Sparse wind turbine wake reconstruction using physics-informed proper orthogonal decomposition

Wind turbine wake modeling from sparse measurements remains challenging due to spatiotemporal variability and limited full-field data availability in operational wind farms. This study introduces a physics-informed neural network with proper orthogonal decomposition (PINN-POD) framework for reconstructing unsteady wake fields and extracting coherent structures from sparse velocity measurements. The reconstruction is formulated as a physics-constrained forward problem, where PINNs estimate velocity fields by minimizing the measurement error and the Navier–Stokes equation residuals. Sparse spatial–temporal coordinates serve as inputs while automatic differentiation enforces physical constraints. POD then extracts dominant coherent structures while assessing training convergence through loss reduction and variations in mode energy. A dual-convergence strategy tracks training loss and mode variation, with robustness assessed under different noise levels. The framework accurately reconstructs instantaneous and time-averaged wake features for both non-yaw and yaw conditions. Comprehensive noise analysis reveals reconstruction errors below 5.81% for non-yaw cases and 7.00% for 30° yaw cases under 24% measurement noise, with errors concentrated in high-gradient shear regions while preserving wake core accuracy. Sensor distribution analysis demonstrates that 5 × 3 configurations provide adequate reconstruction quality, requiring minimum five cross-stream sensors for acceptable flow structure capture. Extracted POD modes preserve spatial coherence and capture characteristic wake asymmetries. PINN-POD demonstrates superior flow continuity and mode accuracy, especially under noisy conditions. The approach enables physics-consistent wake reconstruction and reduced-order modeling from limited measurements, providing practical utility for wind farm monitoring, control, and layout optimization.