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REVIEW 2 major objections 1 minor 63 references

A transformer-based dual-attention neural operator predicts 3D wind fields over complex mountainous terrain rapidly with zero-shot real-site transfer.

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T0 review · grok-4.3

2026-06-29 20:37 UTC pith:LUIDHR4M

load-bearing objection The paper introduces a dual-attention transformer neural operator for 3D mountain wind fields with claimed zero-shot CFD-to-real transfer and sparse-data gains, but the transfer evidence rests on an unverified assumption that the synthetic data matches real flow statistics. the 2 major comments →

arxiv 2605.25679 v1 pith:LUIDHR4M submitted 2026-05-25 physics.flu-dyn

Transformer-based Neural Operators for 3D Wind Field Prediction over Complex Mountainous Terrain

Yujia Zhang , Jiaxi Qi , Ruiyan Chen , Yong Liu , Yuzhou Zhang , Lyulin Kuang , Rita Zhang , Shengze Cai This is my paper
classification physics.flu-dyn
keywords neural operatorswind field predictioncomplex terraintransformer attentionCFD simulationszero-shot transfersparse data
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a transformer-based framework to predict three-dimensional wind fields over irregular mountainous terrain. Traditional CFD simulations require expert mesh generation and long iterative runs, while earlier neural operators often fail to capture sharp velocity gradients from terrain. The dual-attention design, built into point-based and graph-based operator forms, trains on varied CFD cases to deliver fast steady-state predictions at competitive accuracy. It transfers directly to real locations without retraining and improves further when sparse observations are supplied as extra input.

Core claim

Trained on a large CFD-generated dataset spanning diverse terrain geometries and inflow conditions, the transformer-based dual-attention neural-operator framework enables rapid prediction of steady-state wind field while maintaining competitive accuracy. It also demonstrates robust zero-shot transfer to real-world mountainous sites across several diverse locations, outperforming existing neural operator baselines by 10% in relative error. Incorporating sparse observational data at 1% spatial coverage reduces prediction error by 16.89% relative to the corresponding model without sparse data input and by 32.75% relative to advanced neural operator baselines on unseen terrains.

What carries the argument

Transformer-based dual-attention mechanism instantiated in Patch-solver (point-based) and Patch-GTO (graph-based) neural operator architectures that map terrain geometry plus inflow conditions to 3D velocity fields.

Load-bearing premise

The CFD-generated dataset spanning diverse terrain geometries and inflow conditions is representative enough for the model to generalize to real-world mountainous sites without significant domain shift.

What would settle it

Collecting 3D wind measurements at multiple points over a new mountainous site absent from training or validation and comparing them quantitatively to the model's zero-shot output.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Steady-state wind field prediction becomes feasible in seconds rather than hours or days on high-performance clusters.
  • Zero-shot transfer allows the same trained model to apply across multiple real mountainous locations without site-specific retraining.
  • Adding sparse observational data at 1% spatial coverage further lowers error on terrains not seen during training.
  • The approach supplies a computational route for wind resource assessment and atmosphere-surface interaction studies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The dual-attention structure could be tested on time-dependent wind problems to move beyond steady-state cases.
  • Similar operator designs might address other fluid problems that involve sharp gradients over irregular boundaries.
  • Operational deployment would require checking sensitivity to the exact density and placement of the sparse observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The paper claims to introduce a transformer-based dual-attention neural-operator framework for 3D wind field prediction over complex mountainous terrain. It presents two instantiations: Patch-solver (point-based mesh-free) and Patch-GTO (graph-based). Trained on a large CFD-generated dataset spanning diverse terrain geometries and inflow conditions, the framework is said to enable rapid prediction of steady-state wind fields with competitive accuracy. It demonstrates robust zero-shot transfer to real-world mountainous sites across several diverse locations, outperforming existing neural operator baselines by 10% in relative error. Incorporating sparse observational data with 1% spatial coverage reduces prediction error by 16.89% relative to the model without sparse data and by 32.75% relative to advanced neural operator baselines on unseen terrains.

