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GeoWind2Plan: Mission-Time 3D Urban Wind Prediction for Energy-Efficient UAV Planning

Shaoxiang Qin, Yucheng Zhao, Fuyuan Lyu, Di Zhou, Jiachen Yao, Xue Liu, Anima Anandkumar, Liangzhu Leon Wang, Xiongye Xiao

arXiv:2609.36056v1cs.AIcs.RO

TL;DR

Urban buildings reshape wind into local 3D flows that affect UAV energy, while CFD is too slow and tied to fixed inflow conditions for mission-time planning. GeoWind2Plan predicts corridor-localized wind from geometry and background wind, then optimizes a feasible 3D path and speed profile. Under CFD evaluation, it reduces energy relative to wind-agnostic planning across tailwind, headwind, and crosswind missions.

  • Problem

    Building-resolved urban wind is rarely available at planning time, while CFD is costly and must be rerun when inflow conditions change.

    Source: §1 · pp. 1–2

  • Method

    GeoWind2Plan rotates building geometry into a reference-wind frame, predicts mission-relevant wind patches, and uses the resulting local field to optimize UAV path and speed.

    Source: §1 · p. 2, §2.2 · p. 4

  • Results

    Averaged over four blocks, Ours reduces energy over wind-agnostic planning by 6.9%, 12.7%, and 4.5% in tailwind, headwind, and crosswind missions.

    Source: §3.2 · p. 8

  • Takeaways & Limitations

    Across diverse geometries, wind speeds, and wind-angle regimes, decision-useful corridor wind prediction brings urban wind-aware UAV planning within mission-time reach.

    Source: §4 · p. 9

    The energy model uses time-averaged wind and quasi-steady rotor power, omitting gusts, short-time turbulence, controller transients, and vehicle-specific attitude dynamics.

    Source: §2.3 · p. 6

Abstract

from arXiv · show

In urban low-altitude flight, buildings reshape ambient wind into spatially varying 3D flow, making unmanned aerial vehicle (UAV) energy depend on local wind exposure as well as path length. However, building-resolved wind information is rarely available when a mission must be planned. Computational fluid dynamics (CFD) can produce high-fidelity urban flow fields, but each simulation is tied to a fixed inflow boundary condition and can take hours to days, which is incompatible with urban UAV missions that typically last minutes to tens of minutes. We present GeoWind2Plan, a geometry-to-wind-to-planning framework for mission-time 3D urban wind prediction and energy-efficient UAV planning. Given only a background wind vector, 3D building geometry, and a start-goal pair, GeoWind2Plan transforms the building geometry into a reference-wind frame, predicts mission-relevant 3D wind patches with a localized geometry-conditioned neural operator, stitches them into a queryable local wind field, and optimizes a feasible 3D path and speed profile using a physically grounded UAV energy model. Rather than pursuing CFD-perfect reconstruction, GeoWind2Plan targets decision-useful wind prediction: trajectories are planned with predicted wind and evaluated under high-fidelity CFD wind. Across held-out urban domains, wind speeds, and mission wind-angle regimes, GeoWind2Plan performs corridor-localized wind inference in about 3 seconds, compared with roughly 8 hours for CFD. Under CFD evaluation, trajectories planned with GeoWind2Plan reduce energy by 6.9%, 12.7%, and 4.5% in tailwind, headwind, and crosswind missions relative to wind-agnostic planning, recovering 87.9%, 85.7%, and 75.0% of CFD-reference savings. These results show that fast, corridor-localized 3D urban wind prediction can make wind-aware UAV energy planning practical at mission time.

1 Introduction

Buildings reshape urban wind into spatially varying 3D flows that affect UAV energy, but mission-time planners lack building-resolved wind because CFD is slow and tied to fixed inflow conditions. GeoWind2Plan predicts corridor-localized wind and uses it for continuous, energy-aware path and speed planning.

