
Learning invariance preserving moment closure model for BoltzmannBGK equation
As one of the main governing equations in kinetic theory, the Boltzmann ...
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Datadriven, structurepreserving approximations to entropybased moment closures for kinetic equations
We present a datadriven approach to construct entropybased closures fo...
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Deep Learning Moment Closure Approximations using Dynamic Boltzmann Distributions
The moments of spatial probabilistic systems are often given by an infin...
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Deep Learning of the Eddington Tensor in the Corecollapse Supernova Simulation
We trained deep neural networks (DNNs) as a function of the neutrino ene...
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Spline Moment Models for the onedimensional BoltzmannBGK equation
We introduce Spline Moment Equations (SME) for kinetic equations using a...
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Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures
This is the second paper in a series in which we develop machine learnin...
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Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds
This is the third paper in a series in which we develop machine learning...
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A structurepreserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
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 illconditioned 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.
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