基于Transformer-CNN混合架构的地下水流预测替代模型研究

A Surrogate Model for Groundwater Flow Prediction Based on a Transformer-CNN Hybrid Architecture

摘要: 地下水数值模拟是水资源管理的重要工具，但传统物理模型存在计算成本高、参数化复杂等局限性。本文提出一种新型的Transformer-CNN混合替代模型，通过引入相对位置编码机制增强Transformer对序列长期依赖关系的捕捉能力，并结合卷积神经网络(CNN)提取空间特征，以高效预测地下水头场的时空演化。模型采用多尺度特征融合与跨模态注意力机制，整合渗透系数场、抽水量等物理先验知识，提升预测精度与泛化能力。基于澳大利亚东南部典型含水层的数值算例验证表明，该模型在测试集上的决定系数(R²)达0.993，均方误差(MSE)为0.0011，结构相似性指数(SSIM)为0.989，且训练效率较基准模型(DSCNN-GRU)提升25.5%。实验结果表明，该模型在复杂水文地质条件下显著优于现有方法，尤其擅长捕捉长期时空依赖关系与局部异质性特征，为地下水动态预测提供了一种高精度、高效率的解决方案。

Abstract: Groundwater numerical simulation is a vital tool for water resources management; however, conventional physics-based models face limitations such as high computational costs and complex parameterization. This paper proposes a novel Transformer-CNN hybrid surrogate model for efficiently predicting the spatiotemporal evolution of hydraulic head fields. The model enhances the Transformer’s ability to capture long-term dependencies in sequences by introducing a relative position encoding mechanism and leveraging Convolutional Neural Networks (CNN) to extract spatial features. It incorporates multi-scale feature fusion and cross-modal attention mechanisms to integrate physical prior knowledge, such as hydraulic conductivity fields and pumping rates, thereby improving prediction accuracy and generalization capability. Validation based on a numerical case study of a typical aquifer in southeastern Australia demonstrates that the model achieves a coefficient of determination (R²) of 0.993, a Mean Squared Error (MSE) of 0.0011, and a Structural Similarity Index (SSIM) of 0.989 on the test set. Furthermore, the training efficiency is improved by 25.5% compared to the baseline model (DSCNN-GRU). Experimental results indicate that the proposed model significantly outperforms existing methods under complex hydrogeological conditions, particularly excelling in capturing long-term spatiotemporal dependencies and local heterogeneous features. It provides a high-accuracy and efficient solution for dynamic groundwater prediction.