1 Introduction

  • Urban buildings create local wind acceleration, wakes, and turning that single-vector or height-only profiles miss, while prior wind-aware planners typically assume a realistic 3D field is already available.CFD can supply building-resolved fields, but each simulation is tied to one inflow condition and takes roughly 8 hours in the reported high-resolution case.Source: §1 · p. 2
  • GeoWind2Plan uses background wind, building geometry, and a start-goal pair to predict local wind patches and optimize a feasible 3D path and speed profile.It rotates geometry into a reference-wind frame, stitches corridor-relevant predictions into a queryable field, and rescales for the mission wind speed.Source: §1 · p. 2, Figure 1 · p. 3
  • About 3 seconds versus roughly 8 hours for CFD, GeoWind2Plan performs corridor-localized inference across held-out geometries, wind speeds, domains, and mission regimes while reducing energy and recovering most CFD-reference savings.Evaluation plans with predicted wind and scores trajectories under high-fidelity CFD wind.Source: §1 · p. 2
  • The framework learns geometry-conditioned wind prediction that generalizes to unseen urban layouts by transforming mission wind directions into a reference-wind frame.The predicted vector field is rotated back to city coordinates.Source: §1 · pp. 2–3
  • GeoWind2Plan evaluates only route-relevant patches and jointly optimizes continuous 3D route geometry and speed, rather than relying on fixed-speed or grid-edge planning.Multiple RRT warm starts provide feasible collision-free candidates for nonlinear refinement under wind-dependent energy and vehicle constraints.Source: §1 · p. 3

2 Method

GeoWind2Plan formulates mission-time UAV energy planning as a coupled geometry-to-wind-to-planning problem. It predicts a local wind field from geometry and background wind, models wind-dependent UAV energy, and refines feasible paths and speeds through continuous optimization.

2 Method

  • The method couples corridor-localized 3D wind prediction with a physically grounded energy model and an RRT-initialized continuous optimizer for route, altitude, timing, and speed.The optimizer refines trajectories subject to vehicle and obstacle constraints.Source: §2 · p. 3

2.1 Problem Setup

  • Planning uses geometry, background wind, and start-goal inputs to predict a local field, then minimizes predicted-wind trajectory energy while evaluating the final decision under CFD wind.Trajectories must connect endpoints, avoid buildings with clearance, and satisfy airspeed, acceleration, and thrust limits; the objective prioritizes decision-level energy rather than pointwise wind error.Source: §2.1 · p. 4

2.2 Localized Geometry-Conditioned Neural Operator for Wind Prediction

  • The wind predictor is trained at a reference inflow; yaw covariance adapts direction by rotating geometry and then rotating predicted velocity vectors back to city coordinates.For tested neutral urban flows, the normalized time-averaged mean field varies weakly with inflow speed, motivating rescaling by the mission-to-reference speed ratio.Source: §2.2 · pp. 4–5
  • Only prediction patches intersecting the mission corridor are evaluated and stitched into a queryable local field; occupancy, SDF, and directional distance features encode building geometry.Directional distance features help represent obstacle bearing, channeling, wake exposure, and other geometry-induced structures.Source: §2.2 · p. 5

2.3 UAV Energy Model in 3D Wind Fields

  • The UAV energy model uses air-relative velocity to couple local wind with drag, thrust, power, trajectory geometry, speed, and acceleration.It uses time-averaged wind and quasi-steady rotor power, omitting gusts, short-time turbulence, controller transients, and vehicle-specific attitude dynamics.Source: §2.3 · pp. 5–6

2.4 Energy-Aware Trajectory Optimization

  • Multiple RRT paths initialize nonlinear trajectory optimization, which refines continuous position, velocity, and acceleration while enforcing endpoint, clearance, and vehicle-feasibility constraints.The lowest planning-energy candidate is selected and evaluated under CFD wind.Source: §2.4 · p. 6

3 Results

Across the evaluated urban layouts and wind regimes, GeoWind2Plan reduces CFD-evaluated energy relative to wind-agnostic planning. Its predicted 3D wind field supports wind-responsive route adaptation, while corridor localization reduces inference time with a feasibility trade-off at narrow widths.

