Reduced Order Modelling for Urban UAS Wind Field Estimation: A Neural Galerkin Projection Approach

The inception of Urban Air Mobility (UAM), an emergent aviation ecosystem that leverages compact, unmanned aerial vehicles for transport within low-altitude urban and suburban locales, delineates a subset of the broader Advanced Air Mobility (AAM) concept. The latter aims to interconnect communities underserved by traditional transport systems through diverse intra- and inter-city operations. Notwithstanding the integration of various extant technologies, the safe navigation of Unmanned Aerial Systems (UAS) in urban canopies remains challenging, primarily due to unpredictable external forces such as wind gusts and turbulent wakes.

High-fidelity numerical simulations provide accurate wind predictions, albeit at a prohibitive computational cost for real-time applications. Conversely, Reduced Order Models (ROMs) offer an alternative for generating precise yet computationally economical predictions. In particular, Galerkin Projection (GP)-based ROMs have gained traction due to their innate capacity to incorporate underlying operator forms, ensuring physical and theoretical consistency. Nevertheless, these models suffer from instability and inaccuracies over extended temporal windows.

This study seeks to transcend these limitations by extending the Neural GP ROM framework to accommodate three-dimensional turbulence, characteristic of the flow fields encountered by UAS in urban canopies. By utilizing GP and differentiable programming-based strategies, we propose to learn low-dimensional ROM equations via the parameterization of high-dimensional flow features. Our approach anticipates an enhanced level of interpretability and computational efficiency compared to conventional deep learning-based models.

This research also intends to scrutinize the stability traits of the ROM, perform uncertainty quantification for UAS-relevant scenarios, and discuss the potential applications of our model within diverse fluid dynamics contexts. The results are expected to contribute significantly to the knowledge of efficient and precise prediction models suitable for UAM and similar applications.