TY - GEN
T1 - A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
AU - Schotthöfer, Steffen
AU - Xiao, Tianbai
AU - Frank, Martin
AU - Hauck, Cory D.
N1 - Publisher Copyright:
© 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85126789310&partnerID=8YFLogxK
U2 - 10.2514/6.2021-2895
DO - 10.2514/6.2021-2895
M3 - Conference contribution
AN - SCOPUS:85126789310
SN - 9781624106101
T3 - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
BT - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
PB - American Institute of Aeronautics and Astronautics Inc, AIAA
T2 - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
Y2 - 2 August 2021 through 6 August 2021
ER -