Significance. If the zero-shot transfer and performance claims hold after validation, this could be a significant contribution to accelerating 3D wind predictions for renewable energy and atmospheric modeling, offering a generalizable paradigm that integrates sparse data. The dual instantiations on mesh-free and graph-based architectures are a strength for broader applicability.

major comments (2)
  1. [Abstract] Abstract: The central claims of robust zero-shot transfer to real-world sites (outperforming baselines by 10% relative error) and the specific gains from 1% sparse data (16.89% and 32.75% reductions) are load-bearing. These hinge on the unverified assumption that the CFD training distribution produces flow statistics close enough to real mountainous sites; no quantitative checks (e.g., Kolmogorov-Smirnov tests on velocity histograms or separation bubble sizes) are mentioned, raising the risk that reported improvements are artifacts of domain shift rather than operator superiority.
  2. [Abstract] Abstract: The reported performance metrics lack any details on experimental setup, validation methods, number of real-world test sites, or potential biases in the CFD-to-real transfer. This absence directly undermines assessment of whether the data and methods support the generalization and accuracy claims.
minor comments (1)
  1. [Abstract] The abstract would benefit from explicitly defining the relative error metric (e.g., normalized L2 or pointwise) and listing the specific neural operator baselines used for the 10% and 32.75% comparisons.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for these constructive comments on the abstract. They correctly identify that the zero-shot transfer claims are central and would benefit from stronger supporting evidence and transparency. We respond point-by-point below and will revise the manuscript where the points can be addressed without misrepresentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claims of robust zero-shot transfer to real-world sites (outperforming baselines by 10% relative error) and the specific gains from 1% sparse data (16.89% and 32.75% reductions) are load-bearing. These hinge on the unverified assumption that the CFD training distribution produces flow statistics close enough to real mountainous sites; no quantitative checks (e.g., Kolmogorov-Smirnov tests on velocity histograms or separation bubble sizes) are mentioned, raising the risk that reported improvements are artifacts of domain shift rather than operator superiority.

    Authors: We agree that the absence of explicit distributional comparisons (such as Kolmogorov-Smirnov tests on velocity histograms or separation bubble statistics) leaves the zero-shot transfer claim open to the domain-shift concern raised. The current manuscript relies on empirical performance across the reported real-world sites rather than these statistical tests. In revision we will add a dedicated paragraph (or short subsection) performing such checks on the available real-world velocity data versus the CFD training distribution, provided the site measurements permit direct histogram comparison. If the data volume is insufficient for reliable KS testing we will instead report qualitative and quantitative overlap metrics that are feasible. revision: yes

  2. Referee: [Abstract] Abstract: The reported performance metrics lack any details on experimental setup, validation methods, number of real-world test sites, or potential biases in the CFD-to-real transfer. This absence directly undermines assessment of whether the data and methods support the generalization and accuracy claims.

    Authors: The abstract is intentionally concise and therefore omits the experimental details that appear in Sections 3 (dataset and training) and 4 (real-world zero-shot evaluation). The manuscript does specify “several diverse locations,” the 1 % sparse-data protocol, and the relative-error improvements, but does not enumerate the exact number of real-world sites or list potential biases in the abstract. We will revise the abstract to include one additional sentence summarizing the validation protocol, the number of real-world sites used, and a brief note on the main sources of CFD-to-real discrepancy (e.g., measurement uncertainty and unresolved sub-grid effects). Full experimental details will remain in the body text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is empirical and externally validated

full rationale

The paper trains a transformer-based neural operator on a CFD-generated dataset of synthetic terrains and inflows, then reports empirical performance metrics (relative error reductions, zero-shot transfer to real sites, gains from sparse data) against external baselines and real-world test locations. No equations or claims reduce by construction to fitted inputs, self-definitions, or self-citation chains; the central results are statistical outcomes from held-out testing rather than algebraic identities or renamed fits. The domain-shift assumption is a validity concern but does not create circularity in the reported derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities used in the work.

