116 citations · 387 across the 27 of their papers we have counts for
28 papers
A Novel Randomized XR-Based Preconditioned CholeskyQR Algorithm
Yuwei Fan, Yixiao Guo, Ting Lin
CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a rand…
Multi-Level Fine-Tuning: Closing Generalization Gaps in Approximation of Solution Maps under a Limited Budget for Training Data
Zhihan Li, Yuwei Fan, Lexing Ying
In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schrödinger equation). In this pape…
A Simple Multiscale Method for Mean Field Games
Haoya Li, Yuwei Fan, Lexing Ying
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initia…
Hyperbolic Model Reduction for Kinetic Equations
Zhenning Cai, Yuwei Fan, Ruo Li
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grad's moment method for Boltzmann equation. The focus is on the hyperbol…
Solving Inverse Wave Scattering with Deep Learning
Yuwei Fan, Lexing Ying
This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The…
Solving Traveltime Tomography with Deep Learning
Yuwei Fan, Lexing Ying
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to…
Coarse-Proxy Reduced Basis Methods for Integral Equations
Philip A. Etter, Yuwei Fan, Lexing Ying
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodo…
Solving Optical Tomography with Deep Learning
Yuwei Fan, Lexing Ying
This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT…
Meta-learning Pseudo-differential Operators with Deep Neural Networks
Jordi Feliu-Faba, Yuwei Fan, Lexing Ying
This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-…
Solving Electrical Impedance Tomography with Deep Learning
Yuwei Fan, Lexing Ying
This paper introduces a new approach for solving electrical impedance tomography (EIT) problems using deep neural networks. The mathematical problem of EIT is to invert the electri…
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…
Filtered Hyperbolic Moment Method for the Vlasov Equation
Yana Di, Yuwei Fan, Zhenzhong Kou +2
In this paper, we investigate the effect of the filter for the hyperbolic moment equations(HME) [15] of the Vlasov-Poisson equations and propose a novel quasi time-consistent filte…
Resolving Knudsen Layer by High Order Moment Expansion
Yuwei Fan, Jun Li, Ruo Li +1
We model the Knudsen layer in Kramers' problem by linearized high order hyperbolic moment system. Due to the hyperbolicity, the boundary conditions of the moment system is properly…
An entropic fourier method for the Boltzmann equation
Zhenning Cai, Yuwei Fan, Lexing Ying
We propose an entropic Fourier method for the numerical discretization of the Boltzmann collision operator. The method, which is obtained by modifying a Fourier Galerkin method to…
Linear Stability of Hyperbolic Moment Models for Boltzmann Equation
Yana Di, Yuwei Fan, Ruo Li +1
Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems, and thus the regularized models attain local well-posedness for Cauchy data. T…
13-Moment System with Global Hyperbolicity for Quantum Gas
Yana Di, Yuwei Fan, Ruo Li
We point out that the quantum Grad's 13-moment system [R. Yano, Physica A: Statistical Mechanics and its Applications, 416:231-241, 2014] is lack of global hyperbolicity, and even…
Model Reduction of Kinetic Equations by Operator Projection
Yuwei Fan, Julian Koellermeier, Jun Li +2
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571…
A Framework on Moment Model Reduction for Kinetic Equation
Zhenning Cai, Yuwei Fan, Ruo Li
By a further investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for Boltzmann equation in [Z. Cai, Y. Fan and R. Li, C…
On Hyperbolicity of 13-Moment System
Zhenning Cai, Yuwei Fan, Ruo Li
We point out that the thermodynamic equilibrium is not an interior point of the hyperbolicity region of Grad's 13-moment system. With a compact expansion of the phase density, whic…