Neural networks for rarefied gas dynamics: Relaxation problem, polyatomic shock waves, and hypersonic cylinder flow

This work presents a suite of targeted methodologies based on neural operators, including physics-informed, physics-constrained, and data-driven approaches, for constructing computationally efficient and robust surrogate models in rarefied gas dynamics, where high-fidelity kinetic solvers are often prohibitively expensive. Three key contributions are introduced, demonstrating stability, physics-discovery capability, and strong generalization across different regimes. First, for the Bhatnagar–Gross–Krook kinetic relaxation problem, a perturbation ansatz is proposed to ensure numerical stability within a physics-informed neural network framework. This stabilized model enables simultaneous forward prediction and decay-rate identification, successfully inferring the unknown collision frequency solely from the governing equations and initial conditions. Validation against a supervised Feedforward Neural Network, trained on the exact analytical solution, shows comparable accuracy without requiring labeled data. Second, for one-dimensional shock waves in polyatomic gases, a physics-constrained Deep Operator Network (DeepONet) is developed. By embedding monotonicity constraints directly into the learning process, the model accurately captures nonequilibrium structures for unseen viscosity ratios while substantially reducing nonphysical oscillations. Third, for two-dimensional hypersonic flow over a cylinder, data-driven DeepONet surrogates are constructed for both Mach-number and Knudsen-number parameterizations. For the Mach-parameterized case, the model shows accurate interpolation for monatomic and diatomic gas flow over unseen Mach numbers and extrapolation to Mach 15. For the fixed-M∞=10 Knudsen-number study, the surrogate reproduces temperature and Mach-number fields over unseen rarefaction levels in slip and transition regimes, while additional wall-based models accurately predict surface quantities, including wall heat flux and wall shear stress. Overall, the results highlight physics-consistent surrogate modeling, uncertainty-aware prediction, and a significant reduction in online computational cost for many-query applications.