research
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04/01/2022
Deep neural networks for solving extremely large linear systems
In this paper, we study deep neural networks for solving extremely large...
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12/29/2021
Deep adaptive basis Galerkin method for high-dimensional evolution equations with oscillatory solutions
In this paper, we study deep neural networks (DNNs) for solving high-dim...
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09/09/2021
Stationary Density Estimation of Itô Diffusions Using Deep Learning
In this paper, we consider the density estimation problem associated wit...
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08/26/2021
Deep Ritz method for the spectral fractional Laplacian equation using the Caffarelli-Silvestre extension
In this paper, we propose a novel method for solving high-dimensional sp...
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03/21/2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
Identifying hidden dynamics from observed data is a significant and chal...
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07/07/2020
Structure Probing Neural Network Deflation
Deep learning is a powerful tool for solving nonlinear differential equa...
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01/14/2020