199 citations · 1.3k across the 122 of their papers we have counts for
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SwitchNet: a neural network model for forward and inverse scattering problems
Yuehaw Khoo, Lexing Ying
We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scatter…
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…
Convex relaxation approaches for strictly correlated density functional theory
Yuehaw Khoo, Lexing Ying
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxation…
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…
Recursively Preconditioned Hierarchical Interpolative Factorization for Elliptic Partial Differential Equations
Jordi Feliu-Fabà, Kenneth L. Ho, Lexing Ying
The hierarchical interpolative factorization for elliptic partial differential equations is a fast algorithm for approximate sparse matrix inversion in linear or quasilinear time.…
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…
Stochastic modified equations for the asynchronous stochastic gradient descent
Jing An, Jianfeng Lu, Lexing Ying
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more infor…
Sparsifying preconditioner for the time-harmonic Maxwell's equations
Fei Liu, Lexing Ying
This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the L…
Solving for high dimensional committor functions using artificial neural networks
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical sch…
A simple solver for the fractional Laplacian in multiple dimensions
Victor Minden, Lexing Ying
We present a simple discretization scheme for the hypersingular integral representation of the fractional Laplace operator and solver for the corresponding fractional Laplacian pro…
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…