Analysis of the Rarefied Flow at Micro-Step using a DeepONet Surrogate Model with a Physics-Guided Zonal Loss Function

Abstract: The Direct Simulation Monte Carlo (DSMC) method remains the gold standard for simulating rarefied gas flows but is prohibitively expensive for parametric and many-query applications. To address this limitation, we introduce a Deep Operator Network (DeepONet) surrogate framework featuring an innovative, physics-guided zonal loss function. The zonal loss prioritizes physical fidelity in critical flow regions over global error metrics, leading to predictions with greater engineering relevance. It explicitly emphasizes accuracy in the recirculation zone, ensuring faithful reconstruction of separated flow features that are often under-resolved by conventional, globally averaged error metrics. Two operator-learning tasks are demonstrated: mapping the Knudsen number to the velocity field and mapping the step-height ratio to the flow solution. The results show excellent agreement with high-fidelity DSMC data. An ablation study highlights that, while global error metrics may suggest only marginal improvements, localized error analysis reveals the superior fidelity of the zonal loss in capturing vortex dynamics -- an aspect central to engineering relevance. The proposed surrogate reproduces detailed velocity fields with high physical fidelity and achieves predictions for unseen parameters in milliseconds, representing speedups of several orders of magnitude relative to DSMC. This capability enables the quantification of uncertainty, optimization, and design-space exploration that would otherwise be computationally intractable.