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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.01327 |
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| _version_ | 1866914437712052224 |
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| author | Liang, Hanbing Liu, Fujun |
| author_facet | Liang, Hanbing Liu, Fujun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01327 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach Liang, Hanbing Liu, Fujun Computational Engineering, Finance, and Science Machine Learning 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. |
| title | Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach |
| topic | Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2604.01327 |