Transfer learning enhanced physics-informed neural networks for forward and inverse transport problems in heterogeneous domains

The study of coupled fluid flow and heat transfer processes in heterogeneous domains such as porous media is computationally expensive and often the exact parameters of the system (e.g., the permeability distribution) are not known. Physics-informed neural networks (PINN) provide a hybrid data-driven and physics-based solution to these problems. However, they are computationally not efficient for forward problems. Additionally, in inverse problems, PINN sometimes converges to unrealistic patterns due to the non-uniqueness of the solution. In this presentation, we propose two different approaches using transfer learning to overcome these issues. First, a multi-fidelity approach that combines fast low-fidelity computational fluid dynamics (CFD) solution strategies with transfer learning and PINN is presented for forward problems. Second, we propose an approach where an ensemble of parallel neural networks, each initialized with a meaningful pattern of the unknown parameter, is used to guide PINN to enhance the predictions made in inverse problems. Several forward and inverse problems such as heterogeneous porous media transport are presented to demonstrate the efficiency of the proposed approaches.