Groundwater Seepage Modeling in a River-Canal System based on Physics-Informed Neural Networks

Chong Chen, Yifan Li, Zongyu Han, Yixiao Niu, Xiaoyu Zhu, Yaru Xue

Keywords: Physics-Informed Neural Networks, Groundwater Prediction, Definite condition, Hard constraints, Self-Supervised

Abstract: Neural networks, especially deep learning, have achieved revolutionary advances in several domains, including image and speech recognition, with excellent results. However, their reliance on labeled data, lack of interpretability, and inconsistency with physical principles limit their applicability in groundwater seepage prediction and other scientific disciplines. Physics-Informed Neural Networks (PINNs) significantly improve these issues by integrating physical knowledge with neural networks. This study focuses on modeling the groundwater flow field and proposes a physics-informed river-canal groundwater seepage model (PI-RGSM). This model enables self-supervised learning by incorporating hard constraints of boundary and initial conditions, utilizing hydrogeological parameters and boundary conditions as direct inputs, thus diminishing dependence on observable data. Compared to the baseline PINNs, the PI-RGSM adapts to and accurately predicts diverse seepage situations with just one training session, achieving a mean coefficient of determination of 0.978. To further enhance applicability in complex dynamic groundwater seepage situations, we propose PI-RGSM-K, which builds upon PI-RGSM. This model simulates heterogeneous groundwater seepage fields and improves performance in complex seepage environments through parameterized hydraulic conductivity field $K(x,y)$ and fine-adjusted model architecture, attaining a mean coefficient of determination of 0.982. The physics-informed neural network models proposed in this study demonstrate exceptional efficacy in precisely forecasting groundwater seepage behavior.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Submission Number: 3582