Physics-informed neural networks for microflows: Rarefied gas dynamics in cylinder arrays

Abstract

Accurate prediction of rarefied gas dynamics is crucial for optimizing flows through microelectromechanical systems, air filtration devices, and shale gas extraction. Traditional methods, such as discrete velocity and direct simulation Monte Carlo (DSMC), demand intensive memory and computation, especially for microflows in non-convex domains. Recently, physics-informed neural networks (PINNs) emerged as a meshless and adaptable alternative for solving non-linear partial differential equations. We trained a PINN using a limited number of DSMC-generated rarefied gas microflows in the transition regime $(0.1<\mathrm{Kn}<3)$, incorporating continuity and Cauchy momentum exchange equations in the loss function. The PINN achieved under 2 % error on these residuals and effectively filtered DSMC’s intrinsic statistical noise. Predictions remained strong for a tested flow field with $\mathrm{Kn}=0.7$, and showed limited extrapolation performance on a flow field with $\mathrm{Kn}=5$ with a local overshoot of about 20 %, while maintaining physical consistency. Notably, each DSMC field required $\sim 20$ hours on 4 graphics processing units (GPU), while the PINN training took $<2$ hours on one GPU, with evaluations under $2$ seconds.