pith-pipeline@v0.9.1-grok · 5814 in / 1145 out tokens · 32767 ms · 2026-06-29T20:37:38.336655+00:00 · methodology

0 comments
read the original abstract

Accurate prediction of three-dimensional (3D) wind fields over complex mountainous terrain is essential for renewable energy deployment and regional weather modeling. Traditional computational fluid dynamics (CFD) simulations face two fundamental bottlenecks: expert-intensive mesh generation around irregular topography, and iterative solvers that require hours to days even on high-performance clusters. Recent neural operator approaches accelerate inference, but typically fail to resolve the sharp, localized velocity gradients induced by complex terrain features. Here, we present a transformer-based dual-attention neural-operator framework for 3D wind field prediction over complex mountainous terrain, and validate its effectiveness through two instantiations on representative point-based (mesh-free) and graph-based neural-operator architectures, namely Patch-solver and Patch-GTO. Trained on a large CFD-generated dataset spanning diverse terrain geometries and inflow conditions, the framework enables rapid prediction of steady-state wind field while maintaining competitive accuracy. It also demonstrates robust zero-shot transfer to real-world mountainous sites across several diverse locations, outperforming existing neural operator baselines by 10% in relative error. We further verify that incorporating sparse observational data (1% spatial coverage) reduces prediction error by 16.89% relative to the corresponding model without sparse data input and by 32.75% relative to advanced neural operator baselines on unseen terrains. This framework establishes a generalizable computational paradigm across domains, promising to be a real-time tool for wind resource assessment over complex mountainous terrain and related atmosphere-surface interaction studies.

Figures

Figures reproduced from arXiv: 2605.25679 by Jiaxi Qi, Lyulin Kuang, Rita Zhang, Ruiyan Chen, Shengze Cai, Yong Liu, Yujia Zhang, Yuzhou Zhang.

Figure 1
Figure 1. Figure 1: Illustration of the wind field dataset construction and modeling workflow. a Practical application of the proposed method, which replaces expensive PDE solvers with a mesh-agnostic neural oper￾ator to produce 3D wind velocity fields for wind turbine siting and UAS routing. b The entire computational domain consists of three parts: the inner fine mesh region, the transition region, and the outer coarse mesh… view at source ↗
Figure 2
Figure 2. Figure 2: General wind-field prediction results across test dataset. a Kerneldensity distributions of four terrain descriptorsSlope, Roughness, Rugosity, and TRIcomputed over the dataset (see Appendix C). For each descriptor, we plot the distribution of per-case mean (blue), median (orange), and standard deviation (green), delineating the range of terrain conditions represented in training and testing. b Dataset-ave… view at source ↗
Figure 3
Figure 3. Figure 3: Altituderesolved qualitative comparison and error analysis on a relatively flat case. a Schematic diagram of mountain terrain and wind direction. b Groundtruth windvelocity component at primary direction (v) sampled on multiple (10m, 150m and 300m) altitude planes. c Prediction results (c1) and absolute error (c2) of wind-velocity component v obtained by Transolver at the corresponding altitude planes in 3… view at source ↗
Figure 4
Figure 4. Figure 4: Altituderesolved qualitative comparison and error analysis on a relatively complex case. a Schematic diagram of mountain terrain and wind direction. b Groundtruth windvelocity component at primary direction (v) sampled on multiple (10m, 150m and 300m) altitude planes. c Prediction results (c1) and absolute error (c2) of wind-velocity component v obtained by Transolver at the corresponding altitude planes i… view at source ↗
Figure 5
Figure 5. Figure 5: Zeroshot inference on four unseen mountainous terrains. a Kerneldensity distribution of surface roughness in the training dataset; vertical dashed markers indicate the per-site median roughness for the four selected locations (Chatou-1, Chatou-2, Daguping, Hengdong). b Digital elevation models for the four test sites. c Spatial roughness maps for four selected mountainous terrains. d Boxandwhisker summarie… view at source ↗
Figure 6
Figure 6. Figure 6: Two types of application scenarios. a Sparse-input results on test and zero-shot datasets. a1 The spatial distribution of sparse sensors above the terrain with a sparse input ratio of 0.1% in two typical cases. a2 Relative L2 error (%) of wind speed magnitude Umag with various sparse input ratios (M/N = 0%, 0.1%, 1%) for Transolver (dark gray), Transolver with Gaussian-process interpolation (light gray) an… view at source ↗
Figure 7
Figure 7. Figure 7: Interpretability analysis of dualattention proposed in this paper. a1a3 Schematic diagram of mountain terrain for three test scenes. b1b3 Normalized local entropy Hlocal at 300 m height. c1c3 Normalized global entropy Hglobal at 300 m height. d1d3 The variation of local and global entropies (mean and standard deviation) with height. In subplots d1d3, solid lines denote the mean values, and the shaded band … view at source ↗
Figure 8
Figure 8. Figure 8: Architecture of proposed Patch-solver. a The basic architecture of the proposed Patch-solver model. b Description of the Point Cloud Patcher module. c Description of the physics-Dual Attention. 4.2 Point Cloud Patcher module 807 The PCPM organizes the input points into local patches for efficient attention computa- 808 tion. Importantly, this operation does not resample the irregular point cloud onto a reg… view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

