Machine-Learning Probe of Nonlinear Pore-to-Pore Flow in Sphere Packings

Granular porous media are widely used in groundwater, filtration, drainage, and packed-treatment systems, where pressure loss is commonly represented by macroscopic correlations or reduced pore-network conductance models. These approaches provide useful descriptions of hydraulic response, but the development of nonlinear behaviour across individual pore connections remains incompletely characterised. This study combines pore-resolved computational fluid dynamics (CFD), a Delaunay-based pore–throat–pore representation, and Gaussian Process Regression (GPR) to examine local pressure–velocity responses in four monodisperse sphere-packing realisations. The CFD-derived throat-centre velocity is used together with throat geometry, particle arrangement, and adjacent pore-body geometry to construct a common response mapping across the sampled flow conditions. The analysis reveals a broad distribution of pair-specific nonlinear transition susceptibilities and progressive, network-dependent activation as the inlet velocity increases. Particle arrangement shows the most persistent association with transition susceptibility, while the broader pore–throat–pore geometry contributes to the representation of local hydraulic response. Comparison with the bed-scale CFD pressure loss provides a descriptive, non-mechanistic quantitative cross-scale comparison: the extent of local activation and the relative quadratic contribution to the bed-scale response follow different packing-level orderings and are not directly proportional. The framework therefore provides a pore-pair perspective on heterogeneous nonlinear flow while remaining limited to the investigated packing realisations and the CFD-sampled response domain.