Physics-Guided Generative Surrogates for Parametric Rarefied Flows with Neural-Field Auto-Decoders: A Pipeline-Level Study of Flow Matching and Diffusion

Abstract: We present a conditional latent generative framework for parametric rarefied flows that separates neural-field representation, latent transport, and frozen physics adaptation. Neural-field auto-decoders compress discrete-velocity cavity solutions and direct simulation Monte Carlo cylinder solutions into shared coordinate decoders. Train-only principal-component charts support conditional flow matching (FM) and diffusion without a deterministic condition-to-latent backbone, and structured low-rank adapters correct selected decoder outputs while the upstream pipeline remains frozen. On two steady benchmarks, the frozen pipelines interpolate out-of-sample conditions with cavity kinetic relative $L_1$ errors at the $10<sup>{-5}$ level and cylinder per-field area-weighted RMSEs of 0.038 (density), 0.041 (temperature), and below 0.01 (velocities). For the cavity, physics adaptation reduces the matched-grid Bhatnagar--Gross--Krook diagnostic by 28.65% while preserving field accuracy; for the cylinder, the analytic wall map enforces no-penetration exactly and, jointly with the learned FM adapter, reduces the inlet violation to 0.277 and the global mass-balance ratio to 0.963 of the frozen values with negligible field-error change. A five-seed controlled comparison with deterministic condition-to-chart multilayer perceptrons shows that, although the generative pipelines do not surpass the compact MLP in point accuracy on these single-valued steady problems, the results validate sampling-based conditional transport on the shared representation as an effective steady surrogate, with a natural route to multivalued or stochastic solution families.