63 extracted references · 11 canonical work pages · 3 internal anchors

  1. [1]

    X. Xu, Q. Cao, R. Deng, Z. Guo, Y. Chen, J. Yan, A cross-dataset benchmark for neural 903 network-based wind power forecasting, Renewable Energy (2025) 123463. 904

    2025

  2. [2]

    Q. Wang, K. Luo, C. Wu, Z. Zhu, J. Fan, Mesoscale simulations of a real onshore wind 905 power base in complex terrain: Wind farm wake behavior and power production, Energy 906 241 (2022) 122873. 907

    2022

  3. [3]

    H. Gao, G. Hu, D. Zhang, W. Jiang, H. Ren, W. Chen, Prediction of wind fields 908 in mountains at multiple elevations using deep learning models, Applied Energy 353 909 (2024) 122099. 910

    2024

  4. [4]

    Achermann, T

    F. Achermann, T. Stastny, B. Danciu, A. Kolobov, J. J. Chung, R. Siegwart, 911 N. Lawrance, Windseer: real-time volumetric wind prediction over complex terrain 912 aboard a small uncrewed aerial vehicle, Nature Communications 15 (1) (2024) 3507. 913

    2024

  5. [5]

    Y. Chen, D. Wang, D. Feng, G. Tian, V. Gupta, R. Cao, M. Wan, S. Chen, Three- 914 dimensional spatiotemporal wind field reconstruction based on lidar and multi-scale 915 pinn, Applied Energy 377 (2025) 124577. 916

    2025

  6. [6]

    X. Zhu, R. Liu, Y. Chen, X. Gao, Y. Wang, Z. Xu, Wind speed behaviors feather 917 analysis and its utilization on wind speed prediction using 3d-cnn, Energy 236 (2021) 918 121523. 919

    2021

  7. [7]

    Y. Yang, S. Fan, Z. Liu, Z. Yu, Wd-sgformer: high-precision wind power forecasting via 920 dual-attention dynamic spatio-temporal learning, Energy (2025) 138538. 921

    2025

  8. [8]

    M. Yang, Y. Guo, F. Fan, Ultra-short-term prediction of wind farm cluster power based 922 on embedded graph structure learning with spatiotemporal information gain, IEEE 923 Transactions on Sustainable Energy (2024). 924 33

    2024

  9. [9]

    H. Ren, S. Laima, W.-L. Chen, B. Zhang, A. Guo, H. Li, Numerical simulation and925 prediction of spatial wind field under complex terrain, Journal of Wind Engineering926 and Industrial Aerodynamics 180 (2018) 49–65.927

