Articles | Volume 11, issue 8
https://doi.org/10.5194/wes-11-2869-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-11-2869-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Aug 2026
Research article |
| 11 Aug 2026
| 11 Aug 2026
Convolutional versus graph-based surrogate models for inter-farm wake prediction using multi-fidelity transfer learning
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Frederik Peder Weilmann Rasmussen
CORRESPONDING AUTHOR
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
M. Paul van der Laan
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Alfredo Peña
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Pierre-Elouan Réthoré
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
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The use of wind energy has been growing over the last few decades, and further increase is predicted. As the wind energy industry is starting to consider larger wind farms, the existing numerical methods for analysis of small and medium wind farms need to be improved. In this article, we have explored different strategies to tackle the problem in a feasible and timely way. The final product is a set of recommendations when carrying out trade-off analysis on large wind farms.
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Wind Energ. Sci., 11, 2647–2668, https://doi.org/10.5194/wes-11-2647-2026, https://doi.org/10.5194/wes-11-2647-2026, 2026
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Revised manuscript under review for WES
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Alfredo Peña, Ginka G. Yankova, and Vasiliki Mallini
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Oscar García-Santiago, Andrea N. Hahmann, Jake Badger, and Alfredo Peña
Wind Energ. Sci., 9, 963–979, https://doi.org/10.5194/wes-9-963-2024, https://doi.org/10.5194/wes-9-963-2024, 2024
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This study compares the results of two wind farm parameterizations (WFPs) in the Weather Research and Forecasting model, simulating a two-turbine array under three atmospheric stabilities with large-eddy simulations. We show that the WFPs accurately depict wind speeds either near turbines or in the far-wake areas, but not both. The parameterizations’ performance varies by variable (wind speed or turbulent kinetic energy) and atmospheric stability, with reduced accuracy in stable conditions.
Javier Criado Risco, Rafael Valotta Rodrigues, Mikkel Friis-Møller, Julian Quick, Mads Mølgaard Pedersen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 585–600, https://doi.org/10.5194/wes-9-585-2024, https://doi.org/10.5194/wes-9-585-2024, 2024
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Wind energy developers frequently have to face some spatial restrictions at the time of designing a new wind farm due to different reasons, such as the existence of protected natural areas around the wind farm location, fishing routes, and the presence of buildings. Wind farm design has to account for these restricted areas, but sometimes this is not straightforward to achieve. We have developed a methodology that allows for different inclusion and exclusion areas in the optimization framework.
Rafael Valotta Rodrigues, Mads Mølgaard Pedersen, Jens Peter Schøler, Julian Quick, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 321–341, https://doi.org/10.5194/wes-9-321-2024, https://doi.org/10.5194/wes-9-321-2024, 2024
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The use of wind energy has been growing over the last few decades, and further increase is predicted. As the wind energy industry is starting to consider larger wind farms, the existing numerical methods for analysis of small and medium wind farms need to be improved. In this article, we have explored different strategies to tackle the problem in a feasible and timely way. The final product is a set of recommendations when carrying out trade-off analysis on large wind farms.
Wei Fu, Feng Guo, David Schlipf, and Alfredo Peña
Wind Energ. Sci., 8, 1893–1907, https://doi.org/10.5194/wes-8-1893-2023, https://doi.org/10.5194/wes-8-1893-2023, 2023
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A high-quality preview of the rotor-effective wind speed is a key element of the benefits of feedforward pitch control. We model a one-beam lidar in the spinner of a 15 MW wind turbine. The lidar rotates with the wind turbine and scans the inflow in a circular pattern, mimicking a multiple-beam lidar at a lower cost. We found that a spinner-based one-beam lidar provides many more control benefits than the one on the nacelle, which is similar to a four-beam nacelle lidar for feedforward control.