3.1 Experimental Setup

  • Evaluation uses held-out urban blocks, 256 feasible start-goal missions per block, 30–120 m flight envelopes, and wind-agnostic, vertical-profile, predicted-field, and CFD-reference planning settings.The default inflow is 4 m/s; the flight endpoints are placed at 75 m by default.Source: §3.1 · p. 7

3.2 Trajectory-Level Energy Evaluation

  • GeoWind2Plan reduces energy over wind-agnostic planning by 6.9%, 12.7%, and 4.5% in tailwind, headwind, and crosswind missions, recovering 87.9%, 85.7%, and 75.0% of Ground truth reductions.Source: Table 1 · p. 7, §3.2 · p. 8
  • At 8 m/s in headwinds, energy increases over Ground truth by 41.0% for wind-agnostic planning, 18.9% for vertical profile wind, and 7.6% for Ours.Wind-speed adaptation uses mean-flow rescaling, an approximate high-Reynolds-number similarity assumption.Source: §3.2 · p. 8
  • On the 3 km × 3 km urban block, Ours has a 2.5% all-regime increase versus Ground truth, compared with 14.6% for wind-agnostic planning and 3.8% for vertical profile wind.The model and planner are unchanged; the passage suggests more open or weakly obstructed airspace may make height-only wind approximation less harmful.Source: §3.2 · p. 8

3.3 Trajectory Adaptation Behind Energy Savings

  • Predicted 3D wind yields lateral route bending like Ground truth; across wind angles, wind-aware methods fly higher and faster in tailwinds and lower and slower in headwinds.In tailwinds, higher speed can increase mean drag but shorten mission time; in headwinds, lower speed slightly increases flight time while reducing air-relative velocity and integrated energy.Source: §3.3 · pp. 8–9

3.4 Effect of Corridor Localization

  • A 20% corridor cuts inference from 15 s to 3 s with little change in CFD-evaluated energy, while 10% corridors can fail when buildings taller than 120 m block feasible paths.Source: §3.4 · p. 9

4 Conclusion

GeoWind2Plan targets decision-useful wind prediction rather than pointwise-perfect reconstruction, coupling a geometry-to-wind mapping with local wind fields and trajectory optimization. It produces trajectories close to CFD-reference planning while reducing wind inference from hours to seconds.

4 Conclusion

  • Table 2 reports UAV unit-distance energy consumption across corridor widths on urban block A, averaged over relative wind-angle regimes.Source: Table 2 · p. 9
  • GeoWind2Plan shows that energy-efficient urban UAV planning does not require pointwise-perfect wind reconstruction.Source: §4 · p. 9
  • The framework learns a generalizable geometry-to-wind mapping, predicts mission-relevant 3D wind corridors, and couples them with continuous wind-aware trajectory optimization.Source: §4 · p. 9
  • Across diverse urban geometries, wind speeds, and wind-angle regimes, trajectories stay close to CFD-reference planning while wind inference falls from hours to seconds.Source: §4 · p. 9

A Limitations

The discussion reviews neural operators and urban airflow prediction approaches, then identifies turbulence and time-varying inflow as limitations of the current work.

A Limitations

  • The current work uses time-averaged velocity fields, omits turbulence-induced power fluctuations and safety risks, and assumes fixed background wind during a mission.Future work aims to support faster wind updates and replanning under time-varying inflow.Source: A Limitations · p. 14

B.1 Neural Operators for PDE Surrogate Modeling

  • Neural operators approximate mappings from input functions to solution fields, with FNO operating in the Fourier domain and DeepONet using branch and trunk networks.Source: §B.1 · p. 14

B.2 Deep Learning for Urban Wind Field Prediction

  • Urban airflow models include raster-based 2D methods, which cannot directly recover full 3D flow structures important to height-dependent wind and building wakes.Source: §B.2 · p. 14

B.3 Wind-Aware UAV Planning

  • Prior wind-aware UAV planning methods simplify wind prediction, energy modeling, or trajectory scope, including 2D flow or level-cruise settings.Learning-based risk-avoidance planning also lacks rotary-wing energy modeling and joint speed–trajectory optimization.Source: §B.3 · p. 15

C.1 Additional Task Trajectory Visualization

Additional qualitative examples show GeoWind2Plan trajectories across varied urban layouts and missions, including comparisons with CFD-reference and baseline routes.

C.1 Additional Task Trajectory Visualization

  • Across blocks A–E, GeoWind2Plan paths closely follow reference solutions for randomly selected start–goal tasks in diverse layouts.Source: §C.1 · p. 15
  • Across 40 randomly sampled missions in City D, GeoWind2Plan trajectories generally follow CFD-reference routes more closely than profile-wind and wind-agnostic baselines.Source: §C.1 · p. 15

C.2 Additional Path Planning Results

The additional results provide qualitative trajectory comparisons across urban blocks and wind inputs, alongside flight-characteristic and energy table scopes.