    2018

  10. [10]

    L.-S. An, N. Alinejad, S. Kim, S. Jung, Experimental study on wind characteristics928 and prediction of mean wind profile over complex heterogeneous terrain, Building and929 Environment 243 (2023) 110719.930

    2023

  11. [11]

    Z. Ti, X. W. Deng, M. Zhang, Artificial neural networks based wake model for power931 prediction of wind farm, Renewable energy 172 (2021) 618–631.932

    2021

  12. [12]

    Huang, S

    M. Huang, S. Liao, W. Lou, W. Lin, A. Kareem, Multi-scale simulation of typhoon933 wind field at building scale utilizing mesoscale model with nested large eddy simulation,934 Journal of Wind Engineering and Industrial Aerodynamics 249 (2024) 105733.935

    2024

  13. [13]

    Kim, H.-J

    J. Kim, H.-J. Shin, K. Lee, J. Hong, Enhancement of ann-based wind power forecasting936 by modification of surface roughness parameterization over complex terrain, Journal of937 Environmental Management 362 (2024) 121246.938

    2024

  14. [14]

    C. Ge, J. Yan, W. Song, H. Zhang, H. Wang, Y. Li, Y. Liu, Middle-term wind power939 forecasting method based on long-span nwp and microscale terrain fusion correction,940 Renewable Energy 240 (2025) 122123.941

    2025

  15. [15]

    Mardani, N

    M. Mardani, N. Brenowitz, Y. Cohen, J. Pathak, C.-Y. Chen, C.-C. Liu, A. Vahdat,942 M. A. Nabian, T. Ge, A. Subramaniam, K. Kashinath, J. Kautz, M. Pritchard, Residual943 corrective diffusion modeling for km-scale atmospheric downscaling, Communications944 Earth & Environment 6 (1) (2025) 124.945

    2025

  16. [16]

    K. Bi, L. Xie, H. Zhang, X. Chen, X. Gu, Q. Tian, Accurate medium-range global946 weather forecasting with 3d neural networks, Nature 619 (7970) (2023) 533–538.947

    2023

  17. [17]

    L. Chen, X. Zhong, F. Zhang, Y. Cheng, Y. Xu, Y. Qi, H. Li, Fuxi: A cascade ma-948 chine learning forecasting system for 15-day global weather forecast, npj climate and949 atmospheric science 6 (1) (2023) 190.950

    2023

  18. [18]

    Z. Li, N. B. Kovachki, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, A. Anandku-951 mar, et al., Fourier neural operator for parametric partial differential equations, in:952 International Conference on Learning Representations, 2020.953

    2020

  19. [19]

    L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via954 deeponet based on the universal approximation theorem of operators, Nature machine955 intelligence 3 (3) (2021) 218–229.956

    2021

  20. [20]

    W. Peng, S. Qin, S. Yang, J. Wang, X. Liu, L. L. Wang, Fourier neural operator for957 real-time simulation of 3d dynamic urban microclimate, Building and Environment 248958 (2024) 111063.959 34

    2024

  21. [21]

    H. Gao, W. Qian, J. Dong, J. Liu, Rapid prediction of indoor airflow field using operator 960 neural network with small dataset, Building and Environment 251 (2024) 111175. 961

    2024

  22. [22]

    B. Li, H. Wang, S. Feng, X. Yang, Y. Lin, Solving seismic wave equations on variable 962 velocity models with fourier neural operator, IEEE Transactions on Geoscience and 963 Remote Sensing 61 (2023) 1–18. 964

    2023

  23. [23]

    J. He, S. Koric, D. Abueidda, A. Najafi, I. Jasiuk, Geom-deeponet: A point-cloud-based 965 deep operator network for field predictions on 3d parameterized geometries, Computer 966 Methods in Applied Mechanics and Engineering 429 (2024) 117130. 967

    2024

  24. [24]

