Physics constrained neural collision operators for hard sphere surrogates and <i>ab initio</i> angle prediction in direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity ab initio potentials. This work develops a unified, physics-constrained neural-operator framework that accelerates DSMC while preserving physical invariants and stochasticity required for long-time kinetic simulations. First, we introduce a local neural collision kernel replacing the phenomenological hard sphere (HS) model. To overcome the variance suppression and artificial cooling inherent to purely deterministic regression surrogates, we augment inference with a physics-constrained stochastic layer. Controlled latent-noise injection restores thermal fluctuations, while cell-wise moment-matching is introduced as a numerical stabilization device to suppress long-time energy drift. Remarkably, the proposed operator can be deployed without retraining in a two-dimensional lid-driven cavity after being trained on collision samples harvested from a one-dimensional Couette flow. Since the underlying HS collision law is geometry-independent, this test is intended to assess robustness across flow configurations and collision-state distributions rather than the transfer of a geometry-specific law. The surrogate accurately reproduces the primary fields and higher-order non-equilibrium moments in the cavity case. Second, to bypass the extreme cost of trajectory-based classical scattering, we develop a dedicated ab initio neural operator for the Jäger interaction potential. Trained via a physics harvesting strategy on large-scale collision pairs, it efficiently captures the high-energy scattering dynamics dominating hypersonic regimes. Validated on a Mach 10 rarefied argon flow over a cylinder, the framework reproduces transport behaviors and shock features with high fidelity, achieving an approximate 20% cost reduction relative to direct numerical integration. Collectively, this work establishes physics-constrained neural operators as accurate, stable, and efficient drop-in surrogates for DSMC collision dynamics across both engineering HS setups and ab initio hypersonic simulations.