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.
翻译:宏观无人机(UAV)在三维空域中的交通组织面临静态风场和复杂障碍物的重大挑战。一个关键困难在于同时捕捉由风场引起的强各向异性,同时严格保持输运一致性和边界语义,而这些在标准的物理信息学习方法中常常受到损害。为解决这一问题,我们提出了一种约束保持的混合求解器,该方法将用于各向异性Eikonal值问题的物理信息神经网络与用于稳态密度输运的保守有限体积法相结合。这两个组件通过带有欠松弛的外层Picard迭代进行耦合,其中目标条件被硬编码,并且在输运步骤中强制执行严格保守的无通量边界条件。我们在可复现的归航和点对点场景上评估了该框架,有效捕捉了值切片、诱导运动模式以及带状和瓶颈等稳态密度结构。最终,我们的视角强调了在透明经验诊断支持下构建可复现计算框架的价值,从而能够对宏观交通现象进行可追溯评估。