Sparse data wind field wake reconstruction based on parametric adaptive physics-informed neural networks

Real-time acquisition of wind turbine wake data supports monitoring and layout optimization of smart wind farms, attracting significant attention in the field of wind energy. However, existing measurement technologies, such as light detection and ranging (LiDAR), have notable limitations as they can only collect sparse data points. Previous PINN-based wake reconstruction studies typically treat viscosity or diffusivity as a global constant. To overcome this limitation, we propose a parameterized adaptive physics-informed neural network (PA-PINN) that learns a spatiotemporally adaptive diffusivity λ(x,y,t) through a lightweight sub-network. This design enables the model to adjust the local diffusion intensity according to the wake shear level while strictly satisfying the Navier–Stokes equations. The reference velocity field data are derived from the EllipSys3D Large-Eddy Simulation (LES) under neutral atmospheric conditions. The improved model has the following advantages: (i) it captures two-dimensional information, including the streamwise velocity (U) and lateral velocity (V); (ii) it achieves high-precision reconstruction of the flow field in unknown areas with minimal data; (iii) it employs an adaptive optimization strategy based on the flow field gradient to accelerate convergence speed and reduce error. The experimental results demonstrate that the model achieves high-precision wake reconstruction using only 1% sparse data and can stably reconstruct the overall flow field structure under substantial noise interference, showcasing strong robustness and versatility. Furthermore, the spatiotemporal evolution experiment further verifies the model's advantages in capturing complex flow behaviors, offering an accurate and reliable solution for wake reconstruction and wind farm layout optimization, with broad application prospects in wind energy and other fluid mechanics systems.