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Learning of Viscosity Functions in Rarefied Gas Flows with Physics-informed Neural Networks by Tucny, Jean-Michel; Durve, Mihir; Montessori, Andrea; Succi, Sauro is a scholarly article available to read on EtoBox.

What is Learning of Viscosity Functions in Rarefied Gas Flows with Physics-informed Neural Networks about?

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. O

Author

Tucny, Jean-Michel; Durve, Mihir; Montessori, Andrea; Succi, Sauro

Published

2023

Language

EN