Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach

Hanbing Liang; Fujun Liu

cs.CEApr 1, 2026

Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach

Authors: Hanbing Liang, Fujun Liu

Abstract

Macroscopic unmanned aerial vehicle (UAV) traffic organization in three-dimensional airspace faces significant challenges from static wind fields and complex obstacles. A critical difficulty lies in simultaneously capturing the strong anisotropy induced by wind while strictly preserving transport consistency and boundary semantics, which are often compromised in standard physics-informed learning approaches. To resolve this, we propose a constraint-preserving hybrid solver that integrates a physics-informed neural network for the anisotropic Eikonal value problem with a conservative finite-volume method for steady density transport. These components are coupled through an outer Picard iteration with under-relaxation, where the target condition is hard-encoded and strictly conservative no-flux boundaries are enforced during the transport step. We evaluate the framework on reproducible homing and point-to-point scenarios, effectively capturing value slices, induced-motion patterns, and steady density structures such as bands and bottlenecks. Ultimately, our perspective emphasizes the value of a reproducible computational framework supported by transparent empirical diagnostics to enable the traceable assessment of macroscopic traffic phenomena.

Figures & tables

Panel of Figure 1 — Figure 1: Overall pipeline of the hybrid framework.

Figure 2: Value function slice comparisons. Top row: Homing under baseline, crosswind, and crosswind with an obstacle. Bottom row: point-to-point (P2P) under baseline, vortex wind, and vortex wind with an obstacle. The red dashed circle marks the target (sink); the green circle marks the source (P2P panels); gray squares denote obstacles.

Figure 3: Induced-motion streamlines (white) for P2P under vortex wind with an obstacle, overlaid on the $\phi$ background. The target, source, and obstacle are marked.

Figure 4: Steady density slice ( $\rho$ ) for P2P under vortex wind with an obstacle (source/target/obstacle marked).

Figure 5: Method comparison under the P2P scenario with no wind and no obstacles. Left column: $\phi$ ; right column: $\rho$ . Rows: hybrid (Route B), end-to-end PINN (Route A), and a traditional FSM–FVM reference solver.

Scenario	Hybrid (GPU) (s)	Baseline (CPU) (s)	Speedup
P2P (no wind)	288.4	3884.7	13.47
P2P (xwind)	288.3	2703.8	9.38
P2P (vortex)	312.8	4018.8	12.85
Homing (no wind)	301.3	3078.6	10.22
Homing (xwind)	293.5	3827.5	13.04
Homing (vortex)	301.8	4289.5	14.21

Table 1: Wall-clock runtime comparison under multiple wind fields (no obstacles) for P2P and Homing tasks. The hybrid PINN–FVM solver is evaluated on a desktop GPU (RTX 5090). The FSM–FVM baseline is evaluated on a dual-socket CPU server (2

\times

AMD EPYC 7T83). The results are reported as end-to-end wall-clock times under the stated platforms and should not be interpreted as a hardware-normalized algorithmic benchmark: the reported “speedup” reflects both platform differences and the fact that neural inference and residual evaluation are naturally GPU-parallel. “Speedup” is computed as

T_{\text{baseline}}/T_{\text{hybrid-GPU}}

within each scenario; higher is better.

Figure 6: Representative diagnostics from metrics.csv : MFD consistency and training convergence.

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Shaoxiang Qin, Yucheng Zhao, Fuyuan Lyu, Di Zhou+5

University of Tennessee, Knoxville · Concordia University · McGill University+2

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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.

Abstract

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