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

2026-04-01

AI Summary

This work addresses the challenge of modeling strongly anisotropic macroscopic UAV traffic flows in three-dimensional wind fields, where static wind patterns and complex obstacles induce significant anisotropy and compromise transport consistency. To overcome these issues, the authors propose a constraint-preserving hybrid solver that combines physics-informed neural networks (PINNs) for solving the anisotropic Eikonal equation to obtain value functions with a conservative finite volume method (FVM) for simulating steady-state density transport. The two components are coupled via a relaxed Picard iteration, while target conditions are hard-encoded and no-flux boundaries strictly enforced. This framework simultaneously ensures physical consistency, boundary semantics, and mass conservation throughout training, thereby overcoming key limitations of conventional PINNs in macroscopic traffic modeling. It successfully reproduces homing and point-to-point scenarios, accurately capturing value function slices, induced motion patterns, and steady-state density structures—such as channelized flows and bottlenecks—yielding a traceable and diagnosable computational framework for macroscopic UAV traffic.

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.

Problem

• UAV traffic
• anisotropic wind fields
• transport consistency
• boundary semantics
• macroscopic organization

Innovation

• physics-informed neural network
• finite-volume method
• anisotropic transport
• constraint-preserving
• macroscopic UAV traffic