Title: Extraction of Moment Closures for Strongly Non-Equilibrium Flows via Machine Learning Show Chinese title

Title: 通过机器学习提取强非平衡流的矩闭合方法

Abstract: 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. Show Chinese abstract

Abstract: 我们引入了一个机器学习框架，用于稀薄气体流动的矩方程建模，解决了传统计算流体力学无法处理的强非平衡条件。 我们的方法利用高阶矩和碰撞积分作为关键预测变量，这些变量对非平衡效应高度敏感。 训练数据集来自一维稳态激波模拟，开发了一种计算碰撞积分的方法。 通过直接从DSMC数据中学习热力学一致的闭合关系，我们的R13-ML模型结合矩传输方程的不连续伽辽金求解器，保持了物理结构，并准确预测了法向激波结构，且能推广到高超音速以及一些非定常的一维波场景。 这项工作将机器学习与连续介质力学相结合，为下一代超音速飞行器的高保真气动热预测提供了一条路线图。