An echo state network based adaptive dynamic programming approach for time-varying parameters optimization with application in algal bloom prediction

The prediction of algal bloom is one of the important links in eutrophication prevention. Chlorophyll a concentration is the indicating variable of algal bloom, and its time series is non-stationary and non-linear, which brings challenges to its effective prediction. Although the current algae growth model (AGM) can directly describe the algal bloom dynamics, the fixed parameters limit the adaptability of the model. If the fixed parameters are dynamically adjusted, the trend of chlorophyll a concentration can be better captured. Therefore, the adaptive dynamic programming (ADP) approach is used to optimize the parameters of the AGM. The ADP contains an action network and a critic network by echo state network, where the action network is used to output the increment value of the fixed parameters, and the critic network is used to approximate the performance index function. In this paper, the input of the action network uses the time series features extracted by the relevant variables, so that the time-varying parameters of the AGM have better dynamic characteristics. We verify the effectiveness of the proposed model through the dataset of the North Canal and Taihu Lake, and the convergence analysis proves the theoretical reliability. In this way, the improved mechanism model with time-varying parameters not only maintains the better interpretability of the original AGM, but also further enhances the prediction accuracy and adaptability by extracting inherent interactive features from the relevant variables.