Graph Neural Operator for windfarm wake flow

Abstract. Wind farm flow simulations are computationally expensive. However, numerous simulations are often required in applications such as wind farm layout optimization or when considering multiple neighboring farms, which motivates the development of data-driven surrogate models. However, most existing approaches rely on classical superposition principles, which constrain their ability to capture nonlinear wake interactions. We propose a novel method that embeds a trainable and scalable superposition principle within a Graph Neural Operator (GNO) architecture.

The model consists of two sequential Graph Neural Network (GNN) layers: the first encodes turbine–turbine interactions into a latent representation, while the second combines these latent turbine states to predict the wind speed at a desired location. The GNO is trained on a large dataset of simulated wind farms and achieves a low prediction error, with an RMSE of 0.353 ms⁻¹ and a MAPE of 0.938 % on an unseen test dataset.

The GNO accurately identifies regions of strong wake interaction, although the spatial extent of wakes is slightly underestimated in cases with pronounced wake effects. Overall, the proposed GNO represents a significant advancement in data-driven wind farm flow surrogates, introducing a new conceptual framework inspired by established engineering wake modeling principles.