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

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 (6)

• 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.