A robust multi-model framework for groundwater level prediction: The BFSA-MVMD-GRU-RVM model

•Developed MVMD-GRU-RVM model for accurate monthly GWL prediction.•Introduced BFSA method for selecting most informative features.•Applied MVMD to effectively process nonstationary data.•Enhanced RVM model with GRU for improved GWL predictions. Groundwater level prediction is critical for environmental protection and agricultural planning. Accurate predictions help manage risks associated with excessive groundwater extraction and land subsidence. This study introduces a novel model combining multivariate variational mode decomposition (MVMD), gated recurrent unit (GRU), and relevance vector machine (RVM), along with the Boruta feature selection algorithm (BFSA), for precise groundwater level forecasting. The model operates in several stages. First, BFSA selects the most informative features as input data. Next, the MVMD method decomposes the time series of these features. The GRU model then extracts crucial information from these decompositions. Finally, the extracted data is fed into the RVM model to predict groundwater levels one month ahead in Iran's Bastam Plain. To assess the model's accuracy, multiple error indices were employed. The MVMD-GRU-RVM model outperformed other models, improving the testing Nash–Sutcliffe Efficiency and mean absolute error by 24–31 % and 6–61 %, respectively. Additionally, it enhanced R2 values of the MVMD-CNN, MVMD-RNN, MVMD-MLP, and MVMD-RBFNN models by 1.0–3.33 %. These results demonstrate that the MVMD-GRU-RVM model significantly improves groundwater level prediction accuracy. The key points of the paper are the successful effectiveness of MVMD in processing non-stationary time series and improving the predictive performance of the models, as well as the high ability of the GRU model in data feature extraction. The study also shows that the novel model can provide outputs with lower uncertainty.