# A Hybrid DSCNN-GRU Based Surrogate Model for Transient Groundwater Flow Prediction
###### Abstract  
Sustainable groundwater resource management necessitates dependable and precise predictions of groundwater head fields under fluctuating climatic conditions. The substitution of original simulation models with efficient surrogates presents a challenge in simultaneously accounting for correlations among multiple time series outputs and maintaining overall prediction accuracy. This study develops a novel surrogate modelling approach, DSCNN-GRU, incorporating a deep separable convolutional neural network (DSCNN) and a gated recurrent unit (GRU), to efficiently capture temporal and spatial variations in groundwater head fields from transient groundwater flow models using input hydraulic conductivity field data. The applicability and performance of the proposed method are evaluated for predicting groundwater head fields in a practical research area under three scenarios with different hydraulic conductivity fields. The performance of the DSCNN-GRU model is compared to the traditional convolutional neural network (CNN), CNN-LSTM, and DSCNN-LSTM models to further test its applicability. The numerical study demonstrates that optimizing hyperparameters can result in reasonably accurate performance of the proposed model, and the \"simplest\" DSCNN-GRU outperforms CNN, CNN-LSTM, and DSCNN-LSTM in both prediction accuracy and time-to-solution. t 1 (2025) 15 April 2025 16 April 2025  
offers an advantage by eliminating the need to explicitly define physical relationships and parameters required to describe the physical environment. Machine learning algorithms approximate the relationship between model inputs and outputs through an iterative learning process [10], significantly enhancing the efficiency of model operation. Neural networks (NNs) have proven effective in modeling and predicting nonlinear time series data, such as groundwater levels, and have demonstrated comparable or superior performance to physical-based models in certain cases [11]. This study focuses on introducing a novel neural network coupled model as a surrogate for existing unsteady groundwater flow numerical models, aiming to enhance model efficiency for nonlinear time series water head data while ensuring prediction accuracy. Convolutional neural networks (CNNs) are essential for image recognition and natural language processing due to their powerful feature extraction capabilities [12]. Therefore, 3D convolutional neural networks can be used to predict the head field at a specific time point [13]. [PERSON] et al. [14] applied a CNN-based model to predict the highly variable discharge behavior of karst systems due to their heterogeneous hydraulic properties of Gottsakel in Oberach, North Alps. [PERSON] et al. [15] indicated that increasing the diversity of dataset sizes, utilizing multi-scale feature aggregation, and optimizing architectures can surpass the accuracy of existing state-of-the-art CNN permeability prediction models. However, in studies of groundwater flow, predicting the flow field over long periods at each time point is necessary, and a single CNN model cannot effectively predict long-term sequences. To address the limitations of CNNs, which prioritize local feature detection struggle with long-term temporal dependencies [16], recurrent neural networks (RNNs) are often combined with CNNs to leverage their superior memory capabilities. In previous studies, [PERSON] et al. [17] accurately predicted riverbed water flux (SWF) by integrating CNNs with a Bayesian data value analysis (DWA) framework. Similarly, [PERSON] et al. [18]. effectively evaluated groundwater recharge in the North China Plain using attention-gated recurrent units (ATTENTION-GRU) and CNNs. In addition, [PERSON] et al. [19] combined CNN layers with bidirectional long short-term memory (Bi-LSTM) models for long-term groundwater level prediction at each time point. Recently, [PERSON] et al.