# A Hybrid DSCNN-GRU Based Surrogate Model for Transient Groundwater Flow Prediction
## 5 Conclusions  
This article introduces a new deep learning research method, the DSCNN-GRU coupled model, and applies it to surrogate the physical model established for the southeastern coastal region of Australia. The goal is to predict the continuous time series of complex transient water head fields using neural network models, rather than relying on physical models established based on long-term observational data in the study area. By combining the DSCNN and GRU network architectures, this method effectively and accurately simulates the transient flow field of groundwater. In addition, this method shows good results as an alternative to non-transient aquifer models with complex conditions. The main findings of this study can be summarized as follows:  
1. The alternative model based on general convolutional neural networks (CNNs) is suitable for studying transient groundwater head prediction. However, as the flow state becomes more complex, the prediction accuracy decreases, and the model training time significantly increases, resulting in potential high costs. 2. Compared to traditional CNN models, the coupling model based on DSCNN-GRU exhibits superior performance in both training efficiency and prediction accuracy. A distinctive feature of DSCNN is its two-step convolution process, which includes channel convolution and point convolution. This unique method significantly reduces the computational complexity during the convolution process, thereby improving network efficiency. On the other hand, GRU is a variant of RNN that effectively solves the problems related to long-term memory and vanishing gradients through its specialized gating unit. Therefore, it improves the ability of the model to maintain memory of time series data, thereby improving prediction accuracy. The forward model of groundwater flow developed using DSCNN-GRU effectively solves the problem of continuous time series by transferring it from a general CNN network to a GRU. This innovative method successfully achieved forward deduction and prediction of the groundwater head field in the study area during the study period. Importantly, this method does not require a large amount of computational resources for training. 3. Another focus of this study is to optimize the DSCNN-GRU model by modifying three parameters: the convolutional layer, the optimizer, and the activation function. The experimental results show that when replacing complex physical models, neural networks with five convolutional layers, Tanh activation function, and Adam optimizer perform exceptionally well. Furthermore, the findings indicate that employing the RMSprop or Nadam optimizers, along with the Softmax activation function, notably diminishes the prediction accuracy for the groundwater head field data within the study area. However, due to limited resources, this study only explored the use of Kriging interpolation to establish a groundwater flow model for the region, and did not extensively validate other algorithms. In addition, neural networks contain various parameters such as convolutional layers, regularization parameters, fully connected layers, optimizers, activation functions, pooling layers, and learning rates. This article only briefly compares and analyzes three parameters. Further research is needed to explore other optimization methods and challenges. Conceptualization, X.L. and X.X. ; Methodology, C.P. ; Validation, X.L. and Y.Z. ; Resources, X.L. ; Writing--original draft, C.P. ; Writing--review & editing, X.X. ; Supervision, X.X. ; Funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China grant number 42402252, the open project program of MOE Key Laboratory of Groundwater Circulation and Environmental Evolution, China University of Geosciences (Beijing), the Open Project Program of Key Laboratory of Groundwater Resources and Environment (Jilin University), and the Ministry of Education (Grant No. 202306 ZDKF08).