Neural control of discrete weak formulations: Galerkin, least squares \& minimal-residual methods with quasi-optimal weights

DOI10.1016/j.cma.2022.115716OpenAlexW4308825557MaRDI QIDQ2679332

Ignacio Brevis, Ignacio Muga, Kristoffer G. Van Der Zee

Publication date: 19 January 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.07475

zbMATH Keywords

artificial neural networksquasi-optimal convergencedata-driven discretizationoptimal neural controlquasi-minimizationweighted finite element methods

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

A deep double Ritz method (\(\mathrm{D^2RM}\)) for solving partial differential equations using neural networks ⋮ \(r\)-adaptive deep learning method for solving partial differential equations ⋮ DNN-MG: a hybrid neural network/finite element method with applications to 3D simulations of the Navier-Stokes equations

Uses Software

• DGM
• NeuFENet

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