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12/07/2022
On the Convergence of the Multi-scale Deep Neural Network (MscaleDNN) in Approximating Oscillatory Functions
In this paper, we derive diffusion models for the error evolution for a ...
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12/14/2020
FBSDE based neural network algorithms for high-dimensional quasilinear parabolic PDEs
In this paper, we propose forward and backward stochastic differential e...
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09/27/2020
Multi-scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
In this paper, we study a multi-scale deep neural network (MscaleDNN) as...
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08/03/2020
A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media
A matrix basis formulation is introduced to represent the 3 x 3 dyadic G...
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08/02/2020