Transport-preserving neural ab initio scattering kernels for rarefied binary gas mixtures

Abstract

Neural surrogates for molecular scattering provide a route to continuously evaluable and differentiable direct simulation Monte Carlo (DSMC) collision kernels, but a small pointwise deflection-angle error is not sufficient evidence that a learned map is kinetically reliable. Diffusion, viscosity, representative collision rates, angular redistribution, and mixture relaxation are nonlinear functionals of the same scattering measure. We therefore develop a multiscale validation framework for neural ab initio scattering kernels that combines angular regression, transport cross sections, Ohr-style representative quantities, cumulative angular measures, Fourier spectral content, impact-grid and angular-noise robustness, loss-ablation diagnostics, and three solver-level DSMC mixture tests. The framework is demonstrated on a refined argon--argon Jäger table and on helium--argon ab initio EPAPS data of Sharipov and Benites represented by a neural equal-area scattering surrogate. For He--Ar over $\Er/\kb\ge10~\mathrm{K}$, the surrogate preserves $\QD$, $\Qmu$, $\Qmu/\QD$, $\RCS$, and $\SigVSS$ within $0.75\%$, $1.37\%$, $0.84\%$, $1.21\%$, and $1.46\%$, respectively. The cumulative angular measure agrees within $1.43\%$, the median relative $L_2$ error of $χ(q)$ is $3.4\times10^{-3}$, and the high-mode spectral-energy ratio is essentially unbiased. The same neural He--Ar kernel is then embedded in periodic DSMC mixture problems that separately probe mass diffusion, momentum diffusion, and two-dimensional field-level mixing. A sinusoidal composition mode is reproduced over three independent realizations with a mean normalized-history error of $1.28\pm0.22\%$ and $D_{\NN}/D_{\EPAPS}=1.015\pm0.013$. A transverse shear wave is reproduced with a $1.58\%$ history error and $ν_{\NN}/ν_{\EPAPS}=0.989$.