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Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations.
A new measure of rank correlation
Maurice G Kendall · 1938
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Laminar flow behind a two-dimensional grid
LIG Kovasznay · 1948
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Convergence conditions for ascent methods
Philip Wolfe · 1969
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Numerical optimization
Jorge Nocedal and Stephen Wright · 2006
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Partial differential equations with numerical methods , volume 45
Stig Larsson and Vidar Thomée · 2008
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Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
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Extensions of recurrent neural network language model
Tomáš Mikolov, Stefan Kombrink, Lukáš Burget, Jan Černockỳ, and Sanjeev Khudanpur · 2011
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Going deeper with convolutions
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich · 2015
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Simple and scalable predictive uncertainty estimation using deep ensembles
Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell · 2017
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DGM: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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A unified deep artificial neural network approach to partial differential equations in complex geometries
Jens Berg and Kaj Nyström · 2018
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