Physics-informed neural networks for wind turbine wake prediction: Constraint hierarchy under varying data density

Physics-informed neural networks (PINNs) combine data-driven learning with governing-equation constraints, but their value in wind-turbine wake prediction depends on data density and residual fidelity. We examine this dependence through 36 controlled experiments on large-eddy simulation (LES) data (DTU EllipSys3D, NREL 5 MW, TI = 4% and 12.8%) under a 2D hub-height steady-RANS formulation. The optimized PINN reaches MSE = 0.001 (m s -1 ) 2 and R 2 = 0.999 . The experiments support a physics-constraint accuracy hierarchy : continuity provides consistent benefit and yields approximately 55–70% lower MSE than the tested full RANS residual set at moderate-to-high coverage, whereas the k – ε transport equations provide little measurable benefit, consistent with closure bias in turbine wakes. The hierarchy becomes statistically clear at N ≥ 3,000 observations, while seed variability prevents a definitive ranking at N = 1000 . Against LES-calibrated FLORIS Gaussian and Jensen baselines, the PINN achieves approximately 212 × to 469 × lower full-field MSE. The results indicate that residual fidelity, rather than the number of imposed equations, governs constraint value in this setting.