High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete and noisy. Deep-learning approaches have been shown suitable for such super-resolution tasks. However, a high number of high-resolution examples is needed, which may not be available for many cases. Moreover, the obtained predictions may lack in complying with the physical principles, e.g. mass and momentum conservation. Physics-informed deep learning provides frameworks for integrating data and physical laws for learning. In this study, we apply physics-informed neural networks (PINNs) for super-resolution of flow-field data both in time and space from a limited set of noisy measurements without having any high-resolution reference data. Our objective is to obtain a continuous solution of the problem, providing a physically-consistent prediction at any point in the solution domain. We demonstrate the applicability of PINNs for the super-resolution of flow-field data in time and space through three canonical cases: Burgers' equation, two-dimensional vortex shedding behind a circular cylinder and the minimal turbulent channel flow. The robustness of the models is also investigated by adding synthetic Gaussian noise. Furthermore, we show the capabilities of PINNs to improve the resolution and reduce the noise in a real experimental dataset consisting of hot-wire-anemometry measurements. Our results show the adequate capabilities of PINNs in the context of data augmentation for experiments in fluid mechanics.

翻译：从低分辨率和含噪声测量中高分辨率重建流场数据备受关注，因为实验流体力学中此类问题普遍存在，测量数据通常稀疏、不完整且包含噪声。深度学习方法已被证明适用于此类超分辨率任务，但通常需要大量高分辨率样本，这在许多情况下难以获取。此外，获得的预测结果可能缺乏对物理原理（如质量和动量守恒）的遵循。物理信息深度学习为融合数据和物理定律进行学习提供了框架。本研究应用物理信息神经网络（PINNs），在无任何高分辨率参考数据的情况下，从有限组含噪测量中实现流场数据的时空超分辨率。我们旨在获得问题的连续解，从而在求解域内任一点提供符合物理一致性的预测。通过三个典型算例（Burgers方程、圆柱绕流的二维涡脱落及最小湍流槽道流）验证了PINNs对时空流场数据超分辨率的适用性，并通过添加合成高斯噪声探究了模型的鲁棒性。此外，我们展示了PINNs在实际实验数据集（热线风速仪测量）中提升分辨率与降噪的能力。结果表明，PINNs在实验流体力学数据增强方面具有充分潜力。