  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.
