Extraction of Moment Closures for Strongly Non-Equilibrium Flows via Machine Learning

We introduce a machine learning framework for moment-equation modeling of rarefied gas flows, addressing strongly non-equilibrium conditions inaccessible to conventional computational fluid dynamics. Our approach utilizes high-order moments and collision integrals, highly sensitive to non-equilibrium effects, as key predictive variables. Training datasets are created from one-dimensional steady shock simulations, and a methodology of computing collision integrals is developed. By learning thermodynamically consistent closures directly from DSMC data, our R13-ML model, combined with a discontinuous Galerkin solver for the transfer equations of moments, preserves physical structure and accurately predicts normal shock structures and generalizes to hypersonic and some unsteady, one-dimensional wave scenarios. This work bridges machine learning with continuum mechanics, offering a road map for high-fidelity aerothermal predictions in next-generation supersonic vehicles.