A long-term multivariate time series prediction model for dissolved oxygen

Abstract

Accurate and efficient long-term prediction of marine dissolved oxygen (DO) is crucial for the sustainable development of aquaculture. However, the multidimensional time dependency and lag effects of marine chemical variables present significant challenges when handling multiple inputs in univariate long-term prediction tasks. To address these issues, we designed a multivariate time-series long-term prediction model (LMFormer) based on the Transformer architecture. The proposed multivariate time-series decomposition strategy effectively leverages the feature information of prediction variables at different scales, thereby reducing the loss of critical information. Additionally, a dynamic variable selection strategy based on a gating mechanism was designed to optimize the collinearity problem in the multivariate data feature extraction process. Finally, an efficient two-stage attention architecture is proposed to effectively capture the long-range dependencies between dynamic features. This study conducted high-precision 7-day advance DO long-term predictions in two case studies, the environmentally stable Shandong Peninsula in China and the San Juan Islands in the United States, which are affected by extreme conditions such as ocean currents. The experimental results demonstrate the superior prediction performance and generalizability of the designed model. In the Shandong Peninsula case, the mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2), and Kling–Gupta efficiency (KGE) reached 0.0159, 0.126, 0.9743, and 0.9625, respectively. In the San Juan Islands case, the MAE was reduced by an average of 42.34% compared to that of the baseline model, the RMSE was reduced by an average of 24.57%, the R2 increased by 22.54%, and the KGE improved by an average of 12.04%. Overall, the proposed prediction model effectively achieves long-term prediction of multivariate marine chemical data, providing valuable references for sustainable management and decision-making in aquaculture.