Rarefied gas flow over a micro backward-facing step (BFS) is a canonical non-equilibrium benchmark featuring separation, recirculation and strong Knudsen-layer effects that are highly sensitive to both the Knudsen number and the step-height ratio. High-fidelity Direct Simulation Monte Carlo (DSMC) simulations resolve these phenomena but are prohibitively expensive for parametric studies, uncertainty quantification and design exploration. In this work, we develop a Deep Operator Network (DeepONet) surrogate for rarefied step flows that maps the Knudsen number ( \(\textrm{Kn}\) ) and the geometric ratio (h/H) to the full two-dimensional velocity field in a micro-step geometry. The architecture is augmented with a physics-guided zonal loss that assigns higher weights to errors in the recirculation region ( \(U < 0\) ), thereby enforcing accurate prediction of separation and reattachment. Systematic comparisons with DSMC data in the slip and early transition regimes show that the surrogate reproduces key physical trends, including the shortening and eventual disappearance of the separation bubble with increasing \(\textrm{Kn}\) and the non-monotonic variation of the reattachment length with h/H. A low-data study (reported in the supplementary material) demonstrates that the model attains more than \(90\%\) of its asymptotic accuracy using only about 40– \(50\%\) of the available high-fidelity simulations, substantially mitigating the cost of data generation. Furthermore, stochastic weight averaging Gaussian (SWAG) provides epistemic uncertainty estimates that are naturally localized near the shear layer and separation point, i.e. in the most non-equilibrium regions of the flow. The resulting framework offers a fast, robust and data-efficient tool for exploring rarefied micro-step flows, enabling many-query analyses in regimes where direct DSMC sampling is computationally intractable.
