116 citations · 387 across the 27 of their papers we have counts for
6 papers · 1 filter
A Nonlinear Moment Model for Radiative Transfer Equation in Slab Geometry
Yuwei Fan, Ruo Li, Lingchao Zheng
This paper is concerned with the approximation of the radiative transfer equation for a grey medium in the slab geometry by the moment method. We develop a novel moment model inspi…
BCR-Net: a neural network based on the nonstandard wavelet form
Yuwei Fan, Cindy Orozco Bohorquez, Lexing Ying
This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematic…
Burnett Spectral Method for the Spatially Homogeneous Boltzmann Equation
Zhenning Cai, Yuwei Fan, Yanli Wang
We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expans…
A multiscale neural network based on hierarchical nested bases
Yuwei Fan, Jordi Feliu-Faba, Lin Lin +2
In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear map…
A multiscale neural network based on hierarchical matrices
Yuwei Fan, Lin Lin, Lexing Ying +1
In this work we introduce a new multiscale artificial neural network based on the structure of -matrices. This network generalizes the latter to the nonlinear case by…
Fast algorithms for integral formulations of steady-state radiative transfer equation
Yuwei Fan, Jing An, Lexing Ying
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a s…