Physics-Informed Neural Networks for microflows: Rarefied Gas Dynamics in Cylinder Arrays

TL;DR

This paper demonstrates that physics-informed neural networks can efficiently and accurately predict rarefied gas microflows, reducing computational time significantly compared to traditional DSMC methods, and effectively filtering statistical noise.

Contribution

The study introduces a PINN approach trained on DSMC data for rarefied microflows, offering a meshless, faster, and noise-filtering alternative to traditional simulation methods.

Findings

PINN achieved under 2% residual error.

PINN training took less than 2 hours on a single GPU.

Predictions remained accurate within the transition regime, with limited extrapolation performance.

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 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 with Knudsen number from 0.1 to 3, incorporating continuity and Cauchy momentum exchange equations in the loss function. The PINN achieved under 2 percent error on these residuals and effectively filtered DSMC intrinsic statistical noise. Predictions remained strong for a tested flow field with Kn equal to 0.7, and showed limited extrapolation performance on a flow field with Kn equal to 5 with a local overshoot of about 20 percent, while maintaining physical consistency. Notably, each DSMC field required about 20 hours on 4 graphics processing units (GPU), while the PINN training took less than 2 hours on one GPU, with evaluations under 2 seconds.