    Z. Li, N. Kovachki, C. Choy, B. Li, J. Kossaifi, S. Otta, M. A. Nabian, M. Stadler, 968 C. Hundt, K. Azizzadenesheli, et al., Geometry-informed neural operator for large-scale 969 3d pdes, Advances in Neural Information Processing Systems 36 (2023) 35836–35854. 970

    2023

  25. [25]

    Z. Hao, Z. Wang, H. Su, C. Ying, Y. Dong, S. Liu, Z. Cheng, J. Song, J. Zhu, Gnot: A 971 general neural operator transformer for operator learning, in: International Conference 972 on Machine Learning, PMLR, 2023, pp. 12556–12569. 973

    2023

  26. [26]

    H. Wu, H. Luo, H. Wang, J. Wang, M. Long, Transolver: A fast transformer solver for 974 pdes on general geometries, arXiv preprint arXiv:2402.02366 (2024). 975

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  27. [27]

    P. Liu, P. Wang, X. Ren, H. Yuan, Z. Hao, C. Xu, S. Cai, D. Ni, Aerogto: An efficient 976 graph-transformer operator for learning large-scale aerodynamics of 3d vehicle geome- 977 tries, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 39, 2025, 978 pp. 18924–18932. 979

    2025

  28. [28]

    Q. Wang, C. Wang, M. Zhang, J. Sun, P. Yang, S. Tang, S. Xiang, Mno: Multiscale neu- 980 ral operator for computational fluid dynamics with 3d point cloud data, arXiv preprint 981 arXiv:2510.16071 (2025). 982

    work page arXiv 2025

  29. [29]

    S. Wen, A. Kumbhat, L. Lingsch, S. Mousavi, Y. Zhao, P. Chandrashekar, S. Mishra, 983 Geometry aware operator transformer as an efficient and accurate neural surrogate 984 for pdes on arbitrary domains, in: The Thirty-ninth Annual Conference on Neural 985 Information Processing Systems. 986

  30. [30]

    Liu-Schiaffini, J

    M. Liu-Schiaffini, J. Berner, B. Bonev, T. Kurth, K. Azizzadenesheli, A. Anandku- 987 mar, Neural operators with localized integral and differential kernels, in: International 988 Conference on Machine Learning, PMLR, 2024, pp. 32576–32594. 989

    2024

  31. [31]

    C. Zeng, Y. Zhang, J. Zhou, Y. Wang, Z. Wang, Y. Liu, L. Wu, D. Z. Huang, Point cloud 990 neural operator for parametric pdes on complex and variable geometries, Computer 991 Methods in Applied Mechanics and Engineering 443 (2025) 118022. 992 35

    2025

  32. [32]

    Elrefaie, A

    M. Elrefaie, A. Dai, F. Ahmed, Drivaernet: A parametric car dataset for data-driven993 aerodynamic design and graph-based drag prediction, in: International Design Engineer-994 ing Technical Conferences and Computers and Information in Engineering Conference,995 Vol. 88360, American Society of Mechanical Engineers, 2024, p. V03AT03A019.996

    2024

  33. [33]

    Dri- vAerML: High-fidelity computational fluid dynamics dataset for road-car external aerodynamics

    N. Ashton, C. Mockett, M. Fuchs, L. Fliessbach, H. Hetmann, T. Knacke, N. Schonwald,997 V. Skaperdas, G. Fotiadis, A. Walle, et al., Drivaerml: High-fidelity computational fluid998 dynamics dataset for road-car external aerodynamics, arXiv preprint arXiv:2408.11969999 (2024).1000

    work page arXiv 2024

  34. [34]

    Bonnet, J

    F. Bonnet, J. Mazari, P. Cinnella, P. Gallinari, Airfrans: High fidelity computational1001 fluid dynamics dataset for approximating reynolds-averaged navier–stokes solutions,1002 Advances in Neural Information Processing Systems 35 (2022) 23463–23478.1003

    work page arXiv 2022

  35. [35]

