Integration of MODFLOW and deep learning models for groundwater level prediction

• Using Deep Learning techniques to predict groundwater levels. • Combining MODFLOW with Transformer and PatchTST to improve prediction accuracy. • Hybrid models improved prediction accuracy better than MODFLOW alone. • PatchTST outperforms Transformer due to capturing temporal hydrologic characteristics. Groundwater depletion is undoubtedly one of humanity's most significant sustainability concerns in the 21st century. Therefore, developing modern tools to improve the accuracy of groundwater level predictions and support effective groundwater management is essential. This study presents a novel hybrid approach combining the advantages of physics-based models such as MODFLOW with data-driven deep learning models. The MODFLOW model was calibrated at a steady state utilizing data from observation wells in the study area, achieving a coefficient of determination (R²) of 0.999. Then, it was calibrated to one year of transient data with an R² of 0.912. Generated data based on the calibrated model has been used to train the deep learning models. The Transformer and PatchTST models have been utilized to forecast hydraulic heads, employing aquifer type, well coordinates, pumping rate, recharge, and drawdown as inputs. The results demonstrated that the two hybrid models outperformed MODFLOW alone in prediction. The mean squared error (MSE) values were 0.21 for MODFLOW, 0.0039 for Transformer, and 0.000514 for PatchTST. This improvement is attributed to the ability of deep learning models learn to temporal patterns and recurring behaviour from historical data, whereas numerical models rely on physical equations without learning future patterns. Additionally, when comparing the deep learning models, PatchTST performed better, with a lower MSE of 0.00027, while the Transformer had an MSE of 0.0408 during testing phase. The enhanced performance of PatchTST is due to its patch-based learning mechanism, which enables more efficient recognition of temporal patterns in hydrological data.