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Direct simulation of physical processes on a kinetic level is prohibitivelyexpensive in aerospace applications due to the extremely high dimension of thesolution spaces. In this paper, we consider the moment system of the Boltzmannequation, which projects the kinetic physics onto the hydrodynamic scale. Theunclosed moment system can be solved in conjunction with the entropy closurestrategy. Using an entropy closure provides structural benefits to the physicalsystem of partial differential equations. Usually computing such closure of thesystem spends the majority of the total computational cost, since one needs tosolve an ill-conditioned constrained optimization problem. Therefore, we builda neural network surrogate model to close the moment system, which preservesthe structural properties of the system by design, but reduces thecomputational cost significantly. Numerical experiments are conducted toillustrate the performance of the current method in comparison to thetraditional closure.

A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks