The efficient removal of solid particles and liquid droplets is of crucial importance in many industrial processes. The main objective is to achieve a high separation efficiency while minimizing the associated pressure drop. This trade-off represents a central challenge in the design of filter media, where the goal is to optimize filtration performance without compromising energy efficiency or operational safety. Over the past decades, both experimental techniques and numerical modeling approaches have advanced significantly. Nevertheless, understanding remains limited due to the microscopic nature of filtration. Experiments often suffer from limited reproducibility and require costly test media. Conventional numerical approaches, such as the finite volume method, can resolve the relevant transport mechanisms, but the small spatial and temporal scales involved require extremely fine grids and time steps. These limitations make classical computational fluid dynamics (CFD) simulations expensive and, in some cases, impractical. In this work, a modeling approach for simulating the filtration process is presented that couples a Physics-Informed Neural Network (PINN) with the Smoothed Particle Hydrodynamics (SPH) method. Using the PINN, the three-dimensional velocity and pressure fields within the fiber network are determined directly from the Navier–Stokes equations without relying on training data. The resulting flow field is passed to the SPH solver, which computes droplet trajectories, droplet impacts on the fibers, and the motion of fluid films. Since both PINN and SPH are mesh-free methods, the complex mesh generation step is eliminated. Once the deposited droplets become large enough to influence the flow field, their geometric information is transferred to the PINN, which then recomputes the flow field using transfer learning. A comparison between the flow fields predicted by the PINN models and those computed using a CFD solver for four representative filter structures shows very good agreement between PINN and CFD.