Enhanced Physics-Informed Neural Networks for Deep Tunnel Seepage Field Prediction: A Bayesian Optimization Approach

Predicting tunnel seepage field is a critical challenge in the construction of underground engineering projects. While traditional analytical solutions and numerical methods struggle with complex geometric boundaries, standard Physics-Informed Neural Networks (PINNs) encounter additional challenges in tunnel seepage problems, including training instability, boundary handling difficulties, and low sampling efficiency. This paper develops an enhanced PINN framework designed specifically for predicting tunnel seepage field by integrating Exponential Moving Average (EMA) weight stabilization, Residual Adaptive Refinement with Distribution (RAR-D) sampling, and Bayesian optimization for collaborative training. The framework introduces a trial function method based on an approximate distance function (ADF) to address the precise handling of circular tunnel boundaries. The results demonstrate that the enhanced PINN framework achieves an exceptional prediction accuracy with an overall average relative error of 5 × 10−5. More importantly, the method demonstrates excellent practical applicability in data-scarce scenarios, maintaining acceptable prediction accuracy even when monitoring points are severely limited. Bayesian optimization reveals the critical insight that loss weight configuration is more important than network architecture in physics-constrained problems. This study is a systematic application of PINNs to prediction of tunnel seepage field and holds significant value for tunnel construction monitoring and risk assessment.