68 citations · 92 across the 7 of their papers we have counts for
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Deep neural networks for solving large linear systems arising from high-dimensional problems
Yiqi Gu, Michael K. Ng
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to…
Deep adaptive basis Galerkin method for high-dimensional evolution equations with oscillatory solutions
Yiqi Gu, Micheal K. Ng
In this paper, we study deep neural networks (DNNs) for solving high-dimensional evolution equations with oscillatory solutions. Different from deep least-squares methods that deal…
Stationary Density Estimation of Itô Diffusions Using Deep Learning
Yiqi Gu, John Harlim, Senwei Liang +1
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic Itô diffusions from a discrete-time series that approximate the solution…
Deep Ritz method for the spectral fractional Laplacian equation using the Caffarelli-Silvestre extension
Yiqi Gu, Micheal K. Ng
In this paper, we propose a novel method for solving high-dimensional spectral fractional Laplacian equations. Using the Caffarelli-Silvestre extension, the -dimensional spectra…
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
Qiang Du, Yiqi Gu, Haizhao Yang +1
Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) a…
Structure Probing Neural Network Deflation
Yiqi Gu, Chunmei Wang, Haizhao Yang
Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the…
SelectNet: Self-paced Learning for High-dimensional Partial Differential Equations
Yiqi Gu, Haizhao Yang, Chao Zhou
The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully…