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05/16/2023
Deep Fourier Residual method for solving time-harmonic Maxwell's equations
Solving PDEs with machine learning techniques has become a popular alter...
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04/04/2023
Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach
The efficient approximation of parametric PDEs is of tremendous importan...
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03/31/2023
Adaptive stabilized finite elements via residual minimization onto bubble enrichments
The Adaptive Stabilized Finite Element method (AS-FEM) developed in Calo...
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12/24/2022
Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices
Petrov-Galerkin formulations with optimal test functions allow for the s...
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11/07/2022
A Deep Double Ritz Method (D^2RM) for solving Partial Differential Equations using Neural Networks
Residual minimization is a widely used technique for solving Partial Dif...
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10/25/2022
A Deep Fourier Residual Method for solving PDEs using Neural Networks
When using Neural Networks as trial functions to numerically solve PDEs,...
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10/01/2022
An adaptive superconvergent finite element method based on local residual minimization
We introduce an adaptive superconvergent finite element method for a cla...
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06/15/2022
Neural Control of Discrete Weak Formulations: Galerkin, Least-Squares and Minimal-Residual Methods with Quasi-Optimal Weights
There is tremendous potential in using neural networks to optimize numer...
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03/08/2021
Isogeometric Residual Minimization Method (iGRM) with Direction Splitting for Non-Stationary Advection-Diffusion Problems
In this paper, we propose a novel computational implicit method, which w...
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01/08/2021
Projection in negative norms and the regularization of rough linear functionals
In order to construct regularizations of continuous linear functionals a...
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03/10/2020
Data-Driven Finite Elements Methods: Machine Learning Acceleration of Goal-Oriented Computations
We introduce the concept of data-driven finite element methods. These ar...
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01/01/2020
Isogeometric Residual Minimization Method (iGRM) for Stokes and Time-Dependent Stokes Problems
We investigate the application of the residual minimization method (RM) ...
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07/29/2019
An adaptive stabilized finite element method based on residual minimization
We devise and analyze a new adaptive stabilized finite element method. W...
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06/16/2019