Water Quality by Spectral Proper Orthogonal Decomposition and Deep Learning Algorithms

Water quality plays a pivotal role in human health and environmental sustainability. However, traditional water quality prediction models are limited by high model complexity and long computation time, whereas AI models often struggle with high-dimensional time series and lack physical interpretability. This paper proposes a two-dimensional water quality surrogate model that couples physical numerical models and AI. The model employs physical simulation results as input, applies spectral proper orthogonal decomposition to reduce the dimensionality of the simulation results, utilizes a long short-term memory neural network for matrix forecasting, and reconstructs the two-dimensional concentration field. The simulation and predictive performance of the surrogate model were systematically evaluated through four design scenarios and three sampling dataset lengths, with a particular focus on the convection–diffusion zone and high-concentration zone. The results indicated that the model achieves high prediction accuracy for up to 7 h into the future, with sampling dataset lengths ranging from 20 to 80 h. Specifically, the model achieved an average R2 of 0.92, a MAE of 0.38, and a MAPE of 1.77%, demonstrating its suitability for short-term water quality predictions. The methodology and findings of this study demonstrate the significant potential of integrating spectral proper orthogonal decomposition and deep learning for water quality prediction. By overcoming the limitations of traditional models, the proposed surrogate model provides high-accuracy predictions with enhanced physical interpretability, even in complex, dynamic environments. This work offers a practical tool for rapid responses to water pollution incidents and supports improved watershed water quality management by effectively capturing pollutant diffusion dynamics. Furthermore, the model’s scalability and adaptability make it a valuable resource for addressing intelligent management in environmental science.