Summary Numerical simulations of pore-scale fluid flow in oil and gas reservoirs remain challenging due to complex boundary conditions from intricate pore geometries and the computational complexity of solving the Navier-Stokes equations. To address these issues, we propose an innovative hybrid approach combining Smoothed Particle Hydrodynamics (SPH) and Physics-Informed Neural Networks (PINNs). SPH's mesh-free framework efficiently handles complex boundaries and avoids meshing limitations, while the kernel-based formulation reduces computational costs compared to traditional fully connected PINNs. By representing fluid particles as dynamic nodes in the neural network, our method naturally adapts to evolving geometries and eliminates manual node-selection challenges. Boundary conditions are directly embedded into the PINN framework, enabling stable and efficient simulations. Partial derivatives are computed exactly using automatic differentiation, with second-order operators obtained through repeated differentiation. Our results demonstrate that this hybrid approach significantly improves stability, efficiency, and flexibility in pore-scale flow simulations compared to conventional methods, offering a powerful tool for modeling complex porous media systems.
Zhu et al. (Tue,) studied this question.