Fiber-based structures play a crucial role in technical filtration applications. These structures are inherently complex, characterized by randomly oriented fibres with varying diameters and porosities. Accurately modelling particle deposition within such intricate geometries is challenging—not only due to the irregular structure but also because of the computational effort required for mesh generation.

To overcome these limitations, this study introduces an alternative framework that integrates Physics-Informed Neural Networks (PINNs) as flow solvers with Smoothed Particle Hydrodynamics (SPH) for simulating particle interactions within the fibre network. This combined approach allows for the modelling of complex processes such as particle deposition, liquid film formation, and re-entrainment, providing a robust alternative to conventional CFD techniques. PINNs have recently gained significant traction in the fluid mechanics community. Their appeal lies in their unique loss formulation, which embeds governing physical equations (such as the Navier–Stokes equations) and boundary conditions directly into the optimization process without the need for extensive training data.

The SPH method, on the other hand, is a mesh-free CFD technique that represents fluids as discrete particles. To accurately capture the filtration process in complex fibre geometries, this work couples the PINN and SPH methods into an integrated framework. This coupling is crucial for handling dynamic domain changes such as local blockages caused by extensive film deposition. Although initial PINN training can be computationally demanding, subsequent time steps benefit from transfer learning, enabling rapid adaptation to geometric updates (including new film layers on fibres).

This hybrid PINN–SPH framework provides an efficient and scalable approach for simulating droplet deposition in three-dimensional fibre structures. The proposed numerical model has been validated against data from single-fibre filtration experiments. The simulation results for complex multi-fibre configurations are presented and analysed in detail, demonstrating the capability and accuracy of the coupled PINN–SPH approach...