## 4 Results and Discussion
### Hyperparameter Calibration  
Figure 7 systematically evaluates the validation loss landscape across six distinct sequential deep learning architectures--LSTM, Bi-LSTM, CNN-LSTM, ConvTransformer, Transformer, and Informer--to optimize predictions. Each model's hyperparameters were rigorously tuned through extensive experimentation. In the LSTM model, validation loss is minimized (\(\sim\)0.75) at moderate complexity: first-layer hidden units (u1) at 32-128 and second-layer units (u2) at 64-128, with optimal dropout rate (dr) around 0.2. Excessive regularization (dr = 0.3) or overly large hidden layers sharply elevate loss toward 0.88. The Bi-LSTM, characterized by its single hidden-layer parameter (u2), achieves its lowest validation loss (\(\sim\)0.83) at u2 = 128 units with a modest dr = 0.1, but performance significantly deteriorates with increased dropout (dr \(\geq\) 0.3).  
Figure 6: Deep learning and Transformer models performance in spatiotemporal groundwater level prediction: **(a)** feature importance analysis, **(b)** model performance metrics (R\({}^{2}\), MAE, RMSE, and correlation), **(c)** cumulative distribution function (CDF) and absolute error, **(d)** residual error comparison between all models, and **(e)** training and validation loss curves.  
Figure 7: Sensitivity analysis of the hyperparameters of the models LSTM, Bi-LSTM, ConvTransformer, Transformer, and Informer.  
The hybrid CNN-LSTM architecture, combining convolutional layers (filters, f = 32-64) and recurrent units (lstm_u = 32-128), exhibits the lowest loss (\(\sim\)0.86) at f = 64, lstm_u = 128, and dr = 0.1. Any deviation towards smaller LSTM units (lstm_u = 32) or higher dropout significantly escalates validation loss beyond 0.99, underscoring the sensitivity of this model configuration. For the ConvTransformer, embedding dimensions (d = 64-128), attention heads (2-4), and layers (1-2) yield optimal validation loss (\(\sim\)0.68) when using intermediate settings (d = 64, heads = 2, layers = 2, dr = 0.3). Increased embedding dimensions without sufficient regularization quickly inflate the validation loss (\(>\)0.70). In contrast, the vanilla Transformer architecture achieves its lowest validation loss (\(\sim\)0.72) with maximal model complexity (d = 128, heads = 4, layers = 2) and minimal dropout (dr = 0.1), emphasizing the importance of carefully balancing capacity with regularization.  
Finally, the Informer--a specialized transformer variant optimized for temporal modeling--records the minimal validation loss (\(\sim\)0.79) with parameters set at moderate complexity (d = 128, heads = 2, and layers = 2) and the highest evaluated dropout (dr = 0.3). However, smaller embeddings or fewer attention heads rapidly increase the loss above 0.88. Collectively, this analysis reveals a clear trend across models: a nuanced balance between model capacity (embedding dimensions and hidden units), moderate regularization (dr = 0.1-0.3), and controlled learning rates is essential to achieve optimal predictive performance. These insights provide a rigorous, empirically driven guideline for future hyperparameter selections in sequential deep learning architectures for hydrological forecasting.