Alessandro Sebastiani, James Bleeg, and Alfredo Peña
Wind Energ. Sci., 8, 1795–1808, https://doi.org/10.5194/wes-8-1795-2023, https://doi.org/10.5194/wes-8-1795-2023, 2023
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The power curve of a wind turbine indicates the turbine power output in relation to the wind speed. Therefore, power curves are critically important to estimate the production of future wind farms as well as to assess whether operating wind farms are functioning correctly. Since power curves are often measured in wind farms, they might be affected by the interactions between the turbines. We show that these effects are not negligible and present a method to correct for them.
Julian Quick, Pierre-Elouan Rethore, Mads Mølgaard Pedersen, Rafael Valotta Rodrigues, and Mikkel Friis-Møller
Wind Energ. Sci., 8, 1235–1250, https://doi.org/10.5194/wes-8-1235-2023, https://doi.org/10.5194/wes-8-1235-2023, 2023
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Wind turbine positions are often optimized to avoid wake losses. These losses depend on atmospheric conditions, such as the wind speed and direction. The typical optimization scheme involves discretizing the atmospheric inputs, then considering every possible set of these discretized inputs in every optimization iteration. This work presents stochastic gradient descent (SGD) as an alternative, which randomly samples the atmospheric conditions during every optimization iteration.
Mark Kelly and Maarten Paul van der Laan
Wind Energ. Sci., 8, 975–998, https://doi.org/10.5194/wes-8-975-2023, https://doi.org/10.5194/wes-8-975-2023, 2023
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The turning of the wind with height, which is known as veer, can affect wind turbine performance. Thus far meteorology has only given idealized descriptions of veer, which has not yet been related in a way readily usable for wind energy. Here we derive equations for veer in terms of meteorological quantities and provide practically usable forms in terms of measurable shear (change in wind speed with height). Flow simulations and measurements at turbine heights support these developments.
Maarten Paul van der Laan, Oscar García-Santiago, Mark Kelly, Alexander Meyer Forsting, Camille Dubreuil-Boisclair, Knut Sponheim Seim, Marc Imberger, Alfredo Peña, Niels Nørmark Sørensen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 8, 819–848, https://doi.org/10.5194/wes-8-819-2023, https://doi.org/10.5194/wes-8-819-2023, 2023
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Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses. In this work, an efficient numerical method is presented that can be used to estimate these energy losses. The novel method is verified with higher-fidelity numerical models and validated with measurements of an existing wind farm cluster.
Wei Fu, Alessandro Sebastiani, Alfredo Peña, and Jakob Mann
Wind Energ. Sci., 8, 677–690, https://doi.org/10.5194/wes-8-677-2023, https://doi.org/10.5194/wes-8-677-2023, 2023
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Nacelle lidars with different beam scanning locations and two types of systems are considered for inflow turbulence estimations using both numerical simulations and field measurements. The turbulence estimates from a sonic anemometer at the hub height of a Vestas V52 turbine are used as references. The turbulence parameters are retrieved using the radial variances and a least-squares procedure. The findings from numerical simulations have been verified by the analysis of the field measurements.
Camilla Marie Nyborg, Andreas Fischer, Pierre-Elouan Réthoré, and Ju Feng
Wind Energ. Sci., 8, 255–276, https://doi.org/10.5194/wes-8-255-2023, https://doi.org/10.5194/wes-8-255-2023, 2023
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Our article presents a way of optimizing the wind farm operation by keeping the emitted noise level below a defined limit while maximizing the power output. This is done by switching between noise reducing operational modes. The method has been developed by using two different noise models, one more advanced than the other, to study the advantages of each model. Furthermore, the optimization method is applied to different wind farm cases.
Maarten Paul van der Laan, Mads Baungaard, and Mark Kelly
Wind Energ. Sci., 8, 247–254, https://doi.org/10.5194/wes-8-247-2023, https://doi.org/10.5194/wes-8-247-2023, 2023
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Understanding wind turbine wake recovery is important to mitigate energy losses in wind farms. Wake recovery is often assumed or explained to be dependent on the first-order derivative of velocity. In this work we show that wind turbine wakes recover mainly due to the second-order derivative of the velocity, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms and results of a high-fidelity numerical simulation are illustrated using a simple model.
