  Modern air vehicles perform a wide range of operations, including
transportation, defense, surveillance, and rescue. These aircraft can fly in
calm conditions but avoid operations in gusty environments, encountered in
urban canyons, over mountainous terrains, and in ship wakes. With extreme
weather becoming ever more frequent due to global warming, it is anticipated
that aircraft, especially those that are smaller in size, will encounter
sizeable atmospheric disturbances and still be expected to achieve stable
flight. However, there exists virtually no theoretical fluid-dynamic foundation
to describe the influence of extreme vortical gusts on wings. To compound this
difficulty, there is a large parameter space for gust-wing interactions. While
such interactions are seemingly complex and different for each combination of
gust parameters, we show that the fundamental physics behind extreme
aerodynamics is far simpler and lower-rank than traditionally expected. We
reveal that the nonlinear vortical flow field over time and parameter space can
be compressed to only three variables with a lift-augmented autoencoder while
holding the essence of the original high-dimensional physics. Extreme
aerodynamic flows can be compressed through machine learning into a
low-dimensional manifold, which can enable real-time sparse reconstruction,
dynamical modeling, and control of extremely unsteady gusty flows. The present
findings offer support for the stable flight of next-generation small air
vehicles in atmosphere conditions traditionally considered unflyable.
