GRAPH NEURAL NETWORKS FOR AERODYNAMIC FLOW RECONSTRUCTION FROM SPARSE SENSING Anonymous authors Paper under double-blind review

Abstract

Sensing the fluid flow around an arbitrary geometry entails extrapolating from the physical quantities perceived at its surface in order to reconstruct the features of the surrounding fluid. This is a challenging inverse problem, yet one that if solved could have a significant impact on many engineering applications. The exploitation of such an inverse logic has gained interest in recent years with the advent of widely available cheap but capable MEMS-based sensors. When combined with novel data-driven methods, these sensors may allow for flow reconstruction around immersed structures, benefiting applications such as unmanned airborne/underwater vehicle path planning or control and structural health monitoring of wind turbine blades. In this work, we train deep reversible Graph Neural Networks (GNNs) to perform flow sensing (flow reconstruction) around two-dimensional aerodynamic shapes: airfoils. Motivated by recent work, which has shown that GNNs can be powerful alternatives to mesh-based forward physics simulators, we implement a Message-Passing Neural Network to simultaneously reconstruct both the pressure and velocity fields surrounding simulated airfoils based on their surface pressure distributions, whilst additionally gathering useful farfield properties in the form of context vectors. We generate a unique dataset of Computational Fluid Dynamics simulations by simulating random, yet meaningful combinations of input boundary conditions and airfoil shapes. We show that despite the challenges associated with reconstructing the flow around arbitrary airfoil geometries in high Reynolds turbulent inflow conditions, our framework is able to generalize well to unseen cases.

1. INTRODUCTION

Many engineering applications stand to benefit from the ability to sense and reconstruct fluid flow features from sparse measurements originating at a structure's surface. Flow sensing could be crucial for improvements in the accuracy and resilience of wind turbine and unmanned aircraft controllers. Another possible application is monitoring of wind loaded structures (Barber et al., 2022) , where the use of cheap micro-electromechanical systems (MEMS) in combination with novel methods for flow sensing could lead to robust structural health monitoring solutions. In this work, we focus on common aerodynamic structures: we aim to reconstruct the flow around 2-D airfoils. Traditionally, computing the flow around an airfoil requires approaches from Computational Fluid Dynamics (CFD), which are forward-physics simulators. In CFD, the inflow, outflow and wall boundary conditions are set, and over many iterations a solution for the discretized Navier-Stokes PDEs is reached, which then yields a pressure distribution at the airfoil surface. We aim to solve the inverse problem: given only the pressure distribution at the airfoil surface, a solution for the flow field and farfield boundary conditions is to be found. Moreover, our aim is to do so for any airfoil geometry subject to a wide variety of turbulent inflows. Adopting the notation of Erichson et al. (2020) , the problem can be described in the following manner. An airfoil equipped with p distributed barometric sensors is placed in a steady flow of air, providing surface pressure measurements s ∈ R p at multiple locations around its perimeter. The sensors sample from the surrounding flow field x ∈ R m through a measurement operator H: s = H(x) (1)

