Integrating Numerical Simulation and Machine Learning for Groundwater Level Prediction: A Case Study of Eastern Beijing, China

Accurate prediction of groundwater level (GWL) is of great significance for refined groundwater management. This study establishes a multi-model framework for predicting groundwater level by integrating the three-dimensional transient MODFLOW model, artificial neural networks (ANN) and long short-term memory (LSTM). The results reveal that the numerical model satisfactorily reproduces groundwater level variations during calibration and validation periods, with relative errors within 1.5 m for over 91.67% of the monitoring wells. The performance of LSTM model is significantly outperformed by the ANN model with the NSEs greater than 0.92 and RMSEs smaller than 1.51 m during the training period and validation periods. Multiple scenarios were established to compare and verify the prediction accuracy of the LSTM and numerical models. RMSE values ranged from 0.054 to 0.187 and 0.012 to 0.121, respectively. In addition, the RMSE value increases with the extension of the prediction period. The uncertainty value of the LSTM model gradually decreased from 1.0 to 0.74, while that of the numerical model remained at 0.71. This indicates that the physical process constraints of the numerical model can enhance prediction stability and interpretability under different scenarios, while machine learning can efficiently satisfy high-frequency adjustment requirements and respond to abrupt disturbances. This study provides scientific references for accurately predicting GWL and comparative research between numerical models and machine learning models.