Learning of viscosity functions in rarefied gas flows with physics-informed neural networks

The prediction of 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. A generalized Stokes phenomenological model using an effective viscosity function was used to recover rarefied gas flow fields: however, it is difficult to construct the effective viscosity function on first principles. Physics-informed neural networks (PINNs) show some potential for solving such an inverse problem. 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 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.