  Fluid data completion is a research problem with high potential benefit for
both experimental and computational fluid dynamics. An effective fluid data
completion method reduces the required number of sensors in a fluid dynamics
experiment, and allows a coarser and more adaptive mesh for a Computational
Fluid Dynamics (CFD) simulation. However, the ill-posed nature of the fluid
data completion problem makes it prohibitively difficult to obtain a
theoretical solution and presents high numerical uncertainty and instability
for a data-driven approach (e.g., a neural network model). To address these
challenges, we leverage recent advancements in computer vision, employing the
vector quantization technique to map both complete and incomplete fluid data
spaces onto discrete-valued lower-dimensional representations via a two-stage
learning procedure. We demonstrated the effectiveness of our approach on
Kolmogorov flow data (Reynolds number: 1000) occluded by masks of different
size and arrangement. Experimental results show that our proposed model
consistently outperforms benchmark models under different occlusion settings in
terms of point-wise reconstruction accuracy as well as turbulent energy
spectrum and vorticity distribution.