Andrea N. Hahmann, Oscar García-Santiago, and Alfredo Peña
Wind Energ. Sci., 7, 2373–2391, https://doi.org/10.5194/wes-7-2373-2022, https://doi.org/10.5194/wes-7-2373-2022, 2022
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We explore the changes in wind energy resources in northern Europe using output from simulations from the Climate Model Intercomparison Project (CMIP6) under the high-emission scenario. Our results show that climate change does not particularly alter annual energy production in the North Sea but could affect the seasonal distribution of these resources, significantly reducing energy production during the summer from 2031 to 2050.
Mads Baungaard, Stefan Wallin, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 1975–2002, https://doi.org/10.5194/wes-7-1975-2022, https://doi.org/10.5194/wes-7-1975-2022, 2022
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Wind turbine wakes in the neutral atmospheric surface layer are simulated with Reynolds-averaged Navier–Stokes (RANS) using an explicit algebraic Reynolds stress model. Contrary to standard two-equation turbulence models, it can predict turbulence anisotropy and complex physical phenomena like secondary motions. For the cases considered, it improves Reynolds stress, turbulence intensity, and velocity deficit predictions, although a more top-hat-shaped profile is observed for the latter.
Tuhfe Göçmen, Filippo Campagnolo, Thomas Duc, Irene Eguinoa, Søren Juhl Andersen, Vlaho Petrović, Lejla Imširović, Robert Braunbehrens, Jaime Liew, Mads Baungaard, Maarten Paul van der Laan, Guowei Qian, Maria Aparicio-Sanchez, Rubén González-Lope, Vinit V. Dighe, Marcus Becker, Maarten J. van den Broek, Jan-Willem van Wingerden, Adam Stock, Matthew Cole, Renzo Ruisi, Ervin Bossanyi, Niklas Requate, Simon Strnad, Jonas Schmidt, Lukas Vollmer, Ishaan Sood, and Johan Meyers
Wind Energ. Sci., 7, 1791–1825, https://doi.org/10.5194/wes-7-1791-2022, https://doi.org/10.5194/wes-7-1791-2022, 2022
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The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of wind farm flow control benefits. Here we present the first part of the benchmark results for three blind tests with large-scale rotors and 11 participating models in total, via direct power comparisons at the turbines as well as the observed or estimated power gain at the wind farm level under wake steering control strategy.
Jana Fischereit, Kurt Schaldemose Hansen, Xiaoli Guo Larsén, Maarten Paul van der Laan, Pierre-Elouan Réthoré, and Juan Pablo Murcia Leon
Wind Energ. Sci., 7, 1069–1091, https://doi.org/10.5194/wes-7-1069-2022, https://doi.org/10.5194/wes-7-1069-2022, 2022
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Wind turbines extract kinetic energy from the flow to create electricity. This induces a wake of reduced wind speed downstream of a turbine and consequently downstream of a wind farm. Different types of numerical models have been developed to calculate this effect. In this study, we compared models of different complexity, together with measurements over two wind farms. We found that higher-fidelity models perform better and the considered rapid models cannot fully capture the wake effect.
Alessandro Sebastiani, Alfredo Peña, Niels Troldborg, and Alexander Meyer Forsting
Wind Energ. Sci., 7, 875–886, https://doi.org/10.5194/wes-7-875-2022, https://doi.org/10.5194/wes-7-875-2022, 2022
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The power performance of a wind turbine is often tested with the turbine standing in a row of several wind turbines, as it is assumed that the performance is not affected by the neighbouring turbines. We test this assumption with both simulations and measurements, and we show that the power performance can be either enhanced or lowered by the neighbouring wind turbines. Consequently, we also show how power performance testing might be biased when performed on a row of several wind turbines.
