# A Hybrid DSCNN-GRU Based Surrogate Model for Transient Groundwater Flow Prediction
## 4 Discussion  
This study presents an innovative DSCNN-GRU surrogate modeling framework for simulating transient groundwater head fields through continuous time series prediction. A comprehensive evaluation of surrogate modeling approaches, including CNN-LSTM, DSCNN-LSTM, and the proposed DSCNN-GRU framework, reveals that the proposed DSCNN-GRU model achieves an optimal balance between computational efficiency and predictive accuracy. The comparative analysis demonstrates that while the CNN-LSTM architecture attains comparable predictive accuracy, the DSCNN-GRU surrogate achieves a significant reduction in computational training time. This enhanced efficiency corroborates the theoretical advantages of GRU architectures over conventional LSTM networks, as originally theorized by [PERSON] et al. (2014) [16], particularly regarding GRU's simplified gating mechanism that effectively mitigates the characteristic \"memory saturation\" phenomenon observed in LSTM networks. Furthermore, the DSCNN-GRU exhibits superior training stability compared to CNN-LSTM, with reduced error fluctuations that align with previous findings regarding LSTM instability in large-scale hydrological modeling applications. This study extends the application of GRU networks in groundwater modeling beyond the pure time series prediction demonstrated by [PERSON] et al. [26] through a novel integration with DSCNN, which successfully integrates spatial feature extraction with temporal sequence modeling. This hybrid architecture achieves a robust solution for simultaneous spatiotemporal analysis of transient groundwater flow dynamics, achieving enhanced predictive capability while maintaining computational efficiency comparable to conventional approaches. Systematic parameter optimization analysis demonstrates that the DSCNN-GRU model exhibits pronounced sensitivity to three critical hyperparameters: (1) number of convolutional layers, (2) optimizer selection, and (3) activation function choice. Increasing convolutional layers from three to five significantly enhances prediction accuracy, corroborating [PERSON] et al. 's [19] findings that deeper networks better capture complex relationships in groundwater systems. Notably, contrary to conventional patterns, the five-layer architecture demonstrates higher computational efficiency than the three-layer version, likely due to optimized memory caching that reduces data fragmentation and improved feature extraction hierarchy that accelerates convergence. In optimizer comparisons, Adam exhibits superior performance despite marginally longer training times than RMSprop. The suboptimal performance of Nadam contrasts with some conclusions from [PERSON] [27], suggesting its accelerated convergence may adversely affect groundwater modeling applications requiring smooth loss landscapes, highlighting the importance of problem-specific optimizer selection. The activation function evaluation reveals that Tanh activation provides superior performance for transient hydraulic head prediction, particularly in capturing nonlinear aquifer responses, and Softmax activation proves fundamentally unsuitable for this surrogate modeling task. These results quantitatively confirm [PERSON] et al. 's [28] hypothesis about activation function specialization, demonstrating that hydrological data characteristics should drive function selection rather than relying on default choices from other domains. While the simplified 2D heterogeneous groundwater flow model validates the DSCNN-GRU approach's feasibility, several limitations merit discussion. First, the current implementation simplifies the complex hydrogeological characteristics of karst limestone aquifers (e.g., the Gambier Limestone Aquifer system) by representing hydraulic conductivity through range parameters rather than explicitly modeling dominant flow pathways through karst conduits and fracture networks.