    Nowak, J

    D. Nowak, J. Werner, Q. Parsons, T. Johnson, A. Mark, F. Edelvik, Optimisation1004 of city structures with respect to high wind speeds using u-net models, Engineering1005 Applications of Artificial Intelligence 135 (2024) 108812.1006

    work page arXiv 2024

  36. [36]

    A. M. Campbell, S. C. Warder, B. Bhaskaran, M. D. Piggott, Domain-informed cnn1007 architectures for downscaling regional wind forecasts, Energy and AI 20 (2025) 100485.1008

    work page arXiv 2025

  37. [37]

    Richards, R

    P. Richards, R. Hoxey, Appropriate boundary conditions for computational wind engi-1009 neering models using the k- turbulence model, Journal of wind engineering and industrial1010 aerodynamics 46 (1993) 145–153.1011

    1993

  38. [38]

    T. G. Farr, P. A. Rosen, E. Caro, R. Crippen, R. Duren, S. Hensley, M. Kobrick,1012 M. Paller, E. Rodriguez, L. Roth, et al., The shuttle radar topography mission, Reviews1013 of geophysics 45 (2) (2007).1014

    2007

  39. [39]

    Veers, K

    P. Veers, K. Dykes, E. Lantz, S. Barth, C. L. Bottasso, O. Carlson, A. Clifton, J. Green,1015 P. Green, H. Holttinen, et al., Grand challenges in the science of wind energy, Science1016 366 (6464) (2019) eaau2027.1017

    work page arXiv 2019

  40. [40]

    J. Liew, A. M. Urbán, S. J. Andersen, Analytical model for the power–yaw sensitivity1018 of wind turbines operating in full wake, Wind Energy Science 5 (1) (2020) 427–437.1019

    2020

  41. [41]

    H. Gao, J. Liu, P. Lin, G. Hu, L. Patruno, Y. Xiao, K. Tse, K. Kwok, An optimal1020 sensor placement scheme for wind flow and pressure field monitoring, Building and1021 Environment 244 (2023) 110803.1022

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  42. [42]

    H. Gao, G. Hu, D. Zhang, W. Jiang, K. Tse, K. Kwok, A. Kareem, Urban wind field1023 prediction based on sparse sensors and physics-informed graph-assisted auto-encoder,1024 Computer-Aided Civil and Infrastructure Engineering 39 (10) (2024) 1409–1430.1025 36

    work page arXiv 2024

  43. [43]

    J. E. Santos, Z. R. Fox, A. Mohan, D. OMalley, H. Viswanathan, N. Lubbers, Develop- 1026 ment of the senseiver for efficient field reconstruction from sparse observations, Nature 1027 Machine Intelligence 5 (11) (2023) 1317–1325. 1028

    2023

  44. [44]

    Castorrini, S

    A. Castorrini, S. Gentile, E. Geraldi, A. Bonfiglioli, Increasing spatial resolution of wind 1029 resource prediction using nwp and rans simulation, Journal of Wind Engineering and 1030 Industrial Aerodynamics 210 (2021) 104499. 1031

    2021

  45. [45]

    Cheng, B

    X. Cheng, B. Yan, X. Zhou, Q. Yang, G. Huang, Y. Su, W. Yang, Y. Jiang, Wind 1032 resource assessment at mountainous wind farm: Fusion of rans and vertical multi-point 1033 on-site measured wind field data, Applied Energy 363 (2024) 123116. 1034

    2024

  46. [46]

    Y. Chen, R. Chen, H. Pan, T. Jiang, Numerical simulation of flow over complex terrain 1035 based on modified k-l turbulence model, Acta Energiae Solaris Sinica 45 (7) (2024) 1036 648–655. 1037

    2024

  47. [47]

    J. Berg, J. Mann, A. Bechmann, M. Courtney, H. E. Jørgensen, The bolund experiment, 1038 part i: flow over a steep, three-dimensional hill, Boundary-layer meteorology 141 (2) 1039 (2011) 219–243. 1040

    2011

  48. [48]

