Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure

J Huang, Y Cheng, AJ Christlieb, LF Roberts - Journal of Computational …, 2022 - Elsevier
In this paper, we take a data-driven approach and apply machine learning to the moment
closure problem for the radiative transfer equation in slab geometry. Instead of learning the …

A comparison of moment closures for linear kinetic transport equations: The line source benchmark

CK Garrett, CD Hauck - Transport Theory and Statistical Physics, 2013 - Taylor & Francis
We discuss several moment closure models for linear kinetic equations that have been
developed over the past few years as alternatives to classical spectral and collocation …

A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction

M Sadr, NG Hadjiconstantinou - Journal of Computational Physics, 2023 - Elsevier
We present a variance-reduced method for efficiently solving the Boltzmann equation in all
rarefaction regimes. The proposed method is based on the VRDSMC method of Al-Mohssen …

Hierarchical approximate proper orthogonal decomposition

C Himpe, T Leibner, S Rave - SIAM Journal on Scientific Computing, 2018 - SIAM
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of
low-dimensional approximation spaces from high-dimensional input data. For large-scale …

Machine learning moment closure models for the radiative transfer equation II: Enforcing global hyperbolicity in gradient-based closures

J Huang, Y Cheng, AJ Christlieb, LF Roberts… - Multiscale Modeling & …, 2023 - SIAM
This is the second paper in a series in which we develop machine learning (ML) moment
closure models for the radiative transfer equation (RTE). In our previous work [J. Huang, Y …

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann …

JM Coale, DY Anistratov - Journal of Computational Physics, 2024 - Elsevier
A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative
transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low …

[PDF][PDF] Structure Preserving Neural Networks: A Case Study in the Entropy Closure of the Boltzmann Equation.

S Schotthöfer, T Xiao, M Frank, CD Hauck - ICML, 2022 - researchgate.net
In this paper, we explore applications of deep learning in statistical physics. We choose the
Boltzmann equation as a typical example, where neural networks serve as a closure to its …

Adaptive change of basis in entropy-based moment closures for linear kinetic equations

GW Alldredge, CD Hauck, DP OʼLeary… - Journal of Computational …, 2014 - Elsevier
Entropy-based (MN) moment closures for kinetic equations are defined by a constrained
optimization problem that must be solved at every point in a space–time mesh, making it …

A consistent BGK model with velocity-dependent collision frequency for gas mixtures

J Haack, C Hauck, C Klingenberg, M Pirner… - Journal of Statistical …, 2021 - Springer
We derive a multi-species BGK model with velocity-dependent collision frequency for a non-
reactive, multi-component gas mixture. The model is derived by minimizing a weighted …

A neural network for determination of latent dimensionality in non-negative matrix factorization

BT Nebgen, R Vangara… - Machine Learning …, 2021 - iopscience.iop.org
Non-negative matrix factorization (NMF) has proven to be a powerful unsupervised learning
method for uncovering hidden features in complex and noisy data sets with applications in …