C.2 Additional Path Planning Results

  • Figure 4 samples four start–goal tasks from each of urban blocks A–E to visualize trajectories across layouts and mission settings.Source: Figure 4 · p. 16
  • Figure 5 overlays trajectories for 40 sampled missions in block D planned with CFD-reference, predicted local 3D, height-only profile, and zero-wind inputs.Source: Figure 5 · p. 17
  • Table 3 reports altitude and speed statistics across wind conditions, heights, and wind speeds.Source: Table 3 · p. 18
  • Table 4 compares unit-distance energy across five urban blocks, wind speeds, and relative wind-angle regimes, reporting mean ± standard deviation and extra energy relative to Ground truth.Source: Table 4 · p. 19

C.3 Visualization of Evaluation Urban Geometries

The evaluation uses five randomly selected urban blocks, with four standard-size blocks and one larger block.

C.3 Visualization of Evaluation Urban Geometries

  • Five randomly selected evaluation blocks are visualized: A–D are 1.2 km × 1.2 km, while E is 3 km × 3 km.The figure shows their 3D building geometries.Source: §C.3 · p. 20, Figure 6 · p. 20

D Localized Geometry-Conditioned Neural Operator

The section describes a patch-based geometry-to-wind operator, a physics-based trajectory energy model, and a constrained two-stage planner evaluated with distinct planning wind fields.

D Localized Geometry-Conditioned Neural Operator

  • A shared local neural operator predicts three wind-velocity components from fixed-size 3D geometry patches, blending overlapping predictions into a continuous field.Precomputed occupancy, SDF, MDDF, and coordinate features preserve surrounding building context; mission inference can be restricted to route-relevant regions.Source: D Localized Geometry-Conditioned… · p. 20
  • Offline CityFFD labels supervise randomly sampled 45 × 45 × 45 patches, making each CFD case many training samples for the four-layer 3D FNO.The roughly 20 standard-block cases and one large-block case form a small dataset; training takes around seven hours.Source: D Localized Geometry-Conditioned… · p. 21

E Energy Consumption Model

  • The quasi-steady multirotor model uses air-relative velocity to capture local wind effects on drag, required thrust, and power.It is a consistent planning and evaluation cost, not a full battery model or a model of motor-controller transients, gust loading, or short-time turbulence.Source: E Energy Consumption Model · p. 21, §E.1 · p. 21, §E.2 · pp. 21–22

E.3 Nodal Power

  • Nodal power combines useful mechanical, induced, and blade-profile terms, and trajectory energy is integrated over the discretized trajectory.The useful term can be negative in some descending or strongly wind-assisted configurations; the listed vehicle-model parameters are treated as constants.Source: §E.3 · p. 22, §E.4 · p. 22, §E.5 · p. 22

F.1 Environment Representation and Inputs

  • The planner minimizes energy for a supplied wind field while enforcing flight-envelope, obstacle-clearance, and vehicle-feasibility constraints.The city is represented by occupancy and an SDF whose positive values indicate free space; endpoints are fixed and trapezoidal collocation enforces kinematic consistency.Source: F Energy-Aware Path Planning via RRT… · p. 23, §F.1 · p. 23, §F.3 · p. 24

F.3 Continuous Trajectory Optimization

F.2 Feasible Path Initialization with RRT

  • RRT generates multiple collision-free geometric warm starts, adapting extension length to local clearance before continuous refinement.These paths are initializations, not energy-optimal trajectories, and do not explicitly enforce dynamic limits.Source: §F.2 · p. 23

F.5 Planning Variants

  • Planning variants share the optimizer, constraints, vehicle limits, and energy model, differing only in planning wind; every selected trajectory is evaluated under CFD wind.GeoWind2Plan uses task-local predicted 3D wind, the reference uses CFD wind, the profile baseline uses height-only wind, and the wind-agnostic baseline uses zero wind.Source: §F.4 · p. 24, §F.5 · p. 25

G Compute Resources

The section reports compute costs and explains how GeoWind2Plan adapts a reference-inflow prediction to mission wind direction and speed. Direction adaptation follows yaw covariance, while speed adaptation relies on an empirically tested approximation.

