Integral Delay Inspired Deep Learning Model for Single Pool Water Level Prediction

Abstract

Accurate water level prediction is critical for optimizing water resource allocation in large-scale water transfer projects. Although traditional hydrodynamic models can precisely infer water level evolution, they are highly dependent on foundational data, such as topography, and involve significant computational costs. In contrast, deep learning models overcome the limitations of traditional ones in capturing complex water level dynamics by extensively learning long-term temporal dependencies. However, most deep learning models ignore hydraulic time-delay characteristics, making it difficult to accurately predict abrupt changes. To address the above issue, this study proposes a Hydrological Physics-informed Attention (HPA) model for predicting single-step water level of specific channel pools in the South-to-North Water Diversion Project in China. HPA use Integral Delay (ID) theory as the physical foundation, which constructs a linear relationship between upstream and downstream hydrological information with respect to time-delay. HPA leverages the powerful representational capacity of deep learning to address the challenges in prior knowledge acquisition and computational efficiency posed by traditional hydrodynamic models. Specifically, HPA integrates attention mechanisms with ID theory to dynamically represent complex spatiotemporal interactions and delay effects between upstream and downstream attributes. Moreover, HPA mines the periodicity of hydraulic data by adding the time information of the day and week. To learn time-delay information, HPA applies attention on long--term upstream flow data. Besides, it builds short-term attribute correlations within downstream hydrological data. This study validates the proposed model using sensor data from three stations along the Middle Route of the South-to-North Water Diversion Project. Experimental results demonstrate that HPA significantly reduces three key metrics MAE, RMSE, and MAPE compared to existing deep learning models. The MAE, MAPE, and RMSE exhibit average reductions of 45.36%, 45.35%, and 49.80%, respectively. These results show that the physics-informed mechanism used in HPA can improve water level prediction accuracy and stability across various scenarios, offering its superior practicality and reliability over existing models.

Keywords: physics-informed, integral-delay, Water Level Prediction, attention mechanism, South-to-North Water Diversion