Learning Wind-Turbine Wakes with Generative Adversarial Networks 

by Jamal Toutouh (University of Málaga, Spain), Sergio Nesmachnow (Universidad de la República, Uruguay), Martín Draper (Universidad de la República, Uruguay), and Maximiliano Bove (Universidad de la República, Uruguay)

Data-driven and physics-informed generative adversarial networks provide fast surrogates for wind-turbine wakes, bridging high-fidelity simulation and wind farm design. 

Wind-farm design and control require reliable predictions of how turbines interact through their wakes. Wake interactions determine power losses, mechanical loads, and fatigue in downstream turbines, strongly influencing wind-farm efficiency and lifetime . High-fidelity approaches based on Large Eddy Simulation with Actuator Line Models (LES-ALM) can resolve these flows in detail, but each simulation may require days of computation. That cost limits systematic exploration of new layouts, operating conditions, and control strategies.

Recent work in scientific machine learning has proposed physics-informed generative adversarial networks (PI-GANs) as a way to combine the strengths of first-principles models and deep generative learning [2]. PI-GANs extend the standard generative adversarial network (GAN) framework by adding loss terms that measure how well generated samples satisfy the governing physical laws. The GAN discriminator still distinguishes real and generated data, but the generator is additionally regularised to respect conservation laws or constitutive relations. In fluid mechanics, such models promise to reduce data requirements and improve extrapolation to new regimes, while retaining physical consistency.

The work presented here belongs to a broader research effort on physics-informed generative models for fluid flows in wind energy. The study is a collaboration between the Instituto de Mecánica de los Fluidos e Ingeniería Ambiental and the Instituto de Computación at Universidad de la República (Uruguay), together with the Instituto de Tecnologías e Ingeniería del Software at Universidad de Málaga (Spain) [L1]. The team has developed and analysed a purely data-driven GAN surrogate model for wind-turbine wakes, which provides a baseline against which future PI-GAN variants can be assessed [1].

The proposed surrogate model targets the mean streamwise wind speed at hub height in the wakes of a virtual wind farm with 15 turbines [1]. The dataset is generated with LES-ALM simulations of seven layouts and five inflow wind speeds. The inflow boundary condition comes from precursor simulations of an atmospheric boundary layer with realistic turbulence. For each configuration, the time-averaged velocity field on a horizontal plane at hub height is stored.

Each training sample consists of two elements: the horizontal wind profile two rotor diameters upstream of a selected turbine, and the corresponding mean downstream velocity field in a rectangular region around that turbine. The GAN therefore learns the mapping from local inflow to the surrounding wake, including wake recovery and lateral spreading, for a range of inflow conditions and turbine positions in the farm.

The surrogate follows a conditional GAN architecture. The generator receives the upstream velocity profile and produces a two-dimensional map of the mean hub-height wind speed in a region that extends several rotor diameters upstream and downstream of a turbine. The discriminator processes paired inflow–wake fields and learns to distinguish synthetic wakes produced by the generator from reference wakes extracted from the LES-ALM simulations. Training minimises a combined loss that balances an adversarial term, which encourages realistic global wake structures, and a mean-square error term, which penalises local deviations from the LES-ALM fields.

The experimental analysis explores several training setups by varying the averaging time window used to construct the mean fields and the weight of the error term in the loss [1]. Performance is evaluated using both image-based measures and flow-specific quantities such as wake-centre position and velocity deficit. The best configuration achieves low mean errors when predicting the wake around an individual turbine given the local inflow.

Figure 1 illustrates a representative comparison between the LES-ALM reference and the GAN prediction for the mean streamwise velocity at hub height in a 15-turbine farm. The surrogate reproduces the location and depth of the velocity deficit with moderate errors over most of the wake region, including the gradual recovery of wind speed downstream. Differences concentrate near the rotor plane and at the edges of the wakes, where gradients are sharp and small misalignments translate into visible discrepancies.

Figure 1: Mean streamwise velocity component at hub height. LES-ALM data (left) and GAN prediction (right). Time window: 4000[PK1.1]. Precursor simulation: 7.7 m/s. Inflow angle: 0°.

The study also examines whether the surrogate can reconstruct the hub-height velocity field across the entire farm using only the inlet profile. In that test, the model is applied sequentially along each row, using the predicted profile at one turbine as input for the next. Errors accumulate downstream and become significant in the last rows, especially for shorter averaging windows where inflow variability plays a stronger role. The results indicate that purely data-driven GAN surrogates capture local wake features reliably, but global consistency across multiple wake interactions remains challenging.

Despite these limitations, the surrogate reduces evaluation time from days to seconds once trained. That speed enables integration into optimisation and control studies that require thousands of flow evaluations, such as layout optimisation or yaw control strategies. In the ongoing project, such data-driven models serve as a reference point for the development of PI-GANs that will incorporate momentum conservation and turbulence closures directly into the training objective, with the goal of improving robustness and generalisation.

The combination of PI-GAN concepts with high-fidelity LES-ALM data and evolutionary optimisation defines a research direction in which generative models not only reproduce existing simulations [2], but also explore new operating regimes under explicit physical constraints. The wind-turbine wake surrogate in [1] demonstrates the feasibility of GAN-based flow prediction in wind farms and motivates further work on physics-informed variants that can better handle complex wake interactions in realistic conditions.

Link: 
[L1] https://jamaltoutouh.github.io/pinns/ 

References: 
[1] M. Bove, et al., “Estimation of wind turbine wakes with generative-adversarial networks,” Journal of Physics: Conference Series, 2505, 012053, 2023.
[2] L. Yang, D. Zhang, G.E. Karniadakis: “Physics-informed generative adversarial networks for stochastic differential equations,” SIAM J. Sci. Comput. 42(1), A292–A317, 2020.

Please contact: 
Jamal Toutouh, Universidad de Málaga, Spain 
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