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

TL;DR

A unified, physics-constrained neural-operator framework is developed that accelerates DSMC while preserving physical invariants and stochasticity required for long-time kinetic simulations, and develops a dedicated neural operator for the Jager interaction potential.

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.

Figures (22)

• Figure 1: Schematic of the neural collision operator. Collisions are selected locally in each DSMC cell. For each accepted pair, a conditional MLP predicts the post-collision relative velocity direction given the normalized pre-collision relative velocity and an explicit random latent vector. A hard projection enforces exact pairwise energy conservation before updating particle velocities.
• Figure 2: Comparison of the particle speed distribution from the Hybrid ML-DSMC solver (Blue Histogram) versus the analytical Maxwell-Boltzmann distribution at $T=274.41$ K (Red Line). The histogram exhibits an excellent fit with the theoretical curve, validating the successful restoration of the velocity distribution's shape and width through noise injection and energy rescaling.
• Figure 3: Distribution of individual velocity components ($v_x, v_y, v_z$) obtained from the simulation (histograms) compared against the theoretical Gaussian distribution (red dashed line) at $T=272.78$ K. The strong agreement for all three components confirms the isotropic nature of the simulated gas and the correct treatment of velocity directions by the DNN.
• Figure 4: Macroscopic profiles for high-speed Couette flow ($U_w = 500$ m/s, $Kn=0.2$) comparing the Standard DSMC (Black Line) and the Hybrid DNN-DSMC (Red Dashed Line).
• Figure 5: Validation of the DNN surrogate for 1D Couette flow in the transition regime. The simulation corresponds to a Knudsen number of $Kn=1.0$ and a wall velocity of $U_w = 500$ m/s.