Abstract
High-fidelity computational fluid dynamics simula- tions are often too expensive for rapid analysis across many geometry variations. This work presents a hybrid DeepONet- SHRED-ROM framework for reconstructing parameterized two- dimensional flow fields from sparse sensor measurements. The model combines a SHRED-like recurrent encoder, which captures temporal information from a history of sparse velocity sensor readings, with a geometry-conditioned DeepONet. The DeepONet branch merges the temporal sensor representation with geometry and flow parameters, while the trunk evaluates the predicted flow at arbitrary spatial coordinates. The framework predicts velocity components and speed at the same time, with a consistency constraint between predicted speed and the norm of the predicted velocity vector. The method is evaluated on a parameterized finite-core vortex-wake dataset with varying obstacle position, size, aspect ratio, shedding frequency, and vortex strength. The final enhanced hybrid model uses a 30-step sensor history and evaluates all valid time steps for 20 unseen geometry cases. The model demonstrates a mean relative (L2) error of 0.047, with a median error of 0.045. These results show that a combination of sparse temporal sensing and neural operator learning can provide fast and accurate flow field reconstruction for previously unseen geometry variations.