Research on a Non-Stationary Groundwater Level Prediction Model Based on VMD-iTransformer and Its Application in Sustainable Water Resource Management of Ecological Reserves

The precise forecasting of groundwater levels significantly influences plant growth and the sustainable management of ecosystems. Nonetheless, the non-stationary characteristics of groundwater level data often hinder the current deep learning algorithms from precisely capturing variations in groundwater levels. We used Variational Mode Decomposition (VMD) and an enhanced Transformer model to address this issue. Our objective was to develop a deep learning model called VMD-iTransformer, which aims to forecast variations in the groundwater level. This research used nine groundwater level monitoring stations located in Hangjinqi Ecological Reserve in Kubuqi Desert, China, as case studies to forecast the groundwater level over four months. To enhance the predictive performance of VMD-iTransformer, we introduced a novel approach to model the fluctuations in groundwater levels in the Kubuqi Desert region. This technique aims to achieve precise predictions of the non-stationary groundwater level conditions. Compared with the classic Transformer model, our deep learning model more effectively captured the non-stationarity of groundwater level variations and enhanced the prediction accuracy by 70% in the test set. The novelty of this deep learning model lies in its initial decomposition of multimodal signals using an adaptive approach, followed by the reconfiguration of the conventional Transformer model’s structure (via self-attention and inversion of a feed-forward neural network (FNN)) to effectively address the challenge of multivariate time prediction. Through the evaluation of the prediction results, we determined that the method had a mean absolute error (MAE) of 0.0251, a root mean square error (RMSE) of 0.0262, a mean absolute percentage error (MAPE) of 1.2811%, and a coefficient of determination (R2) of 0.9287. This study validated VMD and the iTransformer deep learning model, offering a novel modeling approach for precisely predicting fluctuations in groundwater levels in a non-stationary context, thereby aiding sustainable water resource management in ecological reserves. The VMD-iTransformer model enhances projections of the water level, facilitating the reasonable distribution of water resources and the long-term preservation of ecosystems, providing technical assistance for ecosystems’ vitality and sustainable regional development.