用混合方法模拟三维风场中无人机交通流，精准保持运输一致性。
Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach
- 结合物理信息神经网络与有限体积法，解决风场各向异性问题。
- 在飞行路径和密度分布上准确捕捉带状结构与瓶颈现象。
- 适合研究复杂空域下无人机交通的可复现仿真与诊断评估。
三维空域中无人机交通组织面临静态风场与复杂障碍物带来的挑战。核心难点在于同时捕捉风引起的强各向异性，并严格保持运输一致性与边界语义，而标准物理信息学习方法常在此方面妥协。为此，我们提出一种约束保持型混合求解器，将物理信息神经网络用于各向异性Eikonal值问题，结合保守有限体积法处理稳态密度输运。二者通过外层Picard迭代与欠松弛耦合，目标条件硬编码，输运步骤强制无通量边界。在可复现的归巢与点对点场景中验证，有效捕捉值切片、诱导运动模式及带状、瓶颈等稳态密度结构。最终强调，基于透明实证诊断的可复现计算框架对宏观交通现象的可追溯评估具有重要价值。
原文摘要 · Abstract (English)
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.
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