![]() Second, the data resolution is often constrained by the ability of the measurement techniques. 1 Hence, scientists could only afford to store a small fraction of data (e.g., temporally sparse sequences, spatially downscaled volumes, or selectively variable subsequences) for post hoc analysis. For example, the direct numerical simulation (DNS) of wall-bounded turbulent flows at Reynolds number of R e τ = 10 4 can generate more than 20 TB files at each time step, and the file size will increase exponentially as R e τ grows. First, flow data are typically spatiotemporal fields in large scales, which poses significant challenges to data analysis, sharing, and visualization due to limited storage space and large communication overhead. Nonetheless, fluid flow data are often sparse, incomplete, and noisy in real-life scenarios due to the following reasons. High-resolution (HR) information of fluid flow is critical for reliable qualitative and quantitative analyses for fluid systems in aerodynamics, mechanical, and biomedical engineering. A series of different LR scenarios, including LR input with Gaussian noises, non-Gaussian magnetic resonance imaging noises, and downsampled measurements given either well-posed or ill-posed physics, are investigated to illustrate the SR, denoising, and inference capabilities of the proposed method. Several flow SR problems relevant to cardiovascular applications have been studied to demonstrate the proposed method's effectiveness and merit. A new network structure is designed to enable not only the parametric SR but also the parametric inference for the first time. 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. By leveraging the conservation laws and boundary conditions of fluid flows, the CNN-SR model is trained without any HR labels. In this work, we present a novel physics-informed DL-based SR solution using convolutional neural networks (CNNs), which is able to produce HR flow fields from low-resolution (LR) inputs in high-dimensional parameter space. 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. How to enhance spatial resolution and decrease the noise level of flow data is essential and practically useful. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources.
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