G Compute Resources

  • For a 1.2 km block, full-field neural prediction takes about 15 seconds and 20% corridor-localized inference about 3 seconds, versus about 8 GPU-hours for one CFD/LES case.Final-model training takes approximately seven GPU-hours; planning takes about two seconds per mission when ten initializations are parallelized.Source: G Compute Resources · p. 25

H.1 Notation: Reference Flow Operator

  • Mission direction is represented by rotating the city into a reference-wind frame and rotating the predicted vector field back; speed adaptation scales the reference prediction.The reference direction is e1, and the mission direction is dθ.Source: §H.1 · p. 25, §H.3 · p. 27

H.2 Yaw Covariance of the Flow Operator

  • Yaw covariance supports direction adaptation under yaw-symmetric boundary conditions, but the vector wind field must be rotated back rather than treated as invariant.The relation is exact for the idealized flow operator with consistently rotated domain and boundary conditions; finite-domain accuracy depends on suitably symmetric or distant outer boundaries.Source: §H.2 · p. 26

H.3 Physical Basis of Inflow-Speed Rescaling

  • Speed rescaling assumes normalized time-averaged mean flow varies weakly with inflow speed over the tested range, as high-Reynolds-number flow is less affected by viscosity.The approximation is narrower than a Navier–Stokes linearity claim and does not assert that turbulence or thermally driven effects are speed-independent.Source: §H.3 · pp. 26–27

H.4 Metrics and Decision-Level Evaluation for Speed Rescaling

The section evaluates whether normalized CFD wind fields agree across inflow speeds and reports both field-level comparisons and decision-level trajectory evaluation.

H.4 Metrics and Decision-Level Evaluation for Speed Rescaling

  • The field comparison holds city geometry, wind direction, and boundary-profile shape fixed while comparing normalized CFD fields at tested inflow speeds.Agreement in normalized magnitude and direction supports scaling the reference-speed prediction by U/Uref.Source: §H.4 · p. 27
  • 6.69% relative normalized vector difference and 6.39° mean angular difference compare U = 2 with Uref = 4; at U = 8, relative normalized vector difference is 11.24% and mean angular difference remains below 8°.The larger discrepancy at 8 m/s suggests checking the approximation through trajectory evaluation under the corresponding CFD wind.Source: Table 5 · p. 28, §H.4 · p. 28
  • Figures 7a and 7b show consistent raw spatial patterns and close alignment after normalization, while decision-level tests evaluate planned trajectories under CFD wind at the corresponding mission speed.The decision-level results for 2, 4, and 8 m/s are reported in Sections 3.1 and 3.2.Source: §H.4 · p. 28

H.5 Scope and Limitations

The wind-direction transformation is valid only under consistent rotations of geometry, inflow, and outer boundary conditions, while speed adaptation is validated only for time-averaged mean flow in neutral mechanically driven conditions. The notation section defines the wind fields, transformations, and planning quantities used to express that scope.

H.5 Scope and Limitations

  • Direction adaptation is not guaranteed when boundary treatments lack yaw symmetry, finite-domain effects intervene, voxel rotation adds interpolation errors, or terrain and boundary conditions are not horizontally homogeneous.The yaw-covariance relation applies when geometry, inflow, and outer boundary conditions are rotated consistently.Source: §H.5 · p. 28
  • Speed-rescaling validation covers the time-averaged mean wind field only under fixed inflow direction, fixed boundary-profile shape, and neutral mechanically driven flow.Thermal stratification, gusty inflow, unsteady turbulence statistics, and arbitrary background-wind sensor noise require additional inputs, CFD data, or separate validation.Source: §H.5 · p. 28
  • The speed-adaptation assumptions match the optimizer’s use of time-averaged mean wind through air-relative velocity rather than short-time turbulent fluctuations.Source: §H.5 · p. 28

I Notation

  • Figure 7 shows that normalizing CFD wind components by inlet speed aligns patterns across varying speeds, while the notation defines predicted wind fields, planning wind fields, trajectories, and energy quantities.The notation also distinguishes the city and reference-wind frames and the task-local wind prediction module.Source: Figure 7 · p. 29, I Notation · p. 30
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