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Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating both data and underlying physics to enrich the neural network's understanding, concerns regarding the effectiveness and practicality of PINNs persist. Over the past few years, extensive efforts in the current literature have been made to enhance this evolving method, by drawing inspiration from both machine learning algorithms and numerical methods. Despite notable progressions in PINNs algorithms, the important and fundamental field of data preprocessing remain unexplored, limiting the applications of PINNs especially in solving inverse problems. Therefore in this paper, a concise yet potent data preprocessing method focusing on data normalization was proposed. By applying a linear transformation to both the data and corresponding equations concurrently, the normalized PINNs approach was evaluated on the task of reconstructing flow fields in three turbulent cases. The results illustrate that by adhering to the data preprocessing procedure, PINNs can robustly achieve higher prediction accuracy for all flow quantities under different hyperparameter setups, without incurring extra computational cost, distinctly improving the utilization of limited training data. Though only verified in Navier-Stokes (NS) equations, this method holds potential for application to various other equations.

Various types of measurement techniques, such as Light Detection and Ranging (LiDAR) devices, anemometers, and wind vanes, are extensively utilized in wind energy to characterize the inflow. However, these methods typically gather data at limited points within local wind fields, capturing only a fraction of the wind field's characteristics at wind turbine sites, thus hindering detailed wind field analysis. This study introduces a framework using Physics-informed Neural Networks to assimilate diverse sensor data types. This includes line-of-sight wind speed, velocity magnitude and direction, velocity components, and pressure. Moreover, the parameterized Navier-Stokes equations are integrated as physical constraints, ensuring that the neural networks accurately represent atmospheric flow dynamics. The framework accounts for the turbulent nature of atmospheric boundary layer flow by including artificial eddy viscosity in the network outputs, enhancing the model's ability to learn and accurately depict large-scale flow structures. The reconstructed flow field and the effective wind speed are in good agreement with the actual data. Furthermore, a transfer learning strategy is employed for the online deployment of pre-trained PINN, which requires less time than that of the actual physical flow. This capability allows the framework to reconstruct wind flow fields in real time based on live data. In the demo cases, the maximum error between the effective wind speed reconstructed online and the actual value at the wind turbine site is only 3.7%. The proposed data assimilation framework provides a universal tool for reconstructing spatiotemporal wind flow fields using various measurement data. Additionally, it presents a viable approach for the online assimilation of real-time measurements. To facilitate the utilization of wind energy, our framework's source code is openly accessible.