Theoretical foundations of physics-informed neural networks and deep neural operators

Author:

Shin Yeonjong,Zhang Zhongqiang,Karniadakis George Em

Publisher

Elsevier

Reference73 articles.

1. Galerkin neural networks: a framework for approximating variational equations with error control;Ainsworth;SIAM Journal on Scientific Computing,2021

2. A unified deep artificial neural network approach to partial differential equations in complex geometries;Berg;Neurocomputing,2018

3. Finite element methods of least-squares type;Bochev;SIAM Review,1998

4. Rayleigh-Ritz-Galerkin methods for Dirichlet's problem using subspaces without boundary conditions;Bramble;Communications on Pure and Applied Mathematics,1970

5. Weakly consistent regularisation methods for ill-posed problems;Burman,2018

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