Wei Fu, Alfredo Peña, and Jakob Mann
Wind Energ. Sci., 7, 831–848, https://doi.org/10.5194/wes-7-831-2022, https://doi.org/10.5194/wes-7-831-2022, 2022
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Measuring the variability of the wind is essential to operate the wind turbines safely. Lidars of different configurations have been placed on the turbines’ nacelle to measure the inflow remotely. This work found that the multiple-beam lidar is the only one out of the three employed nacelle lidars that can give detailed information about the inflow variability. The other two commercial lidars, which have two and four beams, respectively, measure only the fluctuation in the along-wind direction.
Mads Baungaard, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 783–800, https://doi.org/10.5194/wes-7-783-2022, https://doi.org/10.5194/wes-7-783-2022, 2022
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Wind turbine wakes are dependent on the atmospheric conditions, and it is therefore important to be able to simulate in various different atmospheric conditions. This paper concerns the specific case of an unstable atmospheric surface layer, which is the lower part of the typical daytime atmospheric boundary layer. A simple flow model is suggested and tested for a range of single-wake scenarios, and it shows promising results for velocity deficit predictions.
Davide Conti, Nikolay Dimitrov, Alfredo Peña, and Thomas Herges
Wind Energ. Sci., 6, 1117–1142, https://doi.org/10.5194/wes-6-1117-2021, https://doi.org/10.5194/wes-6-1117-2021, 2021
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We carry out a probabilistic calibration of the Dynamic Wake Meandering (DWM) model using high-spatial- and high-temporal-resolution nacelle-based lidar measurements of the wake flow field. The experimental data were collected from the Scaled Wind Farm Technology (SWiFT) facility in Texas. The analysis includes the velocity deficit, wake-added turbulence, and wake meandering features under various inflow wind and atmospheric-stability conditions.
Cited articles
Agarap, A. F.: Deep Learning using Rectified Linear Units (ReLU), arXiv [preprint], https://doi.org/10.48550/arXiv.1803.08375, 2019. a
Akiba, T., Sano, S., Yanase, T., Ohta, T., and Koyama, M.: Optuna: A Next-generation Hyperparameter Optimization Framework, Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2623–2631, https://doi.org/10.1145/3292500.3330701, 2019. a
Anagnostopoulos, S. J., Bauer, J., Clare, M. C., and Piggott, M. D.: Accelerated wind farm yaw and layout optimisation with multi-fidelity deep transfer learning wake models, Renewable Energy, 218, 119293, https://doi.org/10.1016/J.RENENE.2023.119293, 2023. a
Bak, C., Zahle, F., Bitsche, R., Kim, T., Yde, A., Henriksen, L., Hansen, M., Blasques, J., Gaunaa, M., and Natarajan, A.: The DTU 10-MW Reference Wind Turbine, https://orbit.dtu.dk/en/publications/the-dtu-10-mw-reference-wind-turbine/ (last access: 3 August 2026), 2013. a
Bastankhah, M. and Porté-Agel, F.: A new analytical model for wind-turbine wakes, Renewable Energy, 70, 116–123, https://doi.org/10.1016/j.renene.2014.01.002, 2014. a, b
Bleeg, J.: A Graph Neural Network Surrogate Model for the Prediction of Turbine Interaction Loss, J. Phys. Conf. Ser., 1618, https://doi.org/10.1088/1742-6596/1618/6/062054, 2020. a
