Shock-centered low-rank structure and shock-aligned surrogate modeling of rarefied micro-nozzle flows

We examine Direct Simulation Monte Carlo (DSMC)-resolved rarefied micro-nozzle flows with finite-thickness internal compression layers and develop a shock-aligned, scalar-conditioned surrogate for repeated field prediction. The study separates the physics of the moving compression layer, the shock-aligned trunk features, and the branch/trunk conditioning block. Density-gradient and gradient-length Knudsen-number diagnostics show that the dominant compression layer is a localized finite-width macroscopic compression region on the sampled DSMC grid rather than a mathematical discontinuity. A jump-based thickness defines the registered coordinate ξj=(x−xs)/δj, which makes the centerline profiles substantially more compact. For ρ, U, P, and Mach number, the leading proper orthogonal decomposition energy increases from 69.9%–78.9% in physical coordinates to 94.7%–98.0% after shock-centering and thickness scaling. This reduced structure motivates signed-distance and local envelope features in the surrogate. The evaluation includes per-feature ablations, parameter-count-aware and seed-robust baselines, fusion-isolation tests, near-boundary extrapolation stress tests, and a posteriori physical-consistency diagnostics. For the hard 16 kPa case, adding only the signed shock distance reduces the shock-window error of a Cartesian Hadamard branch/trunk model from 57.98% to 10.17% in the single-seed ablation. Across three random seeds, the reduced signed-distance model gives a shock-window error of 9.12±1.01%, comparable to a strong Cartesian multilayer perceptron with 8.86±1.26%. The contribution is, therefore, not a new fusion architecture but a physics-based shock-centered representation and a transparent assessment of when it improves shock-localized surrogate accuracy within a calibrated pressure range.