  The prediction non-equilibrium transport phenomena in disordered media is a
difficult problem for conventional numerical methods. An example of a
challenging problem is the prediction of gas flow fields through porous media
in the rarefied regime, where resolving the six-dimensional Boltzmann equation
or its numerical approximations is computationally too demanding.
Physics-informed neural networks (PINNs) have been recently proposed as an
alternative to conventional numerical methods, but remain very close to the
Boltzmann equation in terms of mathematical formulation. Furthermore, there has
been no systematic study of neural network designs on the performance of PINNs.
In this work, PINNs are employed to predict the velocity field of a rarefied
gas flow in a slit at increasing Knudsen numbers according to a generalized
Stokes phenomenological model using an effective viscosity function. We found
that activation functions with limited smoothness result in orders of magnitude
larger errors than infinitely differentiable functions and that the AdamW is by
far the best optimizer for this inverse problem. The design was found to be
robust from Knudsen numbers ranging from 0.1 to 10. Our findings stand as a
first step towards the use of PINNs to investigate the dynamics of
non-equilibrium flows in complex geometries.
