Real-time estimation of high-resolution flow fields and reduced-order coordinates from event-based imaging velocimetry

Abstract A data-driven framework is proposed to estimate high-resolution (HR) velocity fields and reduced-order flow coordinates from coarse real-time event-based imaging velocimetry (rt-EBIV) measurements. Low-resolution (LR) data are retrieved through fast event analysis on a coarse grid. During offline training, the LR/HR mapping and a linear dynamical model in a proper orthogonal decomposition (POD)-based reduced-order space are identified. Online, each incoming LR snapshot is projected onto the LR basis, and the corresponding HR reduced-order coordinates are estimated and temporally regularized. Three estimators are proposed and compared: a direct Kalman filter (KF), a linear stochastic estimation (LSE) combined with Kalman filtering, and a variance-rescaled implementation (LSE+VR). The full HR velocity field is then reconstructed from the estimated reduced-order coordinates using the retained POD basis. The framework is assessed on two turbulent flows acquired by pulsed event-based imaging velocimetry (EBIV): a submerged water jet and a channel flow over a square rib. All three estimators outperform direct cubic interpolation of the LR fields, recovering physically consistent HR flow states with improved estimation of turbulent kinetic energy, spectral content, reduced-order dynamics, and temporal coherence. The linear stochastic estimator yields the lowest overall reconstruction error, while its variance-rescaled implementation provides nearly identical values and improves the recovery of fluctuation energy and higher-order content. The direct KF formulation remains highly efficient in terms of computational cost and provides the closest agreement with the HR reference in the temporal and spatial spectral analyses. The bulk of the computational cost lies in the full-field HR reconstruction, whereas the reduced-order coordinate estimation alone is negligible compared with the cost of the LR processing itself. The framework enables deliberately coarse real-time EBIV processing to be combined with reduced-order refinement, extending the effective real-time operating range towards higher update frequencies while still providing richer and dynamically more consistent HR flow representations. This makes the approach attractive for high-quality real-time flow diagnostics and as a first step towards future observer-based and closed-loop flow-control applications.