Physics constrained neural collision operators for hard sphere surrogates and ab initio 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.