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We present theoretical expectations for infall toward supercluster-scale cosmological filaments, motivated by the Arecibo Pisces-Perseus Supercluster Survey (APPSS) to map the velocity field around the Pisces-Perseus Supercluster (PPS) filament. We use a minimum spanning tree applied to dark matter halos the size of galaxy clusters to identify 236 large filaments within the Millennium simulation. Stacking the filaments along their principal axes, we determine a well-defined, sharp-peaked velocity profile function that can be expressed in terms of the maximum infall rate $V_{\rm max}$ and the distance $ρ_{\rm max}$ between the location of maximum infall and the principal axis of the filament. This simple, two-parameter functional form is surprisingly universal across a wide range of linear mass densities. $V_{\rm max}$ is positively correlated with the halo mass per length along the filament, and $ρ_{\rm max}$ is negatively correlated with the degree to which the halos are concentrated along the principal axis. We also assess an alternative, single parameter method using $V_{25}$, the infall rate at a distance of 25 Mpc from the axis of the filament. Filaments similar to the PPS have $V_{\rm max} = 612 \ \pm$ 116 km s$^{-1}$, $ρ_{\rm max} = 8.9 \pm 2.1$ Mpc, and $V_{25} =329 \ \pm$ 68 km s$^{-1}$. We create mock observations to model uncertainties associated with viewing angle, lack of three-dimensional velocity information, limited sample size, and distance uncertainties. Our results suggest that it would be especially useful to measure infall for a larger sample of filaments to test our predictions for the shape of the infall profile and the relationships among infall rates and filament properties.