Accelerating Kinetic Fokker-Planck Simulations via a GPU-Native Deep Neural Network Surrogate: Application to Rarefied Internal and Hypersonic External Flows

Abstract

Particle-based Fokker--Planck (FP) models provide an efficient kinetic alternative to direct simulation Monte Carlo (DSMC) in slip and early transitional gas flow regimes, but advanced cubic-FP closures require repeated cell-wise moment evaluation and small dense linear solves. This work develops and validates a GPU-native neural surrogate that replaces the deterministic cubic-FP closure calculation inside the particle simulation loop. The trained weights are evaluated directly with batched \texttt{CuPy} operations, avoiding CPU--GPU transfers during online deployment. The validation emphasizes quantitative evidence: component-level runtime profiles, break-even cost analysis including offline costs, conservation and stability diagnostics, particle-per-cell sensitivity, a direct time-averaged coefficient audit, and covariance-based entropy-proxy fidelity checks. The Couette case is retained as a compact, dimensionless verification problem, while the main internal-flow validation is a 2D lid-driven cavity tested by complete simulation conditions, including unseen moderately rarefied cases at nominal $Kn=0.5$ and $Kn=1.0$. For the hypersonic cylinder, a particle-moment covariance-based entropy-fidelity audit is performed on the front stagnation line and in the cell-centered near-wall gas layer. The same deployed neural $C/Γ$ closure used for the cylinder flow fields closely reproduces the equilibrium and Gaussian kinetic entropy profiles over the reported front-line and near-wall gas bins; these profiles are used as a relatively exact-FP/ML-FP audit. The study establishes GPU-native learned closure as a practical route to accelerating cubic-FP rarefied-flow solvers, delivering substantial online speedups while retaining the macroscopic, high-order, and entropy-proxy structure of the reference kinetic model.