GT-PINN: A groundwater solute transport physics-informed neural network for dispersion coefficients inversion

Physics-Informed Neural Networks (PINNs) demonstrate considerable potential for solving partial differential equation (PDE)-based inverse problems in various practical scenarios. This study leveraged PINN for identifying dispersion coefficients (D) in homogeneous and heterogeneous porous media. The difficulty in inverting dispersion coefficients poses challenges for PINN, covering absence of real-world data validation and low accuracy caused by large dimensional differences. To address these issues, this study proposed an improved groundwater solute transport physics-informed neural network (GT-PINN) for dispersion coefficients inversion, using PDE-scaling to adjust the effective contribution of the governing-equation residual in the loss function and using the real-world breakthrough curve (BTC) data to define boundary conditions. Based on the optimized sensor layout and observation-number strategy, the proposed GT-PINN framework identified the D from short time-series BTC data, and then employed the D for forward prediction of solute transport processes over longer time scales. Four one-dimension studies were introduced to benchmark the coefficient inversion capabilities of the GT-PINN, including two homogeneous linear-transport cases with different inlet boundary conditions, one layered heterogeneous linear-transport case and one homogeneous nonlinear Freundlich sorption case. Additionally, the analysis exploring the influence of the initial conditions, initial coefficient guess, observation noise and random seeds on the coefficient inversion accuracy was presented. The laboratory experiment further indicated improvement of the method in practical coefficient estimation, with small absolute and relative errors. The findings highlight the potential of GT-PINN in solute transport systems.