Bradbury, J., Frostig, R., Hawkins, P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., and Zhang, Q.: JAX: composable transformations of Python+NumPy programs, GitHub [code], http://github.com/jax-ml/jax (last access: 4 August 2026), 2018. a
Bronstein, M. M., Bruna, J., Cohen, T., and Veličković, P.: Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges, arxiv [preprint], https://doi.org/10.48550/arXiv.2104.13478, 2021. a
Cañadillas, B., Beckenbauer, M., Trujillo, J. J., Dörenkämper, M., Foreman, R., Neumann, T., and Lampert, A.: Offshore wind farm cluster wakes as observed by long-range-scanning wind lidar measurements and mesoscale modeling, Wind Energ. Sci., 7, 1241–1262, https://doi.org/10.5194/wes-7-1241-2022, 2022. a
Daenens, S., Verstraeten, T., Daems, P.-J., Nowé, A., and Helsen, J.: Spatio-temporal graph neural networks for power prediction in offshore wind farms using SCADA data, Wind Energ. Sci., 10, 1137–1152, https://doi.org/10.5194/wes-10-1137-2025, 2025. a
Djath, B., Schulz-Stellenfleth, J., and Cañadillas, B.: Impact of atmospheric stability on X-band and C-band synthetic aperture radar imagery of offshore windpark wakes, J. Renew. Sustain. Ener., 10, 17, https://doi.org/10.1063/1.5020437, 2018. a
DTU Wind and Energy Systems: PyWakeEllipSys v6.0 [code], https://topfarm.pages.windenergy.dtu.dk/cuttingedge/pywake/pywake_ellipsys, last access: 4 August 2026. a
Duthé, G., de Nolasco Santos, F., Abdallah, I., Réthore, P.-E., Weijtjens, W., Chatzi, E., and Devriendt, C.: Local flow and loads estimation on wake-affected wind turbines using graph neural networks and PyWake, J. Phys. Conf. Ser., 2505, 012014, https://doi.org/10.1088/1742-6596/2505/1/012014, 2023. a
Duthé, G., de N Santos, F., Abdallah, I., Weijtjens, W., Devriendt, C., and Chatzi, E.: Flexible multi-fidelity framework for load estimation of wind farms through graph neural networks and transfer learning, Data-Centric Engineering, 5, e29, https://doi.org/10.1017/dce.2024.35, 2024. a
Duthé, G., Abdallah, I., and Chatzi, E.: Graph Transformers for inverse physics: reconstructing flows around arbitrary 2D airfoils, arXiv [preprint], https://doi.org/10.48550/arXiv.2501.17081, 2025. a
Fey, M. and Lenssen, J. E.: Fast Graph Representation Learning with PyTorch Geometric, arXiv [preprint], https://doi.org/10.48550/arXiv.1903.02428, 2019. a
García-Santiago, O., Hahmann, A. N., Badger, J., and Peña, A.: Evaluation of wind farm parameterizations in the WRF model under different atmospheric stability conditions with high-resolution wake simulations, Wind Energ. Sci., 9, 963–979, https://doi.org/10.5194/wes-9-963-2024, 2024. a
Godwin, J., Keck, T., Battaglia, P., Bapst, V., Kipf, T., Li, Y., Stachenfeld, K., Veličković, P., and Sanchez-Gonzalez, A.: Jraph: A library for graph neural networks in jax, GitHub [code], http://github.com/deepmind/jraph (last access: 4 August 2026), 2020. a
Harrison-Atlas, D., Glaws, A., King, R. N., and Lantz, E.: Artificial intelligence-aided wind plant optimization for nationwide evaluation of land use and economic benefits of wake steering, Nature Energy, 9, 735–749, https://doi.org/10.1038/s41560-024-01516-8, 2024. a
Hasager, C. B., Vincent, P., Badger, J., Badger, M., Bella, A. D., Peña, A., Husson, R., and Volker, P. J.: Using Satellite SAR to Characterize the Wind Flow around Offshore Wind Farms, Energies, 8, 5413–5439, https://doi.org/10.3390/EN8065413, 2015. a
