Physics Constrained Neural Collision Operators for Variable Hard Sphere Surrogates and Ab Initio Angle Prediction in Direct Simulation Monte Carlo

Abstract: 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 \emph{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 Variable Hard Sphere (VHS) 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 strictly enforces momentum and kinetic-energy conservation. Remarkably, this operator exhibits zero-shot spatial and thermodynamic generalization: a model trained exclusively on 1D Couette flow accurately simulates a complex 2D lid-driven cavity, capturing high-order non-equilibrium moments without retraining.Second, to bypass the extreme cost of quantum-mechanical scattering, we develop a dedicated \emph{ab initio} neural operator for the Jäger interaction potential. Trained via a \emph{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.