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06/24/2023
Current density impedance imaging with PINNs
In this paper, we introduce CDII-PINNs, a computationally efficient meth...
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04/17/2023
Deep Neural Network Approximation of Composition Functions: with application to PINNs
In this paper, we focus on approximating a natural class of functions th...
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03/28/2023
GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
With recent study of the deep learning in scientific computation, the PI...
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11/08/2022
Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations
The stability and convergence analysis of high-order numerical approxima...
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10/28/2022
Upwind-SAV approach for constructing bound-preserving and energy-stable schemes of the Cahn-Hilliard equation with degenerate mobility
This paper establishes an unconditionally bound-preserving and energy-st...
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11/03/2021
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Deep Ritz methods (DRM) have been proven numerically to be efficient in ...
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09/04/2021
