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Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs).
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
Earlier work this paper cites.
Long short-term memory
Sepp Hochreiter and Jürgen Schmidhuber · 1997
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
I.E. Lagaris, A. Likas, and D.I. Fotiadis · 1998
Earlier work this paper cites.
Neural-network methods for boundary value problems with irregular boundaries
I.E. Lagaris, A.C. Likas, and D.G. Papageorgiou · 2000
Cited alongside, same era.
Learning phrase representations using rnn encoder-decoder for statistical machine translation
Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Fethi Bougares, Holger Schwenk, and Yoshua Bengio · 2014
Cited alongside, same era.
Solving nonlinear and high-dimensional partial differential equations via deep learning, 2018
Ali Al-Aradi, Adolfo Correia, Danilo Naiff, Gabriel Jardim, and Yuri Saporito · 2018
Cited alongside, same era.
A unified deep artificial neural network approach to partial differential equations in complex geometries
Jens Berg and Kaj Nyström · 2018
Later among the works it cites.
A deep neural network surrogate for high-dimensional random partial differential equations
Mohammad Amin Nabian and Hadi Meidani · 2018
Later among the works it cites.
DGM: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
Later among the works it cites.
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