  Linear stability analysis is performed using a combination of two-dimensional
Direct Simulation Monte Carlo (DSMC) method for the computation of the basic
state and solution of the pertinent eigenvalue problem, as applied to the
canonical boundary layer on a semi-infinite flat plate. Three different gases
are monitored, namely nitrogen, argon and air, the latter as a mixture of 79\%
Nitrogen and 21\% Oxygen at a range of free-stream Mach numbers corresponding
to flight at an altitude of 55km. A neural network has been utilised to predict
and smooth the raw DSMC data; the steady laminar profiles obtained are in very
good agreement with those computed by (self-similar) boundary layer theory,
under isothermal or adiabatic wall conditions, subject to the appropriate slip
corrections computed in the DSMC method.
  The leading eigenmode results pertaining to the unsmoothed DSMC profiles are
compared against those of the classic boundary layer theory. Small
quantitative, but no significant qualitative differences between the results of
the two classes of steady base flows have been found at all parameters
examined. The frequencies of the leading eigenmodes at all conditions examined
are practically identical, while perturbations corresponding to the DSMC
profiles are found to be systematically more damped than their counterparts
arising in the boundary layer at the conditions examined, when the correct
velocity slip and temperature jump boundary conditions are imposed in the base
flow profiles; by contrast, when the classic no-slip boundary conditions are
used, less damped/more unstable profiles are obtained, which would lead the
flow to earlier transition. On the other hand, the DSMC profiles smoothed by
the neural network are marginally more stable than their unsmoothed
counterparts.
