Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings

The usage of deep neural networks (DNNs) for flow reconstruction (FR) tasks from a limited number of sensors is attracting strong research interest, owing to DNNs' ability to replicate very high dimensional relationships. Trained over a single flow case for a given Reynolds number or over a reduced range of Reynolds numbers, these models are unfortunately not able to handle fluid flows around different objects without re-training. In this work, we propose a new framework called Spatial Multi-Geometry FR (SMGFR) task, capable of reconstructing fluid flows around different two-dimensional objects without re-training, mapping the computational domain as an annulus. Different DNNs for different sensor setups (where information about the flow is collected) are trained with high-fidelity simulation data for a Reynolds number equal to approximately $300$ for 64 objects randomly generated using Bezier curves. The performance of the models and sensor setups are then assessed for the flow around 16 unseen objects. It is shown that our mapping approach improves percentage errors by up to 15\% in SMGFR when compared to a more conventional approach where the models are trained on a Cartesian grid. Finally, the SMGFR task is extended to predictions of fluid flow snapshots in the future, introducing the Spatio-temporal MGFR (STMGFR) task. For this spatio-temporal reconstruction task, a novel approach is developed involving splitting DNNs into a spatial and a temporal component. Our results demonstrate that this approach is able to reproduce, in time and in space, the main features of a fluid flow around arbitrary objects.