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 …

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 …

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 …

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 …

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 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 …

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 …

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 …

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 …

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 …