A Transfer-Learning PINN Framework to Simulate Fluid Flow and Contaminant Transport Under Uncertainty

Accurate prediction of subsurface flow under uncertain, spatially varying conditions remains a core challenge in hydrogeology. This, in turn, has great impacts on our ability to predict and control contaminant transport in subsurface water bodies and control the dynamics of water quality. This work extends a Physics-Informed Neural Network (PINN) framework to incorporate 1) Function-Guided (Parametric Stochasticity) and 2) Latent-Encoded (Generated Stochasticity) heterogeneities. In the former, a parametric function with random inputs generates multiple heterogeneous media, enabling transfer learning to sequentially refine network parameters across different realizations. The second pathway employs the decoder of a pretrained generative autoencoder—trained on numerous Gaussian Random Field realizations—to embed random hydraulic conductivity fields. Illustrated through a two-dimensional Darcy flow case study, the method is broadly applicable to a range of parametric PDE problems in hydrology, engineering, and environmental sciences. In particular the model can also be employed to effectively characterize contaminant transport scenarios, in the presence of uncertain model parameters, such as dispersivity or sorption properties. The model can also be employed to represent specific uncertainties related to the contamimant source location or other features affecting the space-time contaminant plume evolution. Results underscore the advantages of staged learning strategies for high-dimensional parametric PDEs, offering an efficient, physics-consistent tool for hydrological modeling and resource management.