  High-resolution (HR) information of fluid flows, although preferable, is
usually less accessible due to limited computational or experimental resources.
In many cases, fluid data are generally sparse, incomplete, and possibly noisy.
How to enhance spatial resolution and decrease the noise level of flow data is
essential and practically useful. Deep learning (DL) techniques have been
demonstrated to be effective for super-resolution (SR) tasks, which, however,
primarily rely on sufficient HR labels for training. In this work, we present a
novel physics-informed DL-based SR solution using convolutional neural networks
(CNN), which is able to produce HR flow fields from low-resolution (LR) inputs
in high-dimensional parameter space. By leveraging the conservation laws and
boundary conditions of fluid flows, the CNN-SR model is trained without any HR
labels. Moreover, the proposed CNN-SR solution unifies the forward SR and
inverse data assimilation for the scenarios where the physics is partially
known, e.g., unknown boundary conditions. Several flow SR problems relevant to
cardiovascular applications have been studied to demonstrate the proposed
method's effectiveness and merit. Both Gaussian and non-Gaussian MRI noises are
investigated to illustrate the denoising capability.

Fluid Dynamics;Computational Physics