Physics-Informed Neural Networks for One-Dimensional Groundwater Contaminant Transport: A Synthetic Numerical Study of Prediction and Parameter Inversion

This study developed a physics-informed neural network (PINN) surrogate model for a one-dimensional synthetic groundwater contaminant-transport problem with adsorption, using Crank–Nicolson numerical solutions as the reference data. The effects of observation density and noise on predictive accuracy, training uncertainty, and parameter inversion were systematically evaluated. To address the limited attention given to the temporal coverage of physical information and the high training cost of PINNs, this study further examined how the temporal extent of physical constraints affects extrapolation and whether transfer learning can improve training efficiency within and across adsorption mechanisms. The results show that PINNs accurately predict concentration values and reduce initialization-induced uncertainty when the physical constraints—including the ADE residual and the prescribed initial and boundary conditions—cover the target prediction period (0.3 < tD < 0.6 ), outperforming purely data-driven neural networks in both accuracy and stability. For example, at tD = 0.6, PINN-T6 achieved an R2 of 0.990, whereas the DNN yielded an R2 of −1.122. When the target period lies outside the physically constrained interval, however, prediction errors and uncertainty increase with the extrapolation horizon, and the long-term performance of PINNs may approach that of data-driven models. At tD = 0.6, the R2 of PINN-T3 decreased to 0.377 because its physical constraints were imposed only up to tD = 0.3. Transfer learning accelerated early-stage convergence when the source and target tasks shared the same linear-adsorption formulation, although the advantage decreased as the training budget increased. Cross-mechanism transfer from linear to Freundlich adsorption provided only temporary early-stage benefits and eventually resulted in negative transfer, indicating that its effectiveness depends on physical similarity and the available training budget.