Inpainting Computational Fluid Dynamics with Deep Learning
This addresses the problem of fluid data completion for experimental and computational fluid dynamics, offering a novel method to improve efficiency, though it is incremental as it adapts computer vision techniques to a specific domain.
The paper tackled the ill-posed problem of fluid data completion, which reduces sensor needs in experiments and mesh requirements in simulations, by using a vector quantization-based deep learning method; it demonstrated effectiveness on Kolmogorov flow data, outperforming benchmarks in reconstruction accuracy, turbulent energy spectrum, and vorticity distribution under various occlusion settings.
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.