    Bechmann, N

    A. Bechmann, N. N. Sørensen, J. Berg, J. Mann, P.-E. Réthoré, The bolund experiment, 1041 part ii: blind comparison of microscale flow models, Boundary-layer meteorology 141 (2) 1042 (2011) 245–271. 1043

    2011

  49. [49]

    Dhunny, M

    A. Dhunny, M. Lollchund, S. Rughooputh, Wind energy evaluation for a highly complex 1044 terrain using computational fluid dynamics (cfd), Renewable Energy 101 (2017) 1–9. 1045

    2017

  50. [50]

    G. L. Mellor, T. Yamada, Development of a turbulence closure model for geophysical 1046 fluid problems, Reviews of Geophysics 20 (4) (1982) 851–875. 1047

    1982

  51. [51]

    B. K. Horn, Hill shading and the reflectance map, Proceedings of the IEEE 69 (1) (2005) 1048 14–47. 1049

    2005

  52. [52]

    Dartnell, Applying remote sensing techniques to map seafloor geology/habitat rela- 1050 tionships, Ph.D

    P. Dartnell, Applying remote sensing techniques to map seafloor geology/habitat rela- 1050 tionships, Ph.D. thesis, San Francisco State University (2000). 1051

    2000

  53. [53]

    J. S. Jenness, Calculating landscape surface area from digital elevation models, Wildlife 1052 Society Bulletin 32 (3) (2004) 829–839. 1053

    2004

  54. [54]

    S. J. Riley, S. D. DeGloria, R. Elliot, Index that quantifies topographic heterogeneity, 1054 intermountain Journal of sciences 5 (1-4) (1999) 23–27. 1055

    1999

  55. [55]

    Ronneberger, P

    O. Ronneberger, P. Fischer, T. Brox, U-net: Convolutional networks for biomedical 1056 image segmentation, in: International Conference on Medical image computing and 1057 computer-assisted intervention, Springer, 2015, pp. 234–241. 1058 37

    2015

  56. [56]

    An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

    A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner,1059 M. Dehghani, M. Minderer, G. Heigold, S. Gelly, et al., An image is worth 16x16 words:1060 Transformers for image recognition at scale, arXiv preprint arXiv:2010.11929 (2020).1061

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  57. [57]

    Anandkumar, K

    A. Anandkumar, K. Azizzadenesheli, K. Bhattacharya, N. Kovachki, Z. Li, B. Liu,1062 A. Stuart, Neural operator: Graph kernel network for partial differential equations, in:1063 ICLR 2020 workshop on integration of deep neural models and differential equations,1064 2020.1065

    work page arXiv 2020

  58. [58]

    Z. Li, D. Z. Huang, B. Liu, A. Anandkumar, Fourier neural operator with learned1066 deformations for pdes on general geometries, Journal of Machine Learning Research1067 24 (388) (2023) 1–26.1068 38 Appendices 1069 A Numerical simulation of flow over complex terrain 1070 This study uses a modified k-l turbulence model [ 46] specifically adapted for large-sca...

    2023

  59. [59]

    Transolver [26]: a Transformer-based universal PDE solver with global physics at- 1245 tention mechanism; 1246

  60. [60]

    AeroGTO [27]: a graph Transformer operator specifically designed for aerodynamic 1247 flow predictions; 1248

  61. [61]

    GINO [24]: a geometry-informed neural operator that first maps irregular geometries 1249 into a latent regular representation via GNO [ 57] layers and then applies an FNO 1250 backbone for operator learning; 1251

  62. [62]

    GNOT [25]: a graph neural operator that leverages Transformer-based message ag- 1252 gregation for PDE solving; 1253

  63. [63]

    Geo-FNO [58]: a geometry-aware neural operator that incorporates geometry through 1254 coordinate-aware inputs and applies an FNO backbone on a regular reference grid. 1255 It is important to note that our Patch-solver and Patch-GTO are built upon the core 1256 architectures of Transolver and AeroGTO, respectively, by incorporating our proposed dual- 1257...