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.

中文翻译：

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使用凸深度神经网络的玻尔兹曼方程矩系统闭合的结构保持代理模型

由于解空间的维度极高，在航空航天应用中，在动力学层面上直接模拟物理过程的成本高得令人望而却步。在本文中，我们考虑了 Boltzmann 方程的矩系统，它将动力学物理投影到流体动力学尺度上。未闭合力矩系统可以结合熵闭合策略求解。使用熵闭包为偏微分方程的物理系统提供了结构上的好处。通常计算系统的这种闭合会花费大部分总计算成本，因为需要解决病态约束优化问题。因此，我们建立了一个神经网络代理模型来关闭矩系统，通过设计保留了系统的结构特性，但显着降低了计算成本。进行了数值实验来说明当前方法与传统闭合方法的性能。