*Result*: Adaptive pseudo-solution-assisted PINNs for multiscale Darcy and Darcy-Forchheimer equations.

*The Darcy and Darcy-Forchheimer equations with discontinuous coefficients are widely used to model flow in heterogeneous porous media. However, the significant scale variations across the computational domain pose challenges for traditional physics-informed neural networks (PINNs). This paper proposes an adaptive pseudo-solution-assisted PINN framework, which leverages solutions from well-learned regions to guide subsequent training through pseudo-supervision. Our method dynamically generates pseudo-solutions during training and incorporates a regularization term based on these solutions into the optimization objective. Periodic updates refine the pseudo-solutions, while a decaying weight mechanism controls their influence. Experimental results demonstrate that our approach enhances the accuracy of solving multiscale Darcy and Darcy-Forchheimer equations compared to existing deep learning solvers. [ABSTRACT FROM AUTHOR]*