Real-Time Estimation of High-Resolution Flow Fields and Reduced-Order Coordinates from Event-Based Imaging Velocimetry

Abstract

We propose a data-driven framework to estimate high-resolution (HR) velocity fields and reduced-order flow coordinates from real-time Event-Based Imaging Velocimetry (rt-EBIV). Fast event analysis first provides low-resolution (LR) velocity snapshots on a coarse grid. Offline, paired LR/HR fields are used to identify the LR-to-HR mapping and a linear dynamical model in a POD-based latent space. Online, each LR snapshot is projected onto the LR basis, the corresponding HR coordinates are estimated and temporally regularized, and the HR field is reconstructed from the retained POD modes. Three estimators are compared: a direct Kalman filter (KF), a linear stochastic estimator followed by Kalman filtering (LSE), and a variance-rescaled variant (LSE+VR). The method is tested on two turbulent flows acquired with pulsed EBIV: a submerged water jet and a channel flow over a square rib. All estimators outperform direct cubic interpolation of the LR fields, yielding more consistent HR reconstructions of instantaneous flow states, turbulent kinetic energy, spectra, reduced-order dynamics, and temporal coherence. LSE gives the lowest overall reconstruction error, while LSE+VR achieves similar errors with improved recovery of fluctuation energy and higher-order content. The direct KF is the most computationally efficient and provides the closest agreement with the HR reference in spectral analyses. Since most of the cost is associated with full-field HR reconstruction, the latent-coordinate estimation is negligible compared with LR processing. The framework allows deliberately coarse rt-EBIV processing to be combined with reduced-order refinement, extending real-time operation toward higher update rates while preserving richer and dynamically consistent HR flow representations for diagnostics and future observer-based flow-control applications.