Physics-Informed Neural Networks with Transfer Learning for Tunnel Seepage Prediction Using Sparse Measurements

This study proposes an enhanced physics-informed neural network (PINN) framework for predicting seepage fields around deeply buried tunnels with limited field measurements. Hard-constrained boundary enforcement via distance-function trial functions is introduced to exactly satisfy Dirichlet conditions on both the ground surface and tunnel perimeter, and Bayesian optimization automates loss weight tuning to replace costly manual calibration. A systematic evaluation of 15 sensor placement schemes demonstrates that the hydraulic head variance across monitoring points, governed by radial coverage distance, is the primary determinant of prediction accuracy—not the number of sensors or angular density. Remarkably, a strategically designed 12-point configuration outperforms 100 randomly distributed points under the idealized conditions studied, confirming that placement quality can dominate over quantity when physics-informed optimization is applied. Transfer learning experiments across 132 geometric configurations reveal a previously unreported geometric transition zone at D/R ≈ 13–15, where prediction errors exhibit a distinct non-monotonic peak. Finite element benchmarking confirms that this error peak stems from the learning characteristics of PINNs under competing boundary influences rather than from the physical complexity of the problem itself. High-density sampling effectively suppresses this peak error by 32% compared with sparse sampling. These findings establish quantitative sensor deployment guidelines for tunnel seepage monitoring and identify fundamental performance boundaries of physics-informed machine learning under geometry–physics coupling.