AI-Accelerated Operator Learning Framework for Rarefied Microflows

TL;DR

The paper tackles the prohibitive computational cost of kinetic solvers in rarefied gas dynamics, introducing an AI-accelerated framework that combines GPU-native DNN closures and neural-operator surrogates to preserve DSMC-level fidelity. Solver-level acceleration replaces the moment-closure solve in the Fokker--Planck method with a GPU-resident DNN that predicts the $9$ closure coefficients from $16$ local features, delivering near-Amdahl-limit speedups. On the operator side, physics-guided and shock-aware DeepONet architectures learn parametric mappings for micro-nozzle, backward-facing step, and hypersonic cylinder flows, with ensemble uncertainty quantification to bound extrapolations. The results show robust generalization, accurate extrapolation to extreme Mach/Knudsen conditions, and practical potential for real-time surrogate modeling and many-query design in rarefied gas dynamics.

Abstract

The high computational cost of kinetic solvers such as DSMC remains a major challenge in rarefied flow simulations. This work presents a unified framework combining deep neural networks and neural operators to accelerate kinetic and hybrid solvers while preserving physical fidelity. GPU-native DNN surrogates eliminate costly moment-closure operations in Fokker Planck methods, achieving significant speedups without accuracy loss, while physics-guided and shock-aware DeepONet architectures enable accurate, data efficient modeling of multi regime micro nozzle, micro-step, and hypersonic flows. Extensions including ensemble uncertainty quantification and family-of-experts strategies further enhance robustness across wide Mach and Knudsen number ranges. Together, these results demonstrate a scalable and physics-consistent pathway toward real-time surrogate modeling in rarefied gas dynamics.

Figures (7)

• Figure 1: Extrapolation test at $U_{\mathrm{lid}}=800~\mathrm{m/s}$. Comparison of 2D contour fields between the full Physics solver (solid black lines) and the Fast ML solver (dashed red lines). The surrogate model is trained only on lower-velocity cases ($U_{\mathrm{lid}}\le 200~\mathrm{m/s}$), yet maintains excellent agreement at four times the maximum training velocity, demonstrating robust generalization.
• Figure 2: Hypersonic cylinder configuration and boundary conditions. Schematic of the computational setup for rarefied hypersonic flow over a circular cylinder. The freestream conditions are $M_\infty=5$--$15$, $T_\infty=200~\mathrm{K}$, and $Kn=0.01$. The cylinder surface is modeled as a thermally diffuse wall at $T_w=500~\mathrm{K}$. A symmetry line is applied along the centerline to reduce the computational domain.
• Figure 3: Surface property distributions over a cylinder at $M=15$. Comparison between DSMC reference data (green symbols) and DeepONet ensemble predictions (solid orange lines), with shaded regions indicating the epistemic uncertainty ($\pm 2\sigma$). The surrogate accurately captures shock-induced deceleration, pressure amplification, and extreme thermal loading, while maintaining narrow uncertainty bounds except in the immediate shock region.
• Figure 4: Qualitative comparison of velocity fields at $\mathrm{Kn}=0.02$ (unseen test case). Comparison of streamwise ($U$) and wall-normal ($V$) velocity contours obtained from high-fidelity DSMC simulations (ground truth) and DeepONet predictions. The neural operator accurately reproduces the separated flow structure, recirculation bubble, and shear-layer development despite this Knudsen number not being included in the training dataset.
• Figure 5: Generalization to an unseen geometry ($h/H=44\%$). Qualitative comparison of streamwise ($U$) and wall-normal ($V$) velocity contours between the high-fidelity DSMC solution (ground truth) and the DeepONet surrogate. Despite this step-height ratio not being included in the training dataset, the neural operator accurately captures the separation bubble, shear-layer structure, and overall flow topology.