Physics-Informed Neural Networks for Multi-Location ABL Wind Profiling with Minimal Instrumentation
Abstract
The vertical wind profile within the Atmospheric Boundary Layer (ABL) is a critical variable 2 for a wide range of applications, including wind energy, air traffic and unmanned aerial 3 system (UAS) management, pollutant dispersion, and urban air mobility. However, its 4 accurate characterization typically requires expensive vertical-profiling LiDAR instruments, 5 which limits the number of locations that can be simultaneously monitored. Building upon 6 previous work in which machine-learning algorithms were trained on LiDAR data from the 7 University of León (Spain) to reconstruct full ABL wind profiles from a single near-surface 8 measurement, this study replaces the traditional data-driven neural network approach with 9 Physics-Informed Neural Networks (PINNs), embedding a physical constraint directly into 10 the loss function as evaluated by automatic differentiation, and tests two such constraints 11 under architectural control: the Ekman boundary-layer momentum balance, closed with a 12 Monin-Obukhov eddy viscosity, and a shear-constrained formulation based on a power-law 13 profile with an inferred exponent. With dense supervision at the target heights, neither 14 constraint improves on an architecture-matched network without a physical term (RMSE 15 1.35-1.36 m/s, direction MAE 20.1-20.4◦ across all three, Kruskal-Wallis p = 0.0125), and 16 in a vertical-extrapolation protocol, training with gates up to 111 m, selecting models 17 by their skill at 140 m, and testing…
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