32nd International Symposium on Rarefied Gas Dynamics (RGD32)

Physics-informed Neural Network and Functional Interpolation for Rarefied-Gas Dynamics in the BGK Approximation

M. De Florio, E. Schiassi, L. B. Barichello, B. D. Ganapol, R. Furfaro

We present a new accurate, and precise Physics-Informed Neural Network (PINN) approach to solve a class of problems in the Theory of Rarefied--Gas Dynamics using the recently developed Extreme Theory of Functional Connections (X-TFC) by the authors. X-TFC intends to be an improved PINN method to solve parametric Differential Equations (DEs) that combines Theory of Functional Connections, as we approximate the solution with the constrained expression to analytically handle the boundary conditions, and an Extreme Learning Machine algorithm. The method is applied to efficiently and accurately solve the Linear Boundary Value Problems arising from Bhatnagar, Gross, and Krook model of a rarefied--gas between two parallel plates, for a wide range of Knudsen number. In particular, three classical flow problems are studied, such as Poiseuille, Couette, and Thermal Creep Flows. The accuracy of our results is validated via the comparison with the published benchmarks up to at least 7 digits for different Knudsen numbers and accommodation coefficients. The formulation of the problem results to be straightforward with low computational times and it creates a generalized solution which does not require further manipulation or interpolation for obtain the solution outside the training points.