Pre-trained Physics-Informed Neural Networks for Analysis of Contaminant Transport in Soils

Solving the advection-diffusion equation (ADE) for contaminant transport in soil (forward problem) is of crucial importance in many environmental engineering topics, such as assessment of site contamination risks and design of engineered barriers. Although numerical techniques are widely used to solve the ADEs, they are not skilled at addressing inverse problems, such as identifying unknown parameters in the equations based on measurement data, especially when data are sparse or corrupted with noise. In this paper, forward and inverse problems of the contaminant transport in soils are solved using the newly developed physics-informed neural networks (PINN) incorporated with pre-training strategy, uncertainty quantification and domain decomposition method. Four cases are analyzed in detail to demonstrate the capability of the proposed approach. The results show that: (1) for forward problems, the proposed approach can provide spatio-temporal concentration distributions in a high agreement with analytical or numerical solutions, even for the two-dimensional case with layered soils; (2) for inverse problems, unknown parameters in the ADE can be accurately identified by the proposed approach based on a small amount of measured data, even for the case with two-parameter nonlinear adsorption model; (3) pretraining strategy can significantly enhance the training efficiency and prediction accuracy of PINN; (4) the uncertainty of the results can be effectively quantified by the proposed approach through incorporating the latent variable; and (5) the robustness against measured data noise can be ensured by the proposed approach. The proposed approach has the penitential to address contaminant transport problems under coupled multi-physics with multi-fidelity data.