High-Accuracy Parallel Neural Networks with Hard Constraints for a Mixed Stokes/Darcy Model

In this paper, we study numerical algorithms based on Physics-Informed Neural Networks (PINNs) for solving a mixed Stokes/Darcy model that describes a fluid flow coupled with a porous media flow. A Hard Constrained Parallel PINN (HC-PPINN) is proposed for the mixed model, in which the boundary conditions are enforced by modified the neural network architecture. Numerical experiments with different settings are conducted to demonstrate the accuracy and efficiency of our method by comparing it with the methods based on vanilla PINNs for the mixed model.