Event-Based Fluid Velocity Field Reconstruction via Navier–Stokes Constraints

Event cameras capture motion with high temporal resolution, but recovering from raw events a velocity field that also obeys the underlying flow physics remains difficult. Existing event-based methods either require ground-truth velocity or depth, which restricts them to curated datasets, or are unsupervised but impose no conservation constraints, so the recovered fields can violate incompressibility even when they reproduce the events accurately. We introduce PIFlow-Net, which reconstructs continuous, incompressible velocity fields from event streams for two-dimensional flows at low-to-moderate Reynolds numbers (Re≤400) without ground-truth velocity or depth. Events are treated as Lagrangian tracers advected through an implicit neural velocity field, and their trajectories are integrated by a continuous-adjoint ordinary differential equation solver. The incompressible Navier–Stokes equations are enforced as a soft constraint together with an event contrast maximization loss. On synthetic two-dimensional flows, PIFlow-Net achieves an average endpoint root-mean-square error (RMSE) of 0.058 in simulation units and an angular error of 3.1∘, outperforming a supervised optical flow network, although it requires a separate optimization for each sequence. On a real dye-plume sequence, it reduces the RMSE by 25% relative to the strongest hybrid baseline. Ablation experiments identify the Navier–Stokes constraint as the largest single contributor to reconstruction accuracy among the physics terms. A smoothness penalty of matched strength recovers part of that accuracy gain but leaves the mean divergence 67 times that of the full model. These results suggest that physics-constrained implicit representations offer a workable route to unsupervised, physically consistent flow reconstruction from event data.