Staged Learning in Physics-Informed Neural Networks to Model Contaminant Transport under Parametric Uncertainty

Addressing the complexities of groundwater modeling, especially under the veil of uncertain physical parameters and limited observational data, poses significant challenges. This study introduces an approach using Physics-Informed Neural Network (PINN) framework to unravel these uncertainties. Termed PINN under uncertainty, PINN-UU, adeptly integrates uncertain parameters within spatio-temporal domains, focusing on hydrological systems. This approach, exclusively built on underlying physical equations, leverages a staged training methodology, effectively navigating high-dimensional solution spaces. We demonstrate our approach through application of reactive transport modeling in porous media, a problem setting relevant to contaminant transport in soil and groundwater. PINN-UU shows promising capabilities in enhancing model reliability and efficiency, and in conducting sensitivity analysis. Our approach is designed to be accessible and engaging, offering insightful contributions to environmental engineering, and hydrological modeling. It represents a step toward deciphering complex geohydrological systems, with broad implications for resource management and environmental science.