Direct simulation of physical processes on a kinetic level is prohibitively expensive in aerospace applications due to the extremely high dimension of the solution spaces. In this paper, we consider the moment system of the Boltzmann equation, which projects the kinetic physics onto the hydrodynamic scale. The unclosed moment system can be solved in conjunction with the entropy closure strategy. Using an entropy closure provides structural benefits to the physical system of partial differential equations. Usually computing such closure of the system spends the majority of the total computational cost, since one needs to solve an ill-conditioned constrained optimization problem. Therefore, we build a neural network surrogate model to close the moment system, which preserves the structural properties of the system by design, but reduces the computational cost significantly. Numerical experiments are conducted to illustrate the performance of the current method in comparison to the traditional closure.

翻译：在动能水平上直接模拟物理过程,由于解决方案空间的高度,在航空航天应用方面费用太高,令人望而却步。在本文中,我们考虑了Boltzmann方程式的瞬时系统,该方程式将动能物理学投射到流体动力学的尺度上。未关闭的瞬时系统可以与环球封闭战略一起解决。使用环球封闭为局部差异方程式的物理系统提供结构效益。通常,这种系统关闭的计算花费了总计算成本的绝大部分,因为需要解决一个条件不当的有限优化问题。因此,我们建造了一个神经网络代孕模型,以关闭瞬时系统,通过设计来保持系统的结构特性,但大大降低了计算成本。进行了数值实验,以说明当前方法与传统关闭相比的性能。