attention mechanism that emphasizes critical input features and historical moments by learning dynamic weights, and (2) physics-guided constraints that enforce fundamental hydrological principles by considering the monotonic relationships between inputs and outputs. Tested in China's Luan River Basin for 1–6 h flood predictions, the proposed physics-guided feature-time-based multi-head attention mechanism LSTM (PHY-FTMA-LSTM) outperforms standard LSTM and attention-only variants. It achieves exceptional accuracy with Nash-Sutcliffe efficiency (NSE) values of 0.988 at t+1 and maintains strong performance at 0.908 at t+6, offering valuable insights for enhancing interpretability and physical consistency in deep learning approaches.