The hyperparameters in DE.

Water quality indicators are interrelated, and their interactions vary across different monitoring sites. Additionally, environmental management and policies introduce temporal and spatial heterogeneity. Therefore, predicting water quality indicators requires careful consideration of the relationship among all indicators. Traditional machine learning methods often struggle to process data from independent variables to dependent variables in an inexplicable manner. Some variables are both independent and dependent alongside the temporal axis. In contrast, Fuzzy Cognitive Maps (FCMs) could model all variables over time to complete the time series prediction task involved with multi-variables, and then output a graph showing the relationship among all variables. Current research aims to uncover the temporal and spatial heterogeneity hidden in each monitoring site across different years via FCMs. This study aims to reveal the temporal and spatial heterogeneity in water quality data from 12 monitoring sites across nine rivers in Tongzhou, Beijing, China (1st January, 2016–31st December, 2023). Using this comprehensive dataset, we construct interactive and predictive models for each site. The analyzed results from the produced graphs will help infer the interaction between any pair of variables and predict the concrete amount of variables in future time stamps. The effect between each pair of indicators could be qualitatively and quantitatively analyzed with the graph produced by FCMs. This approach helps in curbing and preventing water pollution by understanding the interactions between various factors.