A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems by utilizing the PINN, harnessing the capabilities of Deep Neural Networks (DNNs) to approximate hydraulic head distributions in seepage analysis. To effectively train the PINN model, we introduce a comprehensive loss function comprising three components: one for evaluating differential operators, another for assessing boundary conditions, and a third for appraising initial conditions. The validation of the PINN involves solving four benchmark seepage problems. The results unequivocally demonstrate the exceptional accuracy of the PINN in solving seepage problems, surpassing the accuracy of FEM in addressing both steady-state and free-surface seepage problems. Hence, the presented approach highlights the robustness of the PINN and underscores its precision in effectively addressing a spectrum of seepage challenges. This amalgamation enables the derivation of accurate solutions, overcoming limitations inherent in conventional methods such as mesh generation and adaptability to complex geometries.

翻译：物理信息神经网络（PINN）通过将神经网络的计算能力与问题所遵循的物理定律相结合，展现出显著优势。本研究提出了一种利用PINN求解渗流问题的创新方法，通过深度神经网络（DNNs）近似渗流分析中的水头分布。为有效训练PINN模型，我们构建了包含三个分量的综合损失函数：第一部分用于评估微分算子，第二部分用于评估边界条件，第三部分用于评估初始条件。通过求解四个基准渗流问题对PINN进行验证。结果明确证明，PINN在求解渗流问题时具有卓越的精度，在稳态和自由表面渗流问题的求解中均超越了有限元法（FEM）的精度。因此，本文方法凸显了PINN的稳健性，并强调了其在有效解决各类渗流问题中的精准性。这种融合使得获取精确解成为可能，克服了传统方法在网格生成和复杂几何适应性方面的固有局限性。