Hasanpoor, S., Romero, D. A., Moran, J. E., and Amon, C. H.: Physics-informed deep convolutional hierarchical encoder-decoder neural network for flow field prediction in wind farms, Energy and AI, 21, 100553, https://doi.org/10.1016/J.EGYAI.2025.100553, 2025. a
Heek, J., Levskaya, A., Oliver, A., Ritter, M., Rondepierre, B., Steiner, A., and van Zee, M.: Flax: A neural network library and ecosystem for JAX, GitHub [code], http://github.com/google/flax (last access: 4 August 2026), 2024. a
Hou, G., Zhang, F., Huang, C., and Huang, T.: Multivariate modeling on wake-affected wind farms by two-stage hybrid graph neural network, Applied Energy, 402, 127018, https://doi.org/10.1016/j.apenergy.2025.127018, 2026. a
Hu, E. J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., Wang, L., and Chen, W.: LoRA: Low-Rank Adaptation of Large Language Models, arXiv [preprint], https://doi.org/10.48550/arXiv.2106.09685, 2021. a, b
Hu, J., Shen, L., and Sun, G.: Squeeze-and-Excitation Networks, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 7132–7141, https://doi.org/10.1109/CVPR.2018.00745, 2018. a
Jensen, N. O.: A note on wind generator interaction – RISØ-M-2411, Tech. rep., Risø National Laboratories, https://orbit.dtu.dk/en/publications/a-note-on-wind-generator-interaction/ (last access: 4 August 2026), 1983. a
Joe, S. and Kuo, F. Y.: Constructing Sobol Sequences with Better Two-Dimensional Projections, SIAM J. Sci. Comput., 30, 2635–2654, https://doi.org/10.1137/070709359, 2008. a
Kingma, D. P. and Ba, J.: Adam: A Method for Stochastic Optimization, arXiv [preprint], https://doi.org/10.48550/arXiv.1412.6980, 2014. a
Li, R., Zhang, J., and Zhao, X.: Multi-fidelity modeling of wind farm wakes based on a novel super-fidelity network, Energ. Convers. Manage., 270, 116185, https://doi.org/10.1016/j.enconman.2022.116185, 2022a. a
Li, S., Zhang, M., and Piggott, M. D.: End-to-end Wind Turbine Wake Modelling with Deep Graph Representation Learning, Applied Energy, 339, https://doi.org/10.1016/j.apenergy.2023.120928, 2022b. a
Li, S., Robert, A., Faisal, A. A., and Piggott, M. D.: Learning to optimise wind farms with graph transformers, Applied Energy, 359, 122758, https://doi.org/10.1016/j.apenergy.2024.122758, 2024. a
Loshchilov, I. and Hutter, F.: Decoupled Weight Decay Regularization, arXiv [preprint], https://doi.org/10.48550/arXiv.1711.05101, 2019. a
Michelsen, J.: Basis3D - a Platform for Development of Multiblock PDE Solvers: β – release, vol. AFM 92-05, Technical University of Denmark, https://orbit.dtu.dk/en/publications/basis3d-a-platform-for-development-of-multiblock-pde-solvers-%CE%B2-re/ (last access: 4 August 2026), 1992. a
Misra, D.: Mish: A Self Regularized Non-Monotonic Activation Function, 31st British Machine Vision Conference, BMVC 2020, https://doi.org/10.5244/C.34.191, 2020. a
Nygaard, N. G. and Newcombe, A. C.: Wake behind an offshore wind farm observed with dual-Doppler radars, J. Phys. Conf. Ser., 1037, 072008, https://doi.org/10.1088/1742-6596/1037/7/072008, 2018. a
Nygaard, N. G., Steen, S. T., Poulsen, L., and Pedersen, J. G.: Modelling cluster wakes and wind farm blockage, J. Phys. Conf. Ser., 1618, 062072, https://doi.org/10.1088/1742-6596/1618/6/062072, 2020. a
