Abstract: Accurate prediction of tunnel seepage behavior, which is critical for estimating water inflow and ensuring construction and operational safety, is often hindered by the inherent difficulty in characterizing the formation's permeability properties. To address steady-state and transient seepage around shallow underwater tunnels, a physics-informed neural networks (PINNs) model for forward and inverse analyses was established in this study. By leveraging the automatic differentiation of neural networks to encode the governing equations, the PINNs model's loss function integrates physical constraints (governing equations, boundary conditions and initial conditions) with data mismatch from monitoring points. The effectiveness and reliability of PINNs model were validated through comparisons with benchmark solutions derived from the finite difference method (FDM). Subsequently, forward and inverse analyses were performed for steady-state and transient seepage in tunnel, considering two typical boundary conditions: constant total head and zero water pressure. The results show that in terms of forward solving, by introducing spatiotemporal coordinate affine transformation, the PINNs model can effectively simulate the transient and steady state process of tunnel seepage in anisotropic strata and achieve accurate deduction of its seepage behavior. Inversion analyses of the PINNs model can not only swiftly and accurately acquire key parameters such as the permeability coefficient, but also simultaneously deduce the seepage morphology associated with tunnel seepage. The proposed data-physics fusion PINNs model effectively reconstructs the seepage field and predicts the total head evolution around tunnel, and provides an effective way for accurate and rapid estimation of tunnel water inflow.

Key words: physics-informed neural networks, underwater tunnels, seepage form, spatiotemporal coordinate transformation, parameter inversion