the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Oct 2025
The Deep Wind Method: Physics-Informed Wind Field Reconstruction with Mass Consistency
Abstract. We present the Deep Wind methodology, a physics-informed neural network (PINN) formulation for reconstructing three-dimensional wind fields from incomplete and noisy data. The approach embeds mass conservation and boundary conditions directly into the loss function, enabling physically consistent and stable reconstructions without mesh-based discretization. A series of synthetic benchmarks and real observations from Super Typhoon Kong-Rey (2024) demonstrate the robustness of the method compared to classical variational approaches. We show that Deep Wind consistently maintains stability and accuracy under sparse, irregular, or noisy observations. Overall, the results suggest that physics-informed deep learning is a promising framework for wind field recovery and data assimilation, particularly in meteorology and wind energy.
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RC1: 'Comment on wes-2025-160', Anonymous Referee #1, 02 Nov 2025
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2025-160/wes-2025-160-RC1-supplement.pdfCitation: https://doi.org/
10.5194/wes-2025-160-RC1 -
RC2: 'Comment on wes-2025-160', Anonymous Referee #2, 12 Nov 2025
The manuscript presents a physics-informed neural network (PINN) formulation for reconstructing three-dimensional wind fields from incomplete and noisy data under physical constraints such as the incompressibility constraint. The flow cases considered are two very simple analytical fields and real observations from Super Typhoon Kong-Rey. In my opinions, the paper has several flaws.
The first is that the only comparison of the proposed method with literature is with the paper of Sasaki, dating back to 1958, while a large body of recent literature on flow reconstruction and data assimilation on fluid flows has been completely skipped. A more meaningful comparison can be done with recent works such as, for instance: Mons et al. "Reconstruction of unsteady viscous flows using data assimilation schemes " Journal of Computational Physics (2016) and other successive papers from this group, Gao et al "Data-assimilated computational fluid dynamics modeling of convection-diffusion-reaction problems", J. of Computational Science (2017), Callaham et al. "Robust flow reconstruction from limited measurements via sparse representation" Physical Review Fluids(2019), Quattromini et al. "Mean flow data assimilation using physics-constrained graph neural networks" data-centric engineering (2025). The present paper completely skips this whole body of literature, so that it is not possible to establish whether the proposed algorithm is in fact a novelty and has an interest, or if it is not.
The second drawback is that the claims made in the abstract are not sustained by the remainder of the manuscript. The abstract states that the proposed method reconstructs " three-dimensional wind fields from incomplete and noisy data", which may include reconstruction of flows fields from experimental measures by discrete sensors, incomplete or impainted flow fields. However, the paper presents only cases in which the first and second components of velocity are fully available, and only the third component of the velocity is reconstructed. The two first cases can be solved even analytically imposing the divergence-free and boundary conditions to the first two components of velocity, so that I am not really getting the interest of using them as reference for a physics-informed neural network . The third case might have been interesting if the proposed algorithm was shown able to reconstruct also the first two components of velocity in some grid points. However, also in this case, having fully available the two first components of velocity makes this application very naive. If the authors consider resubmitting the paper, I will suggest to extend the validation to more interesting flow cases, in which the flow field is known only in a portion of grid points.
The third, and maybe most important drawback, is that the paper does not discuss at all how the training is made, in particular which training set and which validation set are used, and how the performance of the method change with these parameters. It is not shown how the loss decrease with the epochs, so that it is not possible to conclude that the training is correctly converging. Also, the error is measured only as MSE, not allowing to establish how the error changes in space in the reconstruction. All in all, in may opinion the paper lacks too many technical details for being considered for publication in this journal, and I doubt that it might be of interest of the wind energy community.
Citation: https://doi.org/10.5194/wes-2025-160-RC2
Status: closed
-
RC1: 'Comment on wes-2025-160', Anonymous Referee #1, 02 Nov 2025
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2025-160/wes-2025-160-RC1-supplement.pdf
-
RC2: 'Comment on wes-2025-160', Anonymous Referee #2, 12 Nov 2025
The manuscript presents a physics-informed neural network (PINN) formulation for reconstructing three-dimensional wind fields from incomplete and noisy data under physical constraints such as the incompressibility constraint. The flow cases considered are two very simple analytical fields and real observations from Super Typhoon Kong-Rey. In my opinions, the paper has several flaws.
The first is that the only comparison of the proposed method with literature is with the paper of Sasaki, dating back to 1958, while a large body of recent literature on flow reconstruction and data assimilation on fluid flows has been completely skipped. A more meaningful comparison can be done with recent works such as, for instance: Mons et al. "Reconstruction of unsteady viscous flows using data assimilation schemes " Journal of Computational Physics (2016) and other successive papers from this group, Gao et al "Data-assimilated computational fluid dynamics modeling of convection-diffusion-reaction problems", J. of Computational Science (2017), Callaham et al. "Robust flow reconstruction from limited measurements via sparse representation" Physical Review Fluids(2019), Quattromini et al. "Mean flow data assimilation using physics-constrained graph neural networks" data-centric engineering (2025). The present paper completely skips this whole body of literature, so that it is not possible to establish whether the proposed algorithm is in fact a novelty and has an interest, or if it is not.
The second drawback is that the claims made in the abstract are not sustained by the remainder of the manuscript. The abstract states that the proposed method reconstructs " three-dimensional wind fields from incomplete and noisy data", which may include reconstruction of flows fields from experimental measures by discrete sensors, incomplete or impainted flow fields. However, the paper presents only cases in which the first and second components of velocity are fully available, and only the third component of the velocity is reconstructed. The two first cases can be solved even analytically imposing the divergence-free and boundary conditions to the first two components of velocity, so that I am not really getting the interest of using them as reference for a physics-informed neural network . The third case might have been interesting if the proposed algorithm was shown able to reconstruct also the first two components of velocity in some grid points. However, also in this case, having fully available the two first components of velocity makes this application very naive. If the authors consider resubmitting the paper, I will suggest to extend the validation to more interesting flow cases, in which the flow field is known only in a portion of grid points.
The third, and maybe most important drawback, is that the paper does not discuss at all how the training is made, in particular which training set and which validation set are used, and how the performance of the method change with these parameters. It is not shown how the loss decrease with the epochs, so that it is not possible to conclude that the training is correctly converging. Also, the error is measured only as MSE, not allowing to establish how the error changes in space in the reconstruction. All in all, in may opinion the paper lacks too many technical details for being considered for publication in this journal, and I doubt that it might be of interest of the wind energy community.
Citation: https://doi.org/10.5194/wes-2025-160-RC2
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