  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.
