  This work addresses the data-driven forecasting of extreme events in the
airfoil flow. These events may be seen as examples of the kind of unsteady and
intermittent dynamics relevant to the flow around airfoils and wings in a
variety of laboratory and real-world applications. W investigate the
instability mechanisms at the heart of these extreme events, and how knowledge
thereof may be harnessed for efficient data driven forecasting. Through a
wavelet and spectral analysis of the flow we find that the extreme events arise
due to the instability of a specific frequency component distinct from the
vortex shedding mode. During these events this extreme event manifold draws
energy from the energetically dominant vortex shedding flow and undergoes an
abrupt energy transfer from small to large scales. We also investigate the
spatial dependence of the temporal correlation and mutual information between
the surface pressure and the aerodynamic forces, with the aim of identifying
regions of the airfoil amenable to sparse sensing and the efficient forecasting
of extremes. Building on previous work, we show that relying solely on the
mutual information for optimal sensor placement fails to improve model
prediction over uniform or random sensor placement. However, we show that by
isolating the extreme event frequency component offline through a wavelet
transform we are able to circumvent the requirement for a recursive long-short
term memory (LSTM) network -- resulting in a significant reduction in
computational complexity over the previous state of the art. Using the wavelet
pre-processed data in conjunction with an extreme event-tailored loss function
we find that our model is capable of forecasting extreme events using only
three pressure sensors. Furthermore, we find our model to be robust to sensor
location -- showing promise for the use of our model in dynamically varying
applications.