Ødegaard Bentsen, L., Warakagoda, N. D., Stenbro, R., and Engelstad, P.: Wind Park Power Prediction: Attention-Based Graph Networks and Deep Learning to Capture Wake Losses, J. Phys. Conf. Ser., 2265, 022035, https://doi.org/10.1088/1742-6596/2265/2/022035, 2022. a
Oktay, O., Schlemper, J., Folgoc, L. L., Lee, M., Heinrich, M., Misawa, K., Mori, K., McDonagh, S., Hammerla, N. Y., Kainz, B., Glocker, B., and Rueckert, D.: Attention U-Net: Learning Where to Look for the Pancreas, arXiv [preprint], https://doi.org/10.48550/arXiv.1804.03999, 2018. a
Park, J. and Park, J.: Physics-induced graph neural network: An application to wind-farm power estimation, Energy, 187, 115883, https://doi.org/10.1016/j.energy.2019.115883, 2019. a
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library, in: Advances in Neural Information Processing Systems 32, edited by Wallach, H., Larochelle, H., Beygelzimer, A., d'Alché Buc, F., Fox, E., and Garnett, R., Curran Associates, Inc., 8024–8035, arXiv [preprint], https://doi.org/10.48550/arXiv.1912.01703, 2019. a
Pedersen, M. M., Forsting, A. M., Paul van der Laan, R. R., Romàn, L. A. A., Risco, J. C., Friis-Møller, M., Quick, J., Schøler, J. P., Rodrigues, R. V., Olsen, B. T., and Réthoré, P.-E.: PyWake 2.5.0: An open-source wind farm simulation tool, GitHub [code] https://gitlab.windenergy.dtu.dk/TOPFARM/PyWake (last access: 3 August 2026), 2023. a, b
Peña, A., Mirocha, J. D., and van der Laan, M. P.: Evaluation of the Fitch Wind-Farm Wake Parameterization with Large-Eddy Simulations of Wakes Using the Weather Research and Forecasting Model, Mon. Weather Rev., 150, 3051–3064, https://doi.org/10.1175/MWR-D-22-0118.1, 2022. a
Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., and Battaglia, P. W.: Learning Mesh-Based Simulation with Graph Networks, arXiv [preprint], https://doi.org/10.48550/arXiv.2010.03409, 2021. a
Platis, A., Siedersleben, S. K., Bange, J., Lampert, A., Bärfuss, K., Hankers, R., Cañadillas, B., Foreman, R., Schulz-Stellenfleth, J., Djath, B., Neumann, T., and Emeis, S.: First in situ evidence of wakes in the far field behind offshore wind farms, Scientific reports, 8, https://doi.org/10.1038/S41598-018-20389-Y, 2018. a
Porté-Agel, F., Bastankhah, M., and Shamsoddin, S.: Wind-Turbine and Wind-Farm Flows: A Review, Bound.-Lay. Meteorol., 174, 1–59, https://doi.org/10.1007/s10546-019-00473-0, 2020. a
Rasmussen, F. P. W., van der Laan, P., Peña, A., and Réthoré, P.-E.: Transfer Learning Approach for Improved Wind Farm Wake Prediction Using Multi-Fidelity Convolutional Neural Networks, in: Proceedings of the ASME 2026 45th International Conference on Ocean, Offshore and Arctic Engineering (OMAE2026), OMAE2026-181761, 2026. a, b, c, d, e, f
Ronneberger, O., Fischer, P., and Brox, T.: U-net: Convolutional networks for biomedical image segmentation, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 9351, 234–241, https://doi.org/10.1007/978-3-319-24574-4_28, 2015. a
Sanchez-Lengeling, B., Reif, E., Pearce, A., and Wiltschko, A.: A Gentle Introduction to Graph Neural Networks, Distill, 6, https://doi.org/10.23915/distill.00033, 2021. a
Schneemann, J., Rott, A., Dörenkämper, M., Steinfeld, G., and Kühn, M.: Cluster wakes impact on a far-distant offshore wind farm's power, Wind Energ. Sci., 5, 29–49, https://doi.org/10.5194/wes-5-29-2020, 2020. a
Sørensen, N.: General purpose flow solver applied to flow over hills, Ph.D. thesis, Risø National Laboratory, https://orbit.dtu.dk/en/publications/general-purpose-flow-solver-applied-to-flow-over-hills/ (last access: 3 August 2026), 1995. a
Sørensen, N. N., Bechmann, A., Johansen, J., Myllerup, L., Botha, P., Vinther, S., and Nielsen, B. S.: Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver, J. Phys. Conf. Ser., 75, 1–13, https://doi.org/10.1088/1742-6596/75/1/012053, 2007. a
Technical University of Denmark: Sophia HPC Cluster, DTU Sophia, https://doi.org/10.57940/FAFC-6M81, 2019. a, b, c
Thuerey, N., Weißenow, K., Prantl, L., and Hu, X.: Deep Learning Methods for Reynolds-Averaged Navier–Stokes Simulations of Airfoil Flows, AIAA, 58, 25–36, https://doi.org/10.2514/1.J058291, 2019. a
van der Laan, M. P., Sørensen, N. N., Réthoré, P. E., Mann, J., Kelly, M. C., and Troldborg, N.: The k-ε-fp model applied to double wind turbine wakes using different actuator disk force methods, Wind Energy, 18, 2223–2240, https://doi.org/10.1002/we.1816, 2015. a, b
van der Laan, M. P., García-Santiago, O., Kelly, M., Meyer Forsting, A., Dubreuil-Boisclair, C., Sponheim Seim, K., Imberger, M., Peña, A., Sørensen, N. N., and Réthoré, P.-E.: A new RANS-based wind farm parameterization and inflow model for wind farm cluster modeling, Wind Energ. Sci., 8, 819–848, https://doi.org/10.5194/wes-8-819-2023, 2023. a, b, c, d
van der Laan, M. P., Meyer Forsting, A., and Réthoré, P.-E.: A Computational Fluid Dynamics surrogate model for wind turbine interaction including atmospheric stability, Wind Energ. Sci. Discuss. [preprint], https://doi.org/10.5194/wes-2025-287, in review, 2026a. a
van der Laan, M. P., Schøler, J. P., Rasmussen, F. P. W., Réthoré, P.-E., and Peña, A.: RANS-AWF Random Cluster Layouts, Zenodo [data set], https://doi.org/10.5281/zenodo.20543178, 2026b. a
Wang, Q., Luo, K., Wu, C., Mu, Y., Tan, J., and Fan, J.: Diurnal impact of atmospheric stability on inter-farm wake and power generation efficiency at neighboring onshore wind farms in complex terrain, Energ. Convers. Manage., 267, 115897, https://doi.org/10.1016/J.ENCONMAN.2022.115897, 2022. a
Wang, Q., Luo, K., Wu, C., Tan, J., He, R., Ye, S., and Fan, J.: Inter-farm cluster interaction of the operational and planned offshore wind power base, J. Clean. Prod., 396, 136529, https://doi.org/10.1016/J.JCLEPRO.2023.136529, 2023. a
Wang, Q., Hu, J., Yang, S., Ti, Z., and Deng, X.: Knowledge-Fusion Graph Transformer network for wind farm assessment with sparse data, Renewable Energy, 256, 124654, https://doi.org/10.1016/j.renene.2025.124654, 2026. a
Zong, H. and Porté-Agel, F.: A momentum-conserving wake superposition method for wind farm power prediction, J. Fluid Mech., 889, A8, https://doi.org/10.1017/jfm.2020.77, 2020. a
Short summary
As offshore wind farms are built closer together, predicting how they affect each other becomes critical. We compared two AI approaches for this task, training both on cheap approximate data before refining them with expensive high-accuracy simulations. One predicts wake boundaries better, while the other estimates wind speeds more accurately, offering complementary tools for future wind farm design.
As offshore wind farms are built closer together, predicting how they affect each other becomes...
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