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

TL;DR

This paper introduces a hybrid physics-informed neural network and finite-volume method to model macroscopic UAV traffic in 3D wind fields, ensuring transport consistency and boundary accuracy.

Contribution

It presents a novel constraint-preserving hybrid solver combining PINN and FVM for UAV traffic modeling in complex wind environments.

Findings

Successfully captures anisotropic wind effects on UAV traffic patterns.

Effectively models steady density structures like bands and bottlenecks.

Provides a reproducible computational framework